Daily Papers

We introduce X-Dyna, a novel zero-shot, diffusion-based pipeline for animating a single human image using facial expressions and body movements derived from a driving video, that generates realistic, context-aware dynamics for both the subject and the surrounding environment. Building on prior approaches centered on human pose control, X-Dyna addresses key shortcomings causing the loss of dynamic details, enhancing the lifelike qualities of human video animations. At the core of our approach is the Dynamics-Adapter, a lightweight module that effectively integrates reference appearance context into the spatial attentions of the diffusion backbone while preserving the capacity of motion modules in synthesizing fluid and intricate dynamic details. Beyond body pose control, we connect a local control module with our model to capture identity-disentangled facial expressions, facilitating accurate expression transfer for enhanced realism in animated scenes. Together, these components form a unified framework capable of learning physical human motion and natural scene dynamics from a diverse blend of human and scene videos. Comprehensive qualitative and quantitative evaluations demonstrate that X-Dyna outperforms state-of-the-art methods, creating highly lifelike and expressive animations. The code is available at https://github.com/bytedance/X-Dyna.

Humans manipulate various kinds of fluids in their everyday life: creating latte art, scooping floating objects from water, rolling an ice cream cone, etc. Using robots to augment or replace human labors in these daily settings remain as a challenging task due to the multifaceted complexities of fluids. Previous research in robotic fluid manipulation mostly consider fluids governed by an ideal, Newtonian model in simple task settings (e.g., pouring). However, the vast majority of real-world fluid systems manifest their complexities in terms of the fluid's complex material behaviors and multi-component interactions, both of which were well beyond the scope of the current literature. To evaluate robot learning algorithms on understanding and interacting with such complex fluid systems, a comprehensive virtual platform with versatile simulation capabilities and well-established tasks is needed. In this work, we introduce FluidLab, a simulation environment with a diverse set of manipulation tasks involving complex fluid dynamics. These tasks address interactions between solid and fluid as well as among multiple fluids. At the heart of our platform is a fully differentiable physics simulator, FluidEngine, providing GPU-accelerated simulations and gradient calculations for various material types and their couplings. We identify several challenges for fluid manipulation learning by evaluating a set of reinforcement learning and trajectory optimization methods on our platform. To address these challenges, we propose several domain-specific optimization schemes coupled with differentiable physics, which are empirically shown to be effective in tackling optimization problems featured by fluid system's non-convex and non-smooth properties. Furthermore, we demonstrate reasonable sim-to-real transfer by deploying optimized trajectories in real-world settings.

In this work, we tackle the problem of real-world fluid animation from a still image. The key of our system is a surface-based layered representation deriving from video decomposition, where the scene is decoupled into a surface fluid layer and an impervious background layer with corresponding transparencies to characterize the composition of the two layers. The animated video can be produced by warping only the surface fluid layer according to the estimation of fluid motions and recombining it with the background. In addition, we introduce surface-only fluid simulation, a 2.5D fluid calculation version, as a replacement for motion estimation. Specifically, we leverage the triangular mesh based on a monocular depth estimator to represent the fluid surface layer and simulate the motion in the physics-based framework with the inspiration of the classic theory of the hybrid Lagrangian-Eulerian method, along with a learnable network so as to adapt to complex real-world image textures. We demonstrate the effectiveness of the proposed system through comparison with existing methods in both standard objective metrics and subjective ranking scores. Extensive experiments not only indicate our method's competitive performance for common fluid scenes but also better robustness and reasonability under complex transparent fluid scenarios. Moreover, as the proposed surface-based layer representation and surface-only fluid simulation naturally disentangle the scene, interactive editing such as adding objects to the river and texture replacing could be easily achieved with realistic results.

Accurately predicting the future fluid is important to extensive areas, such as meteorology, oceanology and aerodynamics. However, since the fluid is usually observed from an Eulerian perspective, its active and intricate dynamics are seriously obscured and confounded in static grids, bringing horny challenges to the prediction. This paper introduces a new Lagrangian-guided paradigm to tackle the tanglesome fluid dynamics. Instead of solely predicting the future based on Eulerian observations, we propose the Eulerian-Lagrangian Dual Recurrent Network (EuLagNet), which captures multiscale fluid dynamics by tracking movements of adaptively sampled key particles on multiple scales and integrating dynamics information over time. Concretely, a EuLag Block is presented to communicate the learned Eulerian and Lagrangian features at each moment and scale, where the motion of tracked particles is inferred from Eulerian observations and their accumulated dynamics information is incorporated into Eulerian fields to guide future prediction. Tracking key particles not only provides a clear and interpretable clue for fluid dynamics but also makes our model free from modeling complex correlations among massive grids for better efficiency. Experimentally, EuLagNet excels in three challenging fluid prediction tasks, covering both 2D and 3D, simulated and real-world fluids.

We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inputs, the PDE foundation model builds in a pathway for including mathematical descriptions of the physical behavior. We pre-train our foundation model on 6 parametric families of equations collected from 13 datasets, including over 60K trajectories. Our model outperforms popular operator learning, computer vision, and multi-physics models, in benchmark forward prediction tasks. We test our architecture choices with ablation studies.

We propose a neural physics system for real-time, interactive fluid simulations. Traditional physics-based methods, while accurate, are computationally intensive and suffer from latency issues. Recent machine-learning methods reduce computational costs while preserving fidelity; yet most still fail to satisfy the latency constraints for real-time use and lack support for interactive applications. To bridge this gap, we introduce a novel hybrid method that integrates numerical simulation, neural physics, and generative control. Our neural physics jointly pursues low-latency simulation and high physical fidelity by employing a fallback safeguard to classical numerical solvers. Furthermore, we develop a diffusion-based controller that is trained using a reverse modeling strategy to generate external dynamic force fields for fluid manipulation. Our system demonstrates robust performance across diverse 2D/3D scenarios, material types, and obstacle interactions, achieving real-time simulations at high frame rates (11~29% latency) while enabling fluid control guided by user-friendly freehand sketches. We present a significant step towards practical, controllable, and physically plausible fluid simulations for real-time interactive applications. We promise to release both models and data upon acceptance.

Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power. Data-driven methods based on large-scale machine learning promise high adaptivity by integrating long-range dependencies more directly and efficiently. In this work, we focus on fluid dynamics and address the shortcomings of a large part of the literature, which are based on fixed support for computations and predictions in the form of regular or irregular grids. We propose a novel setup to perform predictions in a continuous spatial and temporal domain while being trained on sparse observations. We formulate the task as a double observation problem and propose a solution with two interlinked dynamical systems defined on, respectively, the sparse positions and the continuous domain, which allows to forecast and interpolate a solution from the initial condition. Our practical implementation involves recurrent GNNs and a spatio-temporal attention observer capable of interpolating the solution at arbitrary locations. Our model not only generalizes to new initial conditions (as standard auto-regressive models do) but also performs evaluation at arbitrary space and time locations. We evaluate on three standard datasets in fluid dynamics and compare to strong baselines, which are outperformed both in classical settings and in the extended new task requiring continuous predictions.

Realistic simulation of dynamic scenes requires accurately capturing diverse material properties and modeling complex object interactions grounded in physical principles. However, existing methods are constrained to basic material types with limited predictable parameters, making them insufficient to represent the complexity of real-world materials. We introduce a novel approach that leverages multi-modal foundation models and video diffusion to achieve enhanced 4D dynamic scene simulation. Our method utilizes multi-modal models to identify material types and initialize material parameters through image queries, while simultaneously inferring 3D Gaussian splats for detailed scene representation. We further refine these material parameters using video diffusion with a differentiable Material Point Method (MPM) and optical flow guidance rather than render loss or Score Distillation Sampling (SDS) loss. This integrated framework enables accurate prediction and realistic simulation of dynamic interactions in real-world scenarios, advancing both accuracy and flexibility in physics-based simulations.

We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its differentiable form. Our model is based on the insight that solutions to the continuity equation can be expressed as time-dependent density transformations via differentiable and invertible maps. This follows from classical theory of the existence and uniqueness of Lagrangian flows for smooth vector fields. Hence, we model fluid densities by transforming a base density with parameterized diffeomorphisms conditioned on time. The key benefit compared to methods relying on numerical ODE solvers or PINNs is that the analytic expression of the velocity is always consistent with changes in density. Furthermore, we require neither expensive numerical solvers, nor additional penalties to enforce the PDE. LFlows show higher predictive accuracy in density modeling tasks compared to competing models in 2D and 3D, while being computationally efficient. As a real-world application, we model bird migration based on sparse weather radar measurements.

Modeling the mechanics of fluid in complex scenes is vital to applications in design, graphics, and robotics. Learning-based methods provide fast and differentiable fluid simulators, however most prior work is unable to accurately model how fluids interact with genuinely novel surfaces not seen during training. We introduce SURFSUP, a framework that represents objects implicitly using signed distance functions (SDFs), rather than an explicit representation of meshes or particles. This continuous representation of geometry enables more accurate simulation of fluid-object interactions over long time periods while simultaneously making computation more efficient. Moreover, SURFSUP trained on simple shape primitives generalizes considerably out-of-distribution, even to complex real-world scenes and objects. Finally, we show we can invert our model to design simple objects to manipulate fluid flow.

We propose a pipeline to extract and reconstruct dynamic 3D smoke assets from a single in-the-wild video, and further integrate interactive simulation for smoke design and editing. Recent developments in 3D vision have significantly improved reconstructing and rendering fluid dynamics, supporting realistic and temporally consistent view synthesis. However, current fluid reconstructions rely heavily on carefully controlled clean lab environments, whereas real-world videos captured in the wild are largely underexplored. We pinpoint three key challenges of reconstructing smoke in real-world videos and design targeted techniques, including smoke extraction with background removal, initialization of smoke particles and camera poses, and inferring multi-view videos. Our method not only outperforms previous reconstruction and generation methods with high-quality smoke reconstructions (+2.22 average PSNR on wild videos), but also enables diverse and realistic editing of fluid dynamics by simulating our smoke assets. We provide our models, data, and 4D smoke assets at [https://autumnyq.github.io/WildSmoke](https://autumnyq.github.io/WildSmoke).

Animating a still image offers an engaging visual experience. Traditional image animation techniques mainly focus on animating natural scenes with stochastic dynamics (e.g. clouds and fluid) or domain-specific motions (e.g. human hair or body motions), and thus limits their applicability to more general visual content. To overcome this limitation, we explore the synthesis of dynamic content for open-domain images, converting them into animated videos. The key idea is to utilize the motion prior of text-to-video diffusion models by incorporating the image into the generative process as guidance. Given an image, we first project it into a text-aligned rich context representation space using a query transformer, which facilitates the video model to digest the image content in a compatible fashion. However, some visual details still struggle to be preserved in the resultant videos. To supplement with more precise image information, we further feed the full image to the diffusion model by concatenating it with the initial noises. Experimental results show that our proposed method can produce visually convincing and more logical & natural motions, as well as higher conformity to the input image. Comparative evaluation demonstrates the notable superiority of our approach over existing competitors.

Numerical simulation of non-linear partial differential equations plays a crucial role in modeling physical science and engineering phenomena, such as weather, climate, and aerodynamics. Recent Machine Learning (ML) models trained on low-resolution spatio-temporal signals have shown new promises in capturing important dynamics in high-resolution signals, under the condition that the models can effectively recover the missing details. However, this study shows that significant information is often lost in the low-resolution down-sampled features. To address such issues, we propose a new approach, namely Temporal Stencil Modeling (TSM), which combines the strengths of advanced time-series sequence modeling (with the HiPPO features) and state-of-the-art neural PDE solvers (with learnable stencil modeling). TSM aims to recover the lost information from the PDE trajectories and can be regarded as a temporal generalization of classic finite volume methods such as WENO. Our experimental results show that TSM achieves the new state-of-the-art simulation accuracy for 2-D incompressible Navier-Stokes turbulent flows: it significantly outperforms the previously reported best results by 19.9% in terms of the highly-correlated duration time and reduces the inference latency into 80%. We also show a strong generalization ability of the proposed method to various out-of-distribution turbulent flow settings. Our code is available at "https://github.com/Edward-Sun/TSM-PDE".

We study reconstructing and predicting 3D fluid appearance and velocity from a single video. Current methods require multi-view videos for fluid reconstruction. We present FluidNexus, a novel framework that bridges video generation and physics simulation to tackle this task. Our key insight is to synthesize multiple novel-view videos as references for reconstruction. FluidNexus consists of two key components: (1) a novel-view video synthesizer that combines frame-wise view synthesis with video diffusion refinement for generating realistic videos, and (2) a physics-integrated particle representation coupling differentiable simulation and rendering to simultaneously facilitate 3D fluid reconstruction and prediction. To evaluate our approach, we collect two new real-world fluid datasets featuring textured backgrounds and object interactions. Our method enables dynamic novel view synthesis, future prediction, and interaction simulation from a single fluid video. Project website: https://yuegao.me/FluidNexus.

We present MovingParts, a NeRF-based method for dynamic scene reconstruction and part discovery. We consider motion as an important cue for identifying parts, that all particles on the same part share the common motion pattern. From the perspective of fluid simulation, existing deformation-based methods for dynamic NeRF can be seen as parameterizing the scene motion under the Eulerian view, i.e., focusing on specific locations in space through which the fluid flows as time passes. However, it is intractable to extract the motion of constituting objects or parts using the Eulerian view representation. In this work, we introduce the dual Lagrangian view and enforce representations under the Eulerian/Lagrangian views to be cycle-consistent. Under the Lagrangian view, we parameterize the scene motion by tracking the trajectory of particles on objects. The Lagrangian view makes it convenient to discover parts by factorizing the scene motion as a composition of part-level rigid motions. Experimentally, our method can achieve fast and high-quality dynamic scene reconstruction from even a single moving camera, and the induced part-based representation allows direct applications of part tracking, animation, 3D scene editing, etc.

In the literature, flows produced by synthetic jets (SJ) have been studied extensively through experiments and numeric simulations. The essential physics of such a complex system has been simplified successfully to Lumped-element models in a wide range of conditions. LE models effectively predict the pressure in the cavity and the velocity in the neck of SJ. But, this does not comprise the complete dynamics of SJ. As soon as the flow starts separating from the neck of the SJ device, vortices and jets form at some distance downstream. These structures are the result of loosening the flow boundaries. Despite such a dramatic change, predictions of LE models remain unverified by measurements of the fully developed jet. We compared predictions of momentum transfer using an LE model with measurements of size and velocity of a fully developed jet/vortex detached from an SJ. Our SJ device operated with air as an active fluid. Comparing measurements and predictions, we found a constant difference for the higher sound pressures. However, the predictions and the measurements follow similar trends. Additionally, we found that the decay rate of the flow regime given by the relationship between the Reynolds and the Strouhal numbers differs significantly when the flow is studied within the neck and downstream the cavity.

Foundation models have transformed machine learning for language and vision, but achieving comparable impact in physical simulation remains a challenge. Data heterogeneity and unstable long-term dynamics inhibit learning from sufficiently diverse dynamics, while varying resolutions and dimensionalities challenge efficient training on modern hardware. Through empirical and theoretical analysis, we incorporate new approaches to mitigate these obstacles, including a harmonic-analysis-based stabilization method, load-balanced distributed 2D and 3D training strategies, and compute-adaptive tokenization. Using these tools, we develop Walrus, a transformer-based foundation model developed primarily for fluid-like continuum dynamics. Walrus is pretrained on nineteen diverse scenarios spanning astrophysics, geoscience, rheology, plasma physics, acoustics, and classical fluids. Experiments show that Walrus outperforms prior foundation models on both short and long term prediction horizons on downstream tasks and across the breadth of pretraining data, while ablation studies confirm the value of our contributions to forecast stability, training throughput, and transfer performance over conventional approaches. Code and weights are released for community use.

In contrast to entropy, which increases monotonically, the "complexity" or "interestingness" of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex structures at the Big Bang and will also lack them after black holes evaporate and particles are dispersed. This paper makes an initial attempt to quantify this pattern. As a model system, we use a simple, two-dimensional cellular automaton that simulates the mixing of two liquids ("coffee" and "cream"). A plausible complexity measure is then the Kolmogorov complexity of a coarse-grained approximation of the automaton's state, which we dub the "apparent complexity." We study this complexity measure, and show analytically that it never becomes large when the liquid particles are non-interacting. By contrast, when the particles do interact, we give numerical evidence that the complexity reaches a maximum comparable to the "coffee cup's" horizontal dimension. We raise the problem of proving this behavior analytically.

Recent advances in real-world applications of reinforcement learning (RL) have relied on the ability to accurately simulate systems at scale. However, domains such as fluid dynamical systems exhibit complex dynamic phenomena that are hard to simulate at high integration rates, limiting the direct application of modern deep RL algorithms to often expensive or safety critical hardware. In this work, we introduce "Box o Flows", a novel benchtop experimental control system for systematically evaluating RL algorithms in dynamic real-world scenarios. We describe the key components of the Box o Flows, and through a series of experiments demonstrate how state-of-the-art model-free RL algorithms can synthesize a variety of complex behaviors via simple reward specifications. Furthermore, we explore the role of offline RL in data-efficient hypothesis testing by reusing past experiences. We believe that the insights gained from this preliminary study and the availability of systems like the Box o Flows support the way forward for developing systematic RL algorithms that can be generally applied to complex, dynamical systems. Supplementary material and videos of experiments are available at https://sites.google.com/view/box-o-flows/home.

This paper introduces a novel surrogate modeling framework for aerodynamic applications based on Neural Fields. The proposed approach, MARIO (Modulated Aerodynamic Resolution Invariant Operator), addresses non parametric geometric variability through an efficient shape encoding mechanism and exploits the discretization-invariant nature of Neural Fields. It enables training on significantly downsampled meshes, while maintaining consistent accuracy during full-resolution inference. These properties allow for efficient modeling of diverse flow conditions, while reducing computational cost and memory requirements compared to traditional CFD solvers and existing surrogate methods. The framework is validated on two complementary datasets that reflect industrial constraints. First, the AirfRANS dataset consists in a two-dimensional airfoil benchmark with non-parametric shape variations. Performance evaluation of MARIO on this case demonstrates an order of magnitude improvement in prediction accuracy over existing methods across velocity, pressure, and turbulent viscosity fields, while accurately capturing boundary layer phenomena and aerodynamic coefficients. Second, the NASA Common Research Model features three-dimensional pressure distributions on a full aircraft surface mesh, with parametric control surface deflections. This configuration confirms MARIO's accuracy and scalability. Benchmarking against state-of-the-art methods demonstrates that Neural Field surrogates can provide rapid and accurate aerodynamic predictions under the computational and data limitations characteristic of industrial applications.

We consider the problem of modeling high-speed flows using machine learning methods. While most prior studies focus on low-speed fluid flows in which uniform time-stepping is practical, flows approaching and exceeding the speed of sound exhibit sudden changes such as shock waves. In such cases, it is essential to use adaptive time-stepping methods to allow a temporal resolution sufficient to resolve these phenomena while simultaneously balancing computational costs. Here, we propose a two-phase machine learning method, known as ShockCast, to model high-speed flows with adaptive time-stepping. In the first phase, we propose to employ a machine learning model to predict the timestep size. In the second phase, the predicted timestep is used as an input along with the current fluid fields to advance the system state by the predicted timestep. We explore several physically-motivated components for timestep prediction and introduce timestep conditioning strategies inspired by neural ODE and Mixture of Experts. As ShockCast is the first framework for learning high-speed flows, we evaluate our methods by generating two supersonic flow datasets, available at https://huggingface.co/datasets/divelab. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

We demonstrate the feasibility of integrating physics-based animations of solids and fluids with 3D Gaussian Splatting (3DGS) to create novel effects in virtual scenes reconstructed using 3DGS. Leveraging the coherence of the Gaussian splatting and position-based dynamics (PBD) in the underlying representation, we manage rendering, view synthesis, and the dynamics of solids and fluids in a cohesive manner. Similar to Gaussian shader, we enhance each Gaussian kernel with an added normal, aligning the kernel's orientation with the surface normal to refine the PBD simulation. This approach effectively eliminates spiky noises that arise from rotational deformation in solids. It also allows us to integrate physically based rendering to augment the dynamic surface reflections on fluids. Consequently, our framework is capable of realistically reproducing surface highlights on dynamic fluids and facilitating interactions between scene objects and fluids from new views. For more information, please visit our project page at https://amysteriouscat.github.io/GaussianSplashing/.

Implicit Neural Spatial Representation (INSR) has emerged as an effective representation of spatially-dependent vector fields. This work explores solving time-dependent PDEs with INSR. Classical PDE solvers introduce both temporal and spatial discretizations. Common spatial discretizations include meshes and meshless point clouds, where each degree-of-freedom corresponds to a location in space. While these explicit spatial correspondences are intuitive to model and understand, these representations are not necessarily optimal for accuracy, memory usage, or adaptivity. Keeping the classical temporal discretization unchanged (e.g., explicit/implicit Euler), we explore INSR as an alternative spatial discretization, where spatial information is implicitly stored in the neural network weights. The network weights then evolve over time via time integration. Our approach does not require any training data generated by existing solvers because our approach is the solver itself. We validate our approach on various PDEs with examples involving large elastic deformations, turbulent fluids, and multi-scale phenomena. While slower to compute than traditional representations, our approach exhibits higher accuracy and lower memory consumption. Whereas classical solvers can dynamically adapt their spatial representation only by resorting to complex remeshing algorithms, our INSR approach is intrinsically adaptive. By tapping into the rich literature of classic time integrators, e.g., operator-splitting schemes, our method enables challenging simulations in contact mechanics and turbulent flows where previous neural-physics approaches struggle. Videos and codes are available on the project page: http://www.cs.columbia.edu/cg/INSR-PDE/

We delve into the physics-informed neural reconstruction of smoke and obstacles through sparse-view RGB videos, tackling challenges arising from limited observation of complex dynamics. Existing physics-informed neural networks often emphasize short-term physics constraints, leaving the proper preservation of long-term conservation less explored. We introduce Neural Characteristic Trajectory Fields, a novel representation utilizing Eulerian neural fields to implicitly model Lagrangian fluid trajectories. This topology-free, auto-differentiable representation facilitates efficient flow map calculations between arbitrary frames as well as efficient velocity extraction via auto-differentiation. Consequently, it enables end-to-end supervision covering long-term conservation and short-term physics priors. Building on the representation, we propose physics-informed trajectory learning and integration into NeRF-based scene reconstruction. We enable advanced obstacle handling through self-supervised scene decomposition and seamless integrated boundary constraints. Our results showcase the ability to overcome challenges like occlusion uncertainty, density-color ambiguity, and static-dynamic entanglements. Code and sample tests are at https://github.com/19reborn/PICT_smoke.

Biological tissues exhibit complex behaviors with their dynamics often resembling inert soft matter such as liquids, polymers, colloids, and liquid crystals. These analogies enable physics-based approaches for investigations of emergent behaviors in biological processes. A well-studied case is the spreading of cellular aggregates on solid surfaces, where they display dynamics similar to viscous droplets. In vivo, however, cells and tissues are in a confined environment with varying geometries and mechanical properties to which they need to adapt. In this work, we compressed cellular aggregates between two solid surfaces and studied their dynamics using microscopy, and computer simulations. The confined cellular aggregates transitioned from compressed spheres into dynamic living capillary bridges exhibiting bridge thinning and a convex-to-concave meniscus curvature transition. We found that the stability of the bridge is determined by the interplay between cell growth and cell spreading on the confining surfaces. This interaction leads to bridge rupture at a critical length scale determined by the distance between the plates. The force distributions, formation and stability regimes of the living capillary bridges were characterized with full 3D computer simulations that included cell division, migration and growth dynamics, directly showing how mechanical principles govern the behavior of the living bridges; cellular aggregates display jamming and stiffening analogously to granular matter, and cell division along the long axis enhances thinning. Based on our results, we propose a new class of active soft matter behavior, where cellular aggregates exhibit liquid-like adaptation to confinement, but with self-organized rupturing driven by biological activity.

Flow matching has emerged as a compelling generative modeling approach that is widely used across domains. To generate data via a flow matching model, an ordinary differential equation (ODE) is numerically solved via forward integration of the modeled velocity field. To better capture the multi-modality that is inherent in typical velocity fields, hierarchical flow matching was recently introduced. It uses a hierarchy of ODEs that are numerically integrated when generating data. This hierarchy of ODEs captures the multi-modal velocity distribution just like vanilla flow matching is capable of modeling a multi-modal data distribution. While this hierarchy enables to model multi-modal velocity distributions, the complexity of the modeled distribution remains identical across levels of the hierarchy. In this paper, we study how to gradually adjust the complexity of the distributions across different levels of the hierarchy via mini-batch couplings. We show the benefits of mini-batch couplings in hierarchical rectified flow matching via compelling results on synthetic and imaging data. Code is available at https://riccizz.github.io/HRF_coupling.

Recent advances in neural surrogate modeling offer the potential for transformative innovations in applications such as automotive aerodynamics. Yet, industrial-scale problems often involve volumetric meshes with cell counts reaching the 100 millions, presenting major scalability challenges. Complex geometries further complicate modeling through intricate surface-volume interactions, while quantities such as vorticity are highly nonlinear and must satisfy strict divergence-free constraints. To address these requirements, we introduce AB-UPT as a novel modeling scheme for building neural surrogates for CFD simulations. AB-UPT is designed to: (i) decouple geometry encoding and prediction tasks via multi-branch operators; (ii) enable scalability to high-resolution outputs via neural simulation in a low-dimensional latent space, coupled with anchored neural field decoders to predict high-fidelity outputs; (iii) enforce physics consistency by a novel divergence-free formulation. We show that AB-UPT yields state-of-the-art predictive accuracy of surface and volume fields on automotive CFD simulations ranging from 33 thousand up to 150 million mesh cells. Furthermore, our anchored neural field architecture enables the enforcement of hard physical constraints on the physics predictions without degradation in performance, exemplified by modeling divergence-free vorticity fields. Notably, the proposed models can be trained on a single GPU in less than a day and predict industry-standard surface and volume fields within seconds. Additionally, we show that the flexible design of our method enables neural simulation from a CAD geometry alone, omitting the need for costly CFD meshing procedures.

Machine learning based surrogate models offer researchers powerful tools for accelerating simulation-based workflows. However, as standard datasets in this space often cover small classes of physical behavior, it can be difficult to evaluate the efficacy of new approaches. To address this gap, we introduce the Well: a large-scale collection of datasets containing numerical simulations of a wide variety of spatiotemporal physical systems. The Well draws from domain experts and numerical software developers to provide 15TB of data across 16 datasets covering diverse domains such as biological systems, fluid dynamics, acoustic scattering, as well as magneto-hydrodynamic simulations of extra-galactic fluids or supernova explosions. These datasets can be used individually or as part of a broader benchmark suite. To facilitate usage of the Well, we provide a unified PyTorch interface for training and evaluating models. We demonstrate the function of this library by introducing example baselines that highlight the new challenges posed by the complex dynamics of the Well. The code and data is available at https://github.com/PolymathicAI/the_well.

Numerical simulations in climate, chemistry, or astrophysics are computationally too expensive for uncertainty quantification or parameter-exploration at high-resolution. Reduced-order or surrogate models are multiple orders of magnitude faster, but traditional surrogates are inflexible or inaccurate and pure machine learning (ML)-based surrogates too data-hungry. We propose a hybrid, flexible surrogate model that exploits known physics for simulating large-scale dynamics and limits learning to the hard-to-model term, which is called parametrization or closure and captures the effect of fine- onto large-scale dynamics. Leveraging neural operators, we are the first to learn grid-independent, non-local, and flexible parametrizations. Our multiscale neural operator is motivated by a rich literature in multiscale modeling, has quasilinear runtime complexity, is more accurate or flexible than state-of-the-art parametrizations and demonstrated on the chaotic equation multiscale Lorenz96.

Data-driven modeling of fluid dynamics has advanced rapidly with neural PDE solvers, yet a fair and strong benchmark remains fragmented due to the absence of unified PDE datasets and standardized evaluation protocols. Although architectural innovations are abundant, fair assessment is further impeded by the lack of clear disentanglement between spatial, temporal and loss modules. In this paper, we introduce FD-Bench, the first fair, modular, comprehensive and reproducible benchmark for data-driven fluid simulation. FD-Bench systematically evaluates 85 baseline models across 10 representative flow scenarios under a unified experimental setup. It provides four key contributions: (1) a modular design enabling fair comparisons across spatial, temporal, and loss function modules; (2) the first systematic framework for direct comparison with traditional numerical solvers; (3) fine-grained generalization analysis across resolutions, initial conditions, and temporal windows; and (4) a user-friendly, extensible codebase to support future research. Through rigorous empirical studies, FD-Bench establishes the most comprehensive leaderboard to date, resolving long-standing issues in reproducibility and comparability, and laying a foundation for robust evaluation of future data-driven fluid models. The code is open-sourced at https://anonymous.4open.science/r/FD-Bench-15BC.

Advancements in computing power have made it possible to numerically simulate large-scale fluid-mechanical and/or particulate systems, many of which are integral to core industrial processes. Among the different numerical methods available, the discrete element method (DEM) provides one of the most accurate representations of a wide range of physical systems involving granular and discontinuous materials. Consequently, DEM has become a widely accepted approach for tackling engineering problems connected to granular flows and powder mechanics. Additionally, DEM can be integrated with grid-based computational fluid dynamics (CFD) methods, enabling the simulation of chemical processes taking place, e.g., in fluidized beds. However, DEM is computationally intensive because of the intrinsic multiscale nature of particulate systems, restricting simulation duration or number of particles. Towards this end, NeuralDEM presents an end-to-end approach to replace slow numerical DEM routines with fast, adaptable deep learning surrogates. NeuralDEM is capable of picturing long-term transport processes across different regimes using macroscopic observables without any reference to microscopic model parameters. First, NeuralDEM treats the Lagrangian discretization of DEM as an underlying continuous field, while simultaneously modeling macroscopic behavior directly as additional auxiliary fields. Second, NeuralDEM introduces multi-branch neural operators scalable to real-time modeling of industrially-sized scenarios - from slow and pseudo-steady to fast and transient. Such scenarios have previously posed insurmountable challenges for deep learning models. Notably, NeuralDEM faithfully models coupled CFD-DEM fluidized bed reactors of 160k CFD cells and 500k DEM particles for trajectories of 28s. NeuralDEM will open many new doors to advanced engineering and much faster process cycles.

Foundation models have revolutionized natural language processing through a ``train once, deploy anywhere'' paradigm, where a single pre-trained model adapts to countless downstream tasks without retraining. Access to a Physics Foundation Model (PFM) would be transformative -- democratizing access to high-fidelity simulations, accelerating scientific discovery, and eliminating the need for specialized solver development. Yet current physics-aware machine learning approaches remain fundamentally limited to single, narrow domains and require retraining for each new system. We present the General Physics Transformer (GPhyT), trained on 1.8 TB of diverse simulation data, that demonstrates foundation model capabilities are achievable for physics. Our key insight is that transformers can learn to infer governing dynamics from context, enabling a single model to simulate fluid-solid interactions, shock waves, thermal convection, and multi-phase dynamics without being told the underlying equations. GPhyT achieves three critical breakthroughs: (1) superior performance across multiple physics domains, outperforming specialized architectures by up to 29x, (2) zero-shot generalization to entirely unseen physical systems through in-context learning, and (3) stable long-term predictions through 50-timestep rollouts. By establishing that a single model can learn generalizable physical principles from data alone, this work opens the path toward a universal PFM that could transform computational science and engineering.

Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body -- two close positions in a higher-level mesh correspond to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods. Our code is available at https://github.com/yuyudeep/hcmt.

We present an open-source Python library for simulating two-dimensional incompressible Kelvin-Helmholtz instabilities in stratified shear flows. The solver employs a fractional-step projection method with spectral Poisson solution via Fast Sine Transform, achieving second-order spatial accuracy. Implementation leverages NumPy, SciPy, and Numba JIT compilation for efficient computation. Four canonical test cases explore Reynolds numbers 1000--5000 and Richardson numbers 0.1--0.3: classical shear layer, double shear configuration, rotating flow, and forced turbulence. Statistical analysis using Shannon entropy and complexity indices reveals that double shear layers achieve 2.8times higher mixing rates than forced turbulence despite lower Reynolds numbers. The solver runs efficiently on standard desktop hardware, with 384times192 grid simulations completing in approximately 31 minutes. Results demonstrate that mixing efficiency depends on instability generation pathways rather than intensity measures alone, challenging Richardson number-based parameterizations and suggesting refinements for subgrid-scale representation in climate models.

Deep neural networks (DNN) have shown great capacity of modeling a dynamical system; nevertheless, they usually do not obey physics constraints such as conservation laws. This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling to endow the invariant properties. ConCerNet consists of two steps: (i) a contrastive learning method to automatically capture the system invariants (i.e. conservation properties) along the trajectory observations; (ii) a neural projection layer to guarantee that the learned dynamics models preserve the learned invariants. We theoretically prove the functional relationship between the learned latent representation and the unknown system invariant function. Experiments show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics by a large margin. With neural network based parameterization and no dependence on prior knowledge, our method can be extended to complex and large-scale dynamics by leveraging an autoencoder.

Accurate and efficient simulations of physical phenomena governed by partial differential equations (PDEs) are important for scientific and engineering progress. While traditional numerical solvers are powerful, they are often computationally expensive. Recently, data-driven methods have emerged as alternatives, but they frequently suffer from error accumulation and limited physical consistency, especially in multiphysics and complex geometries. To address these challenges, we propose PEGNet, a Physics-Embedded Graph Network that incorporates PDE-guided message passing to redesign the graph neural network architecture. By embedding key PDE dynamics like convection, viscosity, and diffusion into distinct message functions, the model naturally integrates physical constraints into its forward propagation, producing more stable and physically consistent solutions. Additionally, a hierarchical architecture is employed to capture multi-scale features, and physical regularization is integrated into the loss function to further enforce adherence to governing physics. We evaluated PEGNet on benchmarks, including custom datasets for respiratory airflow and drug delivery, showing significant improvements in long-term prediction accuracy and physical consistency over existing methods. Our code is available at https://github.com/Yanghuoshan/PEGNet.

A droplet impacting a deep fluid bath is as common as rain over the ocean. If the impact is sufficiently gentle, the mediating air layer remains intact, and the droplet may rebound completely from the interface. In this work, we experimentally investigate the role of translational bath motion on the bouncing to coalescence transition. Over a range of parameters, we find that the relative bath motion systematically decreases the normal Weber number required to transition from bouncing to merging. Direct numerical simulations demonstrate that the depression created during impact combined with the translational motion of the bath enhances the air layer drainage on the upstream side of the droplet, ultimately favoring coalescence. A simple geometric argument is presented that rationalizes the collapse of the experimental threshold data, extending what is known for the case of axisymmetric normal impacts to the more general 3D scenario of interest herein.

Recently, data-driven simulators based on graph neural networks have gained attention in modeling physical systems on unstructured meshes. However, they struggle with long-range dependencies in fluid flows, particularly in refined mesh regions. This challenge, known as the 'over-squashing' problem, hinders information propagation. While existing graph rewiring methods address this issue to some extent, they only consider graph topology, overlooking the underlying physical phenomena. We propose Physics-Informed Ollivier-Ricci Flow (PIORF), a novel rewiring method that combines physical correlations with graph topology. PIORF uses Ollivier-Ricci curvature (ORC) to identify bottleneck regions and connects these areas with nodes in high-velocity gradient nodes, enabling long-range interactions and mitigating over-squashing. Our approach is computationally efficient in rewiring edges and can scale to larger simulations. Experimental results on 3 fluid dynamics benchmark datasets show that PIORF consistently outperforms baseline models and existing rewiring methods, achieving up to 26.2 improvement.

Deep reinforcement learning (DRL) has shown significant promise for uncovering sophisticated control policies that interact in environments with complicated dynamics, such as stabilizing the magnetohydrodynamics of a tokamak fusion reactor or minimizing the drag force exerted on an object in a fluid flow. However, these algorithms require an abundance of training examples and may become prohibitively expensive for many applications. In addition, the reliance on deep neural networks often results in an uninterpretable, black-box policy that may be too computationally expensive to use with certain embedded systems. Recent advances in sparse dictionary learning, such as the sparse identification of nonlinear dynamics (SINDy), have shown promise for creating efficient and interpretable data-driven models in the low-data regime. In this work we introduce SINDy-RL, a unifying framework for combining SINDy and DRL to create efficient, interpretable, and trustworthy representations of the dynamics model, reward function, and control policy. We demonstrate the effectiveness of our approaches on benchmark control environments and challenging fluids problems. SINDy-RL achieves comparable performance to state-of-the-art DRL algorithms using significantly fewer interactions in the environment and results in an interpretable control policy orders of magnitude smaller than a deep neural network policy.

While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this paper, we present GraphSplineNets, a novel deep-learning method to speed up the forecasting of physical systems by reducing the grid size and number of iteration steps of deep surrogate models. Our method uses two differentiable orthogonal spline collocation methods to efficiently predict response at any location in time and space. Additionally, we introduce an adaptive collocation strategy in space to prioritize sampling from the most important regions. GraphSplineNets improve the accuracy-speedup tradeoff in forecasting various dynamical systems with increasing complexity, including the heat equation, damped wave propagation, Navier-Stokes equations, and real-world ocean currents in both regular and irregular domains.

Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained increased interest. The practical utility of such neural PDE solvers relies on their ability to provide accurate, stable predictions over long time horizons, which is a notoriously hard problem. In this work, we present a large-scale analysis of common temporal rollout strategies, identifying the neglect of non-dominant spatial frequency information, often associated with high frequencies in PDE solutions, as the primary pitfall limiting stable, accurate rollout performance. Based on these insights, we draw inspiration from recent advances in diffusion models to introduce PDE-Refiner; a novel model class that enables more accurate modeling of all frequency components via a multistep refinement process. We validate PDE-Refiner on challenging benchmarks of complex fluid dynamics, demonstrating stable and accurate rollouts that consistently outperform state-of-the-art models, including neural, numerical, and hybrid neural-numerical architectures. We further demonstrate that PDE-Refiner greatly enhances data efficiency, since the denoising objective implicitly induces a novel form of spectral data augmentation. Finally, PDE-Refiner's connection to diffusion models enables an accurate and efficient assessment of the model's predictive uncertainty, allowing us to estimate when the surrogate becomes inaccurate.

Fluid-structure interaction is common in engineering and natural systems, where floating-body motion is governed by added mass, drag, and background flows. Modeling these dissipative dynamics is difficult: black-box neural models regress state derivatives with limited interpretability and unstable long-horizon predictions. We propose Floating-Body Hydrodynamic Neural Networks (FHNN), a physics-structured framework that predicts interpretable hydrodynamic parameters such as directional added masses, drag coefficients, and a streamfunction-based flow, and couples them with analytic equations of motion. This design constrains the hypothesis space, enhances interpretability, and stabilizes integration. On synthetic vortex datasets, FHNN achieves up to an order-of-magnitude lower error than Neural ODEs, recovers physically consistent flow fields. Compared with Hamiltonian and Lagrangian neural networks, FHNN more effectively handles dissipative dynamics while preserving interpretability, which bridges the gap between black-box learning and transparent system identification.

Complex, temporally evolving phenomena, from climate to brain activity, are governed by dynamical systems (DS). DS reconstruction (DSR) seeks to infer generative surrogate models of these from observed data, reproducing their long-term behavior. Existing DSR approaches require purpose-training for any new system observed, lacking the zero-shot and in-context inference capabilities known from LLMs. Here we introduce DynaMix, a novel multivariate ALRNN-based mixture-of-experts architecture pre-trained for DSR, the first DSR model able to generalize zero-shot to out-of-domain DS. Just from a provided context signal, without any re-training, DynaMix faithfully forecasts the long-term evolution of novel DS where existing time series (TS) foundation models, like Chronos, fail -- at a fraction of the number of parameters and orders of magnitude faster inference times. DynaMix outperforms TS foundation models in terms of long-term statistics, and often also short-term forecasts, even on real-world time series, like traffic or weather data, typically used for training and evaluating TS models, but not at all part of DynaMix' training corpus. We illustrate some of the failure modes of TS models for DSR problems, and conclude that models built on DS principles may bear a huge potential also for advancing the TS prediction field.

The aim of the present work is to investigate the influence of the realistic model parameters on the equipartition of energy in a vibrofluidized system. To achieve this, a three-dimensional vertically vibrated granular system consisting of spherical particles is simulated using the discrete element method (DEM) using the open-source software LAMMPS. Interparticle and wall-particle interactions are determined using the linear-spring dashpot model. Simulations are performed for nearly perfectly smooth to nearly perfectly rough particles. Two different values for the ratio of the tangential to normal spring stiffness coefficient kappa (2/7 and 3/4) are chosen. Non-equipartition of energy between the translational and rotational modes is observed for all realistic values in the parametric range.

We present a neural operator architecture to simulate Lagrangian dynamics, such as fluid flow, granular flows, and elastoplasticity. Traditional numerical methods, such as the finite element method (FEM), suffer from long run times and large memory consumption. On the other hand, approaches based on graph neural networks are faster but still suffer from long computation times on dense graphs, which are often required for high-fidelity simulations. Our model, GIOROM or Graph Interaction Operator for Reduced-Order Modeling, learns temporal dynamics within a reduced-order setting, capturing spatial features from a highly sparse graph representation of the input and generalizing to arbitrary spatial locations during inference. The model is geometry-aware and discretization-agnostic and can generalize to different initial conditions, velocities, and geometries after training. We show that point clouds of the order of 100,000 points can be inferred from sparse graphs with sim1000 points, with negligible change in computation time. We empirically evaluate our model on elastic solids, Newtonian fluids, Non-Newtonian fluids, Drucker-Prager granular flows, and von Mises elastoplasticity. On these benchmarks, our approach results in a 25times speedup compared to other neural network-based physics simulators while delivering high-fidelity predictions of complex physical systems and showing better performance on most benchmarks. The code and the demos are provided at https://github.com/HrishikeshVish/GIOROM.

Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour into different regimes, or modes, each with simpler dynamics, and then learning the switching behaviour from one mode to another. Switching Dynamical Systems (SDS) are a powerful tool that automatically discovers these modes and mode-switching behaviour from time series data. While effective, these methods focus on independent objects, where the modes of one object are independent of the modes of the other objects. In this paper, we focus on the more general interacting object setting for switching dynamical systems, where the per-object dynamics also depends on an unknown and dynamically changing subset of other objects and their modes. To this end, we propose a novel graph-based approach for switching dynamical systems, GRAph Switching dynamical Systems (GRASS), in which we use a dynamic graph to characterize interactions between objects and learn both intra-object and inter-object mode-switching behaviour. We introduce two new datasets for this setting, a synthesized ODE-driven particles dataset and a real-world Salsa Couple Dancing dataset. Experiments show that GRASS can consistently outperforms previous state-of-the-art methods.

In an experiment on a turbulent jet, we detect interfacial turbulent layers in a frame that moves, on average, along with the \tnti. This significantly prolongs the observation time of scalar and velocity structures and enables the measurement of two types of Lagrangian coherent structures. One structure, the finite-time Lyapunov field (FTLE), quantifies advective transport barriers of fluid parcels while the other structure highlights barriers of diffusive momentum transport. These two complementary structures depend on large-scale and small-scale motion and are therefore associated with the growth of the turbulent region through engulfment or nibbling, respectively. We detect the \tnti\ from cluster analysis, where we divide the measured scalar field into four clusters. Not only the \tnti\ can be found this way, but also the next, internal, turbulent-turbulent interface. Conditional averages show that these interfaces are correlated with barriers of advective and diffusive transport when the Lagrangian integration time is smaller than the integral time scale. Diffusive structures decorrelate faster since they have a smaller timescale. Conditional averages of these structures at internal turbulent-turbulent interfaces show the same pattern with a more pronounced jump at the interface indicative of a shear layer. This is quite an unexpected outcome, as the internal interface is now defined not by the presence or absence of vorticity, but by conditional vorticity corresponding to two uniform concentration zones. The long-time diffusive momentum flux along Lagrangian paths represents the growth of the turbulent flow into the irrotational domain, a direct demonstration of nibbling. The diffusive flux parallel to the \tnti\ appears to be concentrated in a diffusive superlayer whose width is comparable with the Taylor microscale, which is relatively invariant in time.

Computational Fluid Dynamics (CFD) simulation by the numerical solution of the Navier-Stokes equations is an essential tool in a wide range of applications from engineering design to climate modeling. However, the computational cost and memory demand required by CFD codes may become very high for flows of practical interest, such as in aerodynamic shape optimization. This expense is associated with the complexity of the fluid flow governing equations, which include non-linear partial derivative terms that are of difficult solution, leading to long computational times and limiting the number of hypotheses that can be tested during the process of iterative design. Therefore, we propose DeepCFD: a convolutional neural network (CNN) based model that efficiently approximates solutions for the problem of non-uniform steady laminar flows. The proposed model is able to learn complete solutions of the Navier-Stokes equations, for both velocity and pressure fields, directly from ground-truth data generated using a state-of-the-art CFD code. Using DeepCFD, we found a speedup of up to 3 orders of magnitude compared to the standard CFD approach at a cost of low error rates.

Computational Fluid Dynamics (CFD) is an essential simulation tool in various engineering disciplines, but it often requires substantial domain expertise and manual configuration, creating barriers to entry. We present Foam-Agent, a multi-agent framework that automates complex OpenFOAM-based CFD simulation workflows from natural language inputs. Our innovation includes (1) a hierarchical multi-index retrieval system with specialized indices for different simulation aspects, (2) a dependency-aware file generation system that provides consistency management across configuration files, and (3) an iterative error correction mechanism that diagnoses and resolves simulation failures without human intervention. Through comprehensive evaluation on the dataset of 110 simulation tasks, Foam-Agent achieves an 83.6% success rate with Claude 3.5 Sonnet, significantly outperforming existing frameworks (55.5% for MetaOpenFOAM and 37.3% for OpenFOAM-GPT). Ablation studies demonstrate the critical contribution of each system component, with the specialized error correction mechanism providing a 36.4% performance improvement. Foam-Agent substantially lowers the CFD expertise threshold while maintaining modeling accuracy, demonstrating the potential of specialized multi-agent systems to democratize access to complex scientific simulation tools. The code is public at https://github.com/csml-rpi/Foam-Agent

Simulations of turbulent flows in 3D are one of the most expensive simulations in computational fluid dynamics (CFD). Many works have been written on surrogate models to replace numerical solvers for fluid flows with faster, learned, autoregressive models. However, the intricacies of turbulence in three dimensions necessitate training these models with very small time steps, while generating realistic flow states requires either long roll-outs with many steps and significant error accumulation or starting from a known, realistic flow state - something we aimed to avoid in the first place. Instead, we propose to approach turbulent flow simulation as a generative task directly learning the manifold of all possible turbulent flow states without relying on any initial flow state. For our experiments, we introduce a challenging 3D turbulence dataset of high-resolution flows and detailed vortex structures caused by various objects and derive two novel sample evaluation metrics for turbulent flows. On this dataset, we show that our generative model captures the distribution of turbulent flows caused by unseen objects and generates high-quality, realistic samples amenable for downstream applications without access to any initial state.

Fast, geometry-generalizing surrogates for unsteady flow remain challenging. We present a time-dependent, geometry-aware Deep Operator Network that predicts velocity fields for moderate-Re flows around parametric and non-parametric shapes. The model encodes geometry via a signed distance field (SDF) trunk and flow history via a CNN branch, trained on 841 high-fidelity simulations. On held-out shapes, it attains sim 5% relative L2 single-step error and up to 1000X speedups over CFD. We provide physics-centric rollout diagnostics, including phase error at probes and divergence norms, to quantify long-horizon fidelity. These reveal accurate near-term transients but error accumulation in fine-scale wakes, most pronounced for sharp-cornered geometries. We analyze failure modes and outline practical mitigations. Code, splits, and scripts are openly released at: https://github.com/baskargroup/TimeDependent-DeepONet to support reproducibility and benchmarking.

We develop a deep reinforcement learning method for training a jellyfish-like swimmer to effectively track a moving target in a two-dimensional flow. This swimmer is a flexible object equipped with a muscle model based on torsional springs. We employ a deep Q-network (DQN) that takes the swimmer's geometry and dynamic parameters as inputs, and outputs actions which are the forces applied to the swimmer. In particular, we introduce an action regulation to mitigate the interference from complex fluid-structure interactions. The goal of these actions is to navigate the swimmer to a target point in the shortest possible time. In the DQN training, the data on the swimmer's motions are obtained from simulations conducted using the immersed boundary method. During tracking a moving target, there is an inherent delay between the application of forces and the corresponding response of the swimmer's body due to hydrodynamic interactions between the shedding vortices and the swimmer's own locomotion. Our tests demonstrate that the swimmer, with the DQN agent and action regulation, is able to dynamically adjust its course based on its instantaneous state. This work extends the application scope of machine learning in controlling flexible objects within fluid environments.

We propose a novel approach to animate human hair in a still portrait photo. Existing work has largely studied the animation of fluid elements such as water and fire. However, hair animation for a real image remains underexplored, which is a challenging problem, due to the high complexity of hair structure and dynamics. Considering the complexity of hair structure, we innovatively treat hair wisp extraction as an instance segmentation problem, where a hair wisp is referred to as an instance. With advanced instance segmentation networks, our method extracts meaningful and natural hair wisps. Furthermore, we propose a wisp-aware animation module that animates hair wisps with pleasing motions without noticeable artifacts. The extensive experiments show the superiority of our method. Our method provides the most pleasing and compelling viewing experience in the qualitative experiments and outperforms state-of-the-art still-image animation methods by a large margin in the quantitative evaluation. Project url: https://nevergiveu.github.io/AutomaticHairBlowing/

Representing and rendering dynamic scenes has been an important but challenging task. Especially, to accurately model complex motions, high efficiency is usually hard to maintain. We introduce the 4D Gaussian Splatting (4D-GS) to achieve real-time dynamic scene rendering while also enjoying high training and storage efficiency. An efficient deformation field is constructed to model both Gaussian motions and shape deformations. Different adjacent Gaussians are connected via a HexPlane to produce more accurate position and shape deformations. Our 4D-GS method achieves real-time rendering under high resolutions, 70 FPS at a 800times800 resolution on an RTX 3090 GPU, while maintaining comparable or higher quality than previous state-of-the-art methods. More demos and code are available at https://guanjunwu.github.io/4dgs/.

We study the connection between audio-visual observations and the underlying physics of a mundane yet intriguing everyday activity: pouring liquids. Given only the sound of liquid pouring into a container, our objective is to automatically infer physical properties such as the liquid level, the shape and size of the container, the pouring rate and the time to fill. To this end, we: (i) show in theory that these properties can be determined from the fundamental frequency (pitch); (ii) train a pitch detection model with supervision from simulated data and visual data with a physics-inspired objective; (iii) introduce a new large dataset of real pouring videos for a systematic study; (iv) show that the trained model can indeed infer these physical properties for real data; and finally, (v) we demonstrate strong generalization to various container shapes, other datasets, and in-the-wild YouTube videos. Our work presents a keen understanding of a narrow yet rich problem at the intersection of acoustics, physics, and learning. It opens up applications to enhance multisensory perception in robotic pouring.

We design a physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems. Although existing nonlinear manifold learning methods seem to be compelling tools to reduce the dimensionality of data characterized by a large Kolmogorov n-width, they typically lack a straightforward mapping from the latent space to the high-dimensional physical space. Moreover, the realized latent variables are often hard to interpret. Therefore, many of these methods are often dismissed in the reduced order modeling of dynamical systems governed by the partial differential equations (PDEs). Accordingly, we propose an auto-encoder type nonlinear dimensionality reduction algorithm. The unsupervised learning problem trains a diffeomorphic spatio-temporal grid, that registers the output sequence of the PDEs on a non-uniform parameter/time-varying grid, such that the Kolmogorov n-width of the mapped data on the learned grid is minimized. We demonstrate the efficacy and interpretability of our approach to separate convection/advection from diffusion/scaling on various manufactured and physical systems.

We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems modulated via nonlinear interlinked gates. The resulting models represent dynamical systems with varying (i.e., liquid) time-constants coupled to their hidden state, with outputs being computed by numerical differential equation solvers. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations, and give rise to improved performance on time-series prediction tasks. To demonstrate these properties, we first take a theoretical approach to find bounds over their dynamics and compute their expressive power by the trajectory length measure in latent trajectory space. We then conduct a series of time-series prediction experiments to manifest the approximation capability of Liquid Time-Constant Networks (LTCs) compared to classical and modern RNNs. Code and data are available at https://github.com/raminmh/liquid_time_constant_networks

Surrogate models are necessary to optimize meaningful quantities in physical dynamics as their recursive numerical resolutions are often prohibitively expensive. It is mainly the case for fluid dynamics and the resolution of Navier-Stokes equations. However, despite the fast-growing field of data-driven models for physical systems, reference datasets representing real-world phenomena are lacking. In this work, we develop AirfRANS, a dataset for studying the two-dimensional incompressible steady-state Reynolds-Averaged Navier-Stokes equations over airfoils at a subsonic regime and for different angles of attacks. We also introduce metrics on the stress forces at the surface of geometries and visualization of boundary layers to assess the capabilities of models to accurately predict the meaningful information of the problem. Finally, we propose deep learning baselines on four machine learning tasks to study AirfRANS under different constraints for generalization considerations: big and scarce data regime, Reynolds number, and angle of attack extrapolation.

Modeling the dynamics of deformable objects is challenging due to their diverse physical properties and the difficulty of estimating states from limited visual information. We address these challenges with a neural dynamics framework that combines object particles and spatial grids in a hybrid representation. Our particle-grid model captures global shape and motion information while predicting dense particle movements, enabling the modeling of objects with varied shapes and materials. Particles represent object shapes, while the spatial grid discretizes the 3D space to ensure spatial continuity and enhance learning efficiency. Coupled with Gaussian Splattings for visual rendering, our framework achieves a fully learning-based digital twin of deformable objects and generates 3D action-conditioned videos. Through experiments, we demonstrate that our model learns the dynamics of diverse objects -- such as ropes, cloths, stuffed animals, and paper bags -- from sparse-view RGB-D recordings of robot-object interactions, while also generalizing at the category level to unseen instances. Our approach outperforms state-of-the-art learning-based and physics-based simulators, particularly in scenarios with limited camera views. Furthermore, we showcase the utility of our learned models in model-based planning, enabling goal-conditioned object manipulation across a range of tasks. The project page is available at https://kywind.github.io/pgnd .

Existing video generation models excel at producing photo-realistic videos from text or images, but often lack physical plausibility and 3D controllability. To overcome these limitations, we introduce PhysCtrl, a novel framework for physics-grounded image-to-video generation with physical parameters and force control. At its core is a generative physics network that learns the distribution of physical dynamics across four materials (elastic, sand, plasticine, and rigid) via a diffusion model conditioned on physics parameters and applied forces. We represent physical dynamics as 3D point trajectories and train on a large-scale synthetic dataset of 550K animations generated by physics simulators. We enhance the diffusion model with a novel spatiotemporal attention block that emulates particle interactions and incorporates physics-based constraints during training to enforce physical plausibility. Experiments show that PhysCtrl generates realistic, physics-grounded motion trajectories which, when used to drive image-to-video models, yield high-fidelity, controllable videos that outperform existing methods in both visual quality and physical plausibility. Project Page: https://cwchenwang.github.io/physctrl

Recent advances in text-to-image (T2I) generation have led to impressive visual results. However, these models still face significant challenges when handling complex prompt, particularly those involving multiple subjects with distinct attributes. Inspired by the human drawing process, which first outlines the composition and then incrementally adds details, we propose Detail++, a training-free framework that introduces a novel Progressive Detail Injection (PDI) strategy to address this limitation. Specifically, we decompose a complex prompt into a sequence of simplified sub-prompts, guiding the generation process in stages. This staged generation leverages the inherent layout-controlling capacity of self-attention to first ensure global composition, followed by precise refinement. To achieve accurate binding between attributes and corresponding subjects, we exploit cross-attention mechanisms and further introduce a Centroid Alignment Loss at test time to reduce binding noise and enhance attribute consistency. Extensive experiments on T2I-CompBench and a newly constructed style composition benchmark demonstrate that Detail++ significantly outperforms existing methods, particularly in scenarios involving multiple objects and complex stylistic conditions.

Accurate Subseasonal-to-Seasonal (S2S) ocean simulation is critically important for marine research, yet remains challenging due to its substantial thermal inertia and extended time delay. Machine learning (ML)-based models have demonstrated significant advancements in simulation accuracy and computational efficiency compared to traditional numerical methods. Nevertheless, a significant limitation of current ML models for S2S ocean simulation is their inadequate incorporation of physical consistency and the slow-changing properties of the ocean system. In this work, we propose a neural ocean model (NeuralOM) for S2S ocean simulation with a multi-scale interactive graph neural network to emulate diverse physical phenomena associated with ocean systems effectively. Specifically, we propose a multi-stage framework tailored to model the ocean's slowly changing nature. Additionally, we introduce a multi-scale interactive messaging module to capture complex dynamical behaviors, such as gradient changes and multiplicative coupling relationships inherent in ocean dynamics. Extensive experimental evaluations confirm that our proposed NeuralOM outperforms state-of-the-art models in S2S and extreme event simulation. The codes are available at https://github.com/YuanGao-YG/NeuralOM.

Mimicking realistic dynamics in 3D garment animations is a challenging task due to the complex nature of multi-layered garments and the variety of outer forces involved. Existing approaches mostly focus on single-layered garments driven by only human bodies and struggle to handle general scenarios. In this paper, we propose a novel data-driven method, called LayersNet, to model garment-level animations as particle-wise interactions in a micro physics system. We improve simulation efficiency by representing garments as patch-level particles in a two-level structural hierarchy. Moreover, we introduce a novel Rotation Equivalent Transformation that leverages the rotation invariance and additivity of physics systems to better model outer forces. To verify the effectiveness of our approach and bridge the gap between experimental environments and real-world scenarios, we introduce a new challenging dataset, D-LAYERS, containing 700K frames of dynamics of 4,900 different combinations of multi-layered garments driven by both human bodies and randomly sampled wind. Our experiments show that LayersNet achieves superior performance both quantitatively and qualitatively. We will make the dataset and code publicly available at https://mmlab-ntu.github.io/project/layersnet/index.html .

Foundations of a new projection-based model reduction approach for convection dominated nonlinear fluid flows are summarized. In this method the evolution of the flow is approximated in the Lagrangian frame of reference. Global basis functions are used to approximate both the state and the position of the Lagrangian computational domain. It is demonstrated that in this framework, certain wave-like solutions exhibit low-rank structure and thus, can be efficiently compressed using relatively few global basis. The proposed approach is successfully demonstrated for the reduction of several simple but representative problems.

The proposed method aims to approximate a solution of a fluid-fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplified version of the atmosphere-ocean coupling. Thus, the proposed method should be viewed as potentially applicable to air-sea coupled flows in turbulent regime. The method consists of two key ingredients. The geometric averaging approach is used for efficient and stable decoupling of the problem, which would allow for the usage of preexisting codes for the air and sea domain separately, as "black boxes". This is combined with the variational multiscale stabilization technique for treating flows at high Reynolds numbers. We prove the stability and accuracy of the method and provide several numerical tests to assess both the quantitative and qualitative features of the computed solution.

We consider using deep neural networks to solve time-dependent partial differential equations (PDEs), where multi-scale processing is crucial for modeling complex, time-evolving dynamics. While the U-Net architecture with skip connections is commonly used by prior studies to enable multi-scale processing, our analysis shows that the need for features to evolve across layers results in temporally misaligned features in skip connections, which limits the model's performance. To address this limitation, we propose SineNet, consisting of multiple sequentially connected U-shaped network blocks, referred to as waves. In SineNet, high-resolution features are evolved progressively through multiple stages, thereby reducing the amount of misalignment within each stage. We furthermore analyze the role of skip connections in enabling both parallel and sequential processing of multi-scale information. Our method is rigorously tested on multiple PDE datasets, including the Navier-Stokes equations and shallow water equations, showcasing the advantages of our proposed approach over conventional U-Nets with a comparable parameter budget. We further demonstrate that increasing the number of waves in SineNet while maintaining the same number of parameters leads to a monotonically improved performance. The results highlight the effectiveness of SineNet and the potential of our approach in advancing the state-of-the-art in neural PDE solver design. Our code is available as part of AIRS (https://github.com/divelab/AIRS).

Discovering the underlying physical behavior of complex systems is a crucial, but less well-understood topic in many engineering disciplines. This study proposes a finite-difference inspired convolutional neural network framework to learn hidden partial differential equations from given data and iteratively estimate future dynamical behavior. The methodology designs the filter sizes such that they mimic the finite difference between the neighboring points. By learning the governing equation, the network predicts the future evolution of the solution by using only a few trainable parameters. In this paper, we provide numerical results to compare the efficiency of the second-order Trust-Region Conjugate Gradient (TRCG) method with the first-order ADAM optimizer.

The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards fully end-to-end learned systems. Most works so far can only generalize over a subset of properties to which a generic solver would be faced, including: resolution, topology, geometry, boundary conditions, domain discretization regularity, dimensionality, etc. In this work, we build a solver, satisfying these properties, where all the components are based on neural message passing, replacing all heuristically designed components in the computation graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. In order to encourage stability in training autoregressive models, we put forward a method that is based on the principle of zero-stability, posing stability as a domain adaptation problem. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.

Computational Fluid Dynamics (CFD) is an essential simulation tool in engineering, yet its steep learning curve and complex manual setup create significant barriers. To address these challenges, we introduce Foam-Agent, a multi-agent framework that automates the entire end-to-end OpenFOAM workflow from a single natural language prompt. Our key innovations address critical gaps in existing systems: 1. An Comprehensive End-to-End Simulation Automation: Foam-Agent is the first system to manage the full simulation pipeline, including advanced pre-processing with a versatile Meshing Agent capable of handling external mesh files and generating new geometries via Gmsh, automatic generation of HPC submission scripts, and post-simulation visualization via ParaView. 2. Composable Service Architecture: Going beyond a monolithic agent, the framework uses Model Context Protocol (MCP) to expose its core functions as discrete, callable tools. This allows for flexible integration and use by other agentic systems, such as Claude-code, for more exploratory workflows. 3. High-Fidelity Configuration Generation: We achieve superior accuracy through a Hierarchical Multi-Index RAG for precise context retrieval and a dependency-aware generation process that ensures configuration consistency. Evaluated on a benchmark of 110 simulation tasks, Foam-Agent achieves an 88.2% success rate with Claude 3.5 Sonnet, significantly outperforming existing frameworks (55.5% for MetaOpenFOAM). Foam-Agent dramatically lowers the expertise barrier for CFD, demonstrating how specialized multi-agent systems can democratize complex scientific computing. The code is public at https://github.com/csml-rpi/Foam-Agent.

We formulate a hierarchical rectified flow to model data distributions. It hierarchically couples multiple ordinary differential equations (ODEs) and defines a time-differentiable stochastic process that generates a data distribution from a known source distribution. Each ODE resembles the ODE that is solved in a classic rectified flow, but differs in its domain, i.e., location, velocity, acceleration, etc. Unlike the classic rectified flow formulation, which formulates a single ODE in the location domain and only captures the expected velocity field (sufficient to capture a multi-modal data distribution), the hierarchical rectified flow formulation models the multi-modal random velocity field, acceleration field, etc., in their entirety. This more faithful modeling of the random velocity field enables integration paths to intersect when the underlying ODE is solved during data generation. Intersecting paths in turn lead to integration trajectories that are more straight than those obtained in the classic rectified flow formulation, where integration paths cannot intersect. This leads to modeling of data distributions with fewer neural function evaluations. We empirically verify this on synthetic 1D and 2D data as well as MNIST, CIFAR-10, and ImageNet-32 data. Our code is available at: https://riccizz.github.io/HRF/.

Configuring computational fluid dynamics (CFD) simulations typically demands extensive domain expertise, limiting broader access. Although large language models (LLMs) have advanced scientific computing, their use in automating CFD workflows is underdeveloped. We introduce a novel approach centered on domain-specific LLM adaptation. By fine-tuning Qwen2.5-7B-Instruct on NL2FOAM, our custom dataset of 28716 natural language-to-OpenFOAM configuration pairs with chain-of-thought (CoT) annotations, we enable direct translation from natural language descriptions to executable CFD setups. A multi-agent framework orchestrates the process, autonomously verifying inputs, generating configurations, running simulations, and correcting errors. Evaluation on a benchmark of 21 diverse flow cases demonstrates state-of-the-art performance, achieving 88.7% solution accuracy and 82.6% first-attempt success rate. This significantly outperforms larger general-purpose models like Qwen2.5-72B-Instruct, DeepSeek-R1, and Llama3.3-70B-Instruct, while also requiring fewer correction iterations and maintaining high computational efficiency. The results highlight the critical role of domain-specific adaptation in deploying LLM assistants for complex engineering workflows. Our code and fine-tuned model have been deposited at https://github.com/YYgroup/AutoCFD.

A mesh motion model based on deep operator networks is presented. The model is trained on and evaluated against a biharmonic mesh motion model on a fluid-structure interaction benchmark problem and further evaluated in a setting where biharmonic mesh motion fails. The performance of the proposed mesh motion model is comparable to the biharmonic mesh motion on the test problems.

Modern 3D generation methods can rapidly create shapes from sparse or single views, but their outputs often lack geometric detail due to computational constraints. We present DetailGen3D, a generative approach specifically designed to enhance these generated 3D shapes. Our key insight is to model the coarse-to-fine transformation directly through data-dependent flows in latent space, avoiding the computational overhead of large-scale 3D generative models. We introduce a token matching strategy that ensures accurate spatial correspondence during refinement, enabling local detail synthesis while preserving global structure. By carefully designing our training data to match the characteristics of synthesized coarse shapes, our method can effectively enhance shapes produced by various 3D generation and reconstruction approaches, from single-view to sparse multi-view inputs. Extensive experiments demonstrate that DetailGen3D achieves high-fidelity geometric detail synthesis while maintaining efficiency in training.

We present FloodDiffusion, a new framework for text-driven, streaming human motion generation. Given time-varying text prompts, FloodDiffusion generates text-aligned, seamless motion sequences with real-time latency. Unlike existing methods that rely on chunk-by-chunk or auto-regressive model with diffusion head, we adopt a diffusion forcing framework to model this time-series generation task under time-varying control events. We find that a straightforward implementation of vanilla diffusion forcing (as proposed for video models) fails to model real motion distributions. We demonstrate that to guarantee modeling the output distribution, the vanilla diffusion forcing must be tailored to: (i) train with a bi-directional attention instead of casual attention; (ii) implement a lower triangular time scheduler instead of a random one; (iii) utilize a continues time-varying way to introduce text conditioning. With these improvements, we demonstrate in the first time that the diffusion forcing-based framework achieves state-of-the-art performance on the streaming motion generation task, reaching an FID of 0.057 on the HumanML3D benchmark. Models, code, and weights are available. https://shandaai.github.io/FloodDiffusion/

Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each presents its unique limitations and generally balances training cost, numerical accuracy, and ease of applicability to different problem setups. To address these limitations, we introduce several methods to apply latent diffusion models to physics simulation. Firstly, we introduce a mesh autoencoder to compress arbitrarily discretized PDE data, allowing for efficient diffusion training across various physics. Furthermore, we investigate full spatio-temporal solution generation to mitigate autoregressive error accumulation. Lastly, we investigate conditioning on initial physical quantities, as well as conditioning solely on a text prompt to introduce text2PDE generation. We show that language can be a compact, interpretable, and accurate modality for generating physics simulations, paving the way for more usable and accessible PDE solvers. Through experiments on both uniform and structured grids, we show that the proposed approach is competitive with current neural PDE solvers in both accuracy and efficiency, with promising scaling behavior up to sim3 billion parameters. By introducing a scalable, accurate, and usable physics simulator, we hope to bring neural PDE solvers closer to practical use.

The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction. The study presents a neural operator based on the dynamic mode decomposition algorithm (DMD), mapping functional spaces, which combines DMD and deep learning (DL) for spatiotemporal processes efficient modeling. Solving PDEs for various initial and boundary conditions requires significant computational resources. The method suggested automatically extracts key modes and system dynamics using them to construct predictions, reducing computational costs compared to traditional numerical methods. The approach has demonstrated its efficiency through comparative analysis of performance with closest analogues DeepONet and FNO in the heat equation, Laplaces equation, and Burgers equation solutions approximation, where it achieves high reconstruction accuracy.

Conventional production workflow of high-precision mesh assets necessitates a cumbersome and laborious process of manual sculpting by specialized 3D artists/modelers. The recent years have witnessed remarkable advances in AI-empowered 3D content creation for generating plausible structures and intricate appearances from images or text prompts. However, synthesizing realistic surface details still poses great challenges, and enhancing the geometry fidelity of existing lower-quality 3D meshes (instead of image/text-to-3D generation) remains an open problem. In this paper, we introduce SuperCarver, a 3D geometry super-resolution pipeline for supplementing texture-consistent surface details onto a given coarse mesh. We start by rendering the original textured mesh into the image domain from multiple viewpoints. To achieve detail boosting, we construct a deterministic prior-guided normal diffusion model, which is fine-tuned on a carefully curated dataset of paired detail-lacking and detail-rich normal map renderings. To update mesh surfaces from potentially imperfect normal map predictions, we design a noise-resistant inverse rendering scheme through deformable distance field. Experiments demonstrate that our SuperCarver is capable of generating realistic and expressive surface details depicted by the actual texture appearance, making it a powerful tool to both upgrade historical low-quality 3D assets and reduce the workload of sculpting high-poly meshes.

Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering and mathematical problems involving functions of several variables, such as the propagation of heat or sound, fluid flow, elasticity, electrostatics, electrodynamics, and more. While this has led to solving many complex phenomena, there are some limitations. Conventional approaches such as Finite Element Methods (FEMs) and Finite Differential Methods (FDMs) require considerable time and are computationally expensive. In contrast, data driven machine learning-based methods such as neural networks provide a faster, fairly accurate alternative, and have certain advantages such as discretization invariance and resolution invariance. This article aims to provide a comprehensive insight into how data-driven approaches can complement conventional techniques to solve engineering and physics problems, while also noting some of the major pitfalls of machine learning-based approaches. Furthermore, we highlight, a novel and fast machine learning-based approach (~1000x) to learning the solution operator of a PDE operator learning. We will note how these new computational approaches can bring immense advantages in tackling many problems in fundamental and applied physics.

Numerous biological and physical processes can be modeled as systems of interacting entities evolving continuously over time, e.g. the dynamics of communicating cells or physical particles. Learning the dynamics of such systems is essential for predicting the temporal evolution of populations across novel samples and unseen environments. Flow-based models allow for learning these dynamics at the population level - they model the evolution of the entire distribution of samples. However, current flow-based models are limited to a single initial population and a set of predefined conditions which describe different dynamics. We argue that multiple processes in natural sciences have to be represented as vector fields on the Wasserstein manifold of probability densities. That is, the change of the population at any moment in time depends on the population itself due to the interactions between samples. In particular, this is crucial for personalized medicine where the development of diseases and their respective treatment response depends on the microenvironment of cells specific to each patient. We propose Meta Flow Matching (MFM), a practical approach to integrating along these vector fields on the Wasserstein manifold by amortizing the flow model over the initial populations. Namely, we embed the population of samples using a Graph Neural Network (GNN) and use these embeddings to train a Flow Matching model. This gives MFM the ability to generalize over the initial distributions unlike previously proposed methods. We demonstrate the ability of MFM to improve prediction of individual treatment responses on a large scale multi-patient single-cell drug screen dataset.

In this study, we propose a multi branched network approach to predict the dynamics of a physics attractor characterized by intricate and chaotic behavior. We introduce a unique neural network architecture comprised of Radial Basis Function (RBF) layers combined with an attention mechanism designed to effectively capture nonlinear inter-dependencies inherent in the attractor's temporal evolution. Our results demonstrate successful prediction of the attractor's trajectory across 100 predictions made using a real-world dataset of 36,700 time-series observations encompassing approximately 28 minutes of activity. To further illustrate the performance of our proposed technique, we provide comprehensive visualizations depicting the attractor's original and predicted behaviors alongside quantitative measures comparing observed versus estimated outcomes. Overall, this work showcases the potential of advanced machine learning algorithms in elucidating hidden structures in complex physical systems while offering practical applications in various domains requiring accurate short-term forecasting capabilities.

Intuitive physics understanding in video diffusion models plays an essential role in building general-purpose physically plausible world simulators, yet accurately evaluating such capacity remains a challenging task due to the difficulty in disentangling physics correctness from visual appearance in generation. To the end, we introduce LikePhys, a training-free method that evaluates intuitive physics in video diffusion models by distinguishing physically valid and impossible videos using the denoising objective as an ELBO-based likelihood surrogate on a curated dataset of valid-invalid pairs. By testing on our constructed benchmark of twelve scenarios spanning over four physics domains, we show that our evaluation metric, Plausibility Preference Error (PPE), demonstrates strong alignment with human preference, outperforming state-of-the-art evaluator baselines. We then systematically benchmark intuitive physics understanding in current video diffusion models. Our study further analyses how model design and inference settings affect intuitive physics understanding and highlights domain-specific capacity variations across physical laws. Empirical results show that, despite current models struggling with complex and chaotic dynamics, there is a clear trend of improvement in physics understanding as model capacity and inference settings scale.

We report a flexible multi-modal mechanics language model, MeLM, applied to solve various nonlinear forward and inverse problems, that can deal with a set of instructions, numbers and microstructure data. The framework is applied to various examples including bio-inspired hierarchical honeycomb design, carbon nanotube mechanics, and protein unfolding. In spite of the flexible nature of the model-which allows us to easily incorporate diverse materials, scales, and mechanical features-it performs well across disparate forward and inverse tasks. Based on an autoregressive attention-model, MeLM effectively represents a large multi-particle system consisting of hundreds of millions of neurons, where the interaction potentials are discovered through graph-forming self-attention mechanisms that are then used to identify relationships from emergent structures, while taking advantage of synergies discovered in the training data. We show that the model can solve complex degenerate mechanics design problems and determine novel material architectures across a range of hierarchical levels, providing an avenue for materials discovery and analysis. Looking beyond the demonstrations reported in this paper, we discuss other opportunities in applied mechanics and general considerations about the use of large language models in modeling, design, and analysis that can span a broad spectrum of material properties from mechanical, thermal, optical, to electronic.

Recently, significant advancements have been made in the reconstruction and generation of 3D assets, including static cases and those with physical interactions. To recover the physical properties of 3D assets, existing methods typically assume that all materials belong to a specific predefined category (e.g., elasticity). However, such assumptions ignore the complex composition of multiple heterogeneous objects in real scenarios and tend to render less physically plausible animation given a wider range of objects. We propose OmniPhysGS for synthesizing a physics-based 3D dynamic scene composed of more general objects. A key design of OmniPhysGS is treating each 3D asset as a collection of constitutive 3D Gaussians. For each Gaussian, its physical material is represented by an ensemble of 12 physical domain-expert sub-models (rubber, metal, honey, water, etc.), which greatly enhances the flexibility of the proposed model. In the implementation, we define a scene by user-specified prompts and supervise the estimation of material weighting factors via a pretrained video diffusion model. Comprehensive experiments demonstrate that OmniPhysGS achieves more general and realistic physical dynamics across a broader spectrum of materials, including elastic, viscoelastic, plastic, and fluid substances, as well as interactions between different materials. Our method surpasses existing methods by approximately 3% to 16% in metrics of visual quality and text alignment.

It is well known that the reversibility of Stokes flow makes it difficult for small microorganisms to swim. Inertial effects break this reversibility, allowing new mechanisms of propulsion and feeding. Therefore it is important to understand the effects of unsteady and fluid inertia on the dynamics of microorganisms in flow. In this work, we show how to translate known inertial effects for non-motile organisms to motile ones, from passive to active particles. The method relies on a principle used earlier by Legendre and Magnaudet (1997) to deduce inertial corrections to the lift force on a bubble from the inertial drag on a solid sphere, using the fact that small inertial effects are determined by the far field of the disturbance flow. The method allows for example to compute the inertial effect of unsteady fluid accelerations on motile organisms, and the inertial forces such organisms experience in steady shear flow. We explain why the method fails to describe the effect of convective fluid inertia.

Visual effects (VFX) are key to immersion in modern films, games, and AR/VR. Creating 3D effects requires specialized expertise and training in 3D animation software and can be time consuming. Generative solutions typically rely on computationally intense methods such as diffusion models which can be slow at 4D inference. We reformulate 3D animation as a field prediction task and introduce a text-driven framework that infers a time-varying 4D flow field acting on 3D Gaussians. By leveraging large language models (LLMs) and vision-language models (VLMs) for function generation, our approach interprets arbitrary prompts (e.g., "make the vase glow orange, then explode") and instantly updates color, opacity, and positions of 3D Gaussians in real time. This design avoids overheads such as mesh extraction, manual or physics-based simulations and allows both novice and expert users to animate volumetric scenes with minimal effort on a consumer device even in a web browser. Experimental results show that simple textual instructions suffice to generate compelling time-varying VFX, reducing the manual effort typically required for rigging or advanced modeling. We thus present a fast and accessible pathway to language-driven 3D content creation that can pave the way to democratize VFX further.

Learning complex dynamics driven by partial differential equations directly from data holds great promise for fast and accurate simulations of complex physical systems. In most cases, this problem can be formulated as an operator learning task, where one aims to learn the operator representing the physics of interest, which entails discretization of the continuous system. However, preserving key continuous properties at the discrete level, such as boundary conditions, and addressing physical systems with complex geometries is challenging for most existing approaches. We introduce a family of operator learning architectures, structure-preserving operator networks (SPONs), that allows to preserve key mathematical and physical properties of the continuous system by leveraging finite element (FE) discretizations of the input-output spaces. SPONs are encode-process-decode architectures that are end-to-end differentiable, where the encoder and decoder follows from the discretizations of the input-output spaces. SPONs can operate on complex geometries, enforce certain boundary conditions exactly, and offer theoretical guarantees. Our framework provides a flexible way of devising structure-preserving architectures tailored to specific applications, and offers an explicit trade-off between performance and efficiency, all thanks to the FE discretization of the input-output spaces. Additionally, we introduce a multigrid-inspired SPON architecture that yields improved performance at higher efficiency. Finally, we release a software to automate the design and training of SPON architectures.

Story visualization has become a popular task where visual scenes are generated to depict a narrative across multiple panels. A central challenge in this setting is maintaining visual consistency, particularly in how characters and objects persist and evolve throughout the story. Despite recent advances in diffusion models, current approaches often fail to preserve key character attributes, leading to incoherent narratives. In this work, we propose a collaborative multi-agent framework that autonomously identifies, corrects, and refines inconsistencies across multi-panel story visualizations. The agents operate in an iterative loop, enabling fine-grained, panel-level updates without re-generating entire sequences. Our framework is model-agnostic and flexibly integrates with a variety of diffusion models, including rectified flow transformers such as Flux and latent diffusion models such as Stable Diffusion. Quantitative and qualitative experiments show that our method outperforms prior approaches in terms of multi-panel consistency.

Diffusion models have recently been increasingly applied to temporal data such as video, fluid mechanics simulations, or climate data. These methods generally treat subsequent frames equally regarding the amount of noise in the diffusion process. This paper explores Rolling Diffusion: a new approach that uses a sliding window denoising process. It ensures that the diffusion process progressively corrupts through time by assigning more noise to frames that appear later in a sequence, reflecting greater uncertainty about the future as the generation process unfolds. Empirically, we show that when the temporal dynamics are complex, Rolling Diffusion is superior to standard diffusion. In particular, this result is demonstrated in a video prediction task using the Kinetics-600 video dataset and in a chaotic fluid dynamics forecasting experiment.

Information on liquid jet stream flow is crucial in many real world applications. In a large number of cases, these flows fall directly onto free surfaces (e.g. pools), creating a splash with accompanying splashing sounds. The sound produced is supplied by energy interactions between the liquid jet stream and the passive free surface. In this investigation, we collect the sound of a water jet of varying flowrate falling into a pool of water, and use this sound to predict the flowrate and flowrate trajectory involved. Two approaches are employed: one uses machine-learning models trained using audio features extracted from the collected sound to predict the flowrate (and subsequently the flowrate trajectory). In contrast, the second method directly uses acoustic parameters related to the spectral energy of the liquid-liquid interaction to estimate the flowrate trajectory. The actual flowrate, however, is determined directly using a gravimetric method: tracking the change in mass of the pooling liquid over time. We show here that the two methods agree well with the actual flowrate and offer comparable performance in accurately predicting the flowrate trajectory, and accordingly offer insights for potential real-life applications using sound.

Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial conditions and boundary conditions as soft constraints. These soft constraints are often considered to be the sources of the complexity in the training phase of PINNs. Here, we demonstrate that the challenge of training (i) persists even when the boundary conditions are strictly enforced, and (ii) is closely related to the Kolmogorov n-width associated with problems demonstrating transport, convection, traveling waves, or moving fronts. Given this realization, we describe the mechanism underlying the training schemes such as those used in eXtended PINNs (XPINN), curriculum regularization, and sequence-to-sequence learning. For an important category of PDEs, i.e., governed by non-linear convection-diffusion equation, we propose reformulating PINNs on a Lagrangian frame of reference, i.e., LPINNs, as a PDE-informed solution. A parallel architecture with two branches is proposed. One branch solves for the state variables on the characteristics, and the second branch solves for the low-dimensional characteristics curves. The proposed architecture conforms to the causality innate to the convection, and leverages the direction of travel of the information in the domain. Finally, we demonstrate that the loss landscapes of LPINNs are less sensitive to the so-called "complexity" of the problems, compared to those in the traditional PINNs in the Eulerian framework.

3D Morphable Models (3DMMs) demonstrate great potential for reconstructing faithful and animatable 3D facial surfaces from a single image. The facial surface is influenced by the coarse shape, as well as the static detail (e,g., person-specific appearance) and dynamic detail (e.g., expression-driven wrinkles). Previous work struggles to decouple the static and dynamic details through image-level supervision, leading to reconstructions that are not realistic. In this paper, we aim at high-fidelity 3D face reconstruction and propose HiFace to explicitly model the static and dynamic details. Specifically, the static detail is modeled as the linear combination of a displacement basis, while the dynamic detail is modeled as the linear interpolation of two displacement maps with polarized expressions. We exploit several loss functions to jointly learn the coarse shape and fine details with both synthetic and real-world datasets, which enable HiFace to reconstruct high-fidelity 3D shapes with animatable details. Extensive quantitative and qualitative experiments demonstrate that HiFace presents state-of-the-art reconstruction quality and faithfully recovers both the static and dynamic details. Our project page can be found at https://project-hiface.github.io.

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

Painting embodies a unique form of visual storytelling, where the creation process is as significant as the final artwork. Although recent advances in generative models have enabled visually compelling painting synthesis, most existing methods focus solely on final image generation or patch-based process simulation, lacking explicit stroke structure and failing to produce smooth, realistic shading. In this work, we present a differentiable stroke reconstruction framework that unifies painting, stylized texturing, and smudging to faithfully reproduce the human painting-smudging loop. Given an input image, our framework first optimizes single- and dual-color Bezier strokes through a parallel differentiable paint renderer, followed by a style generation module that synthesizes geometry-conditioned textures across diverse painting styles. We further introduce a differentiable smudge operator to enable natural color blending and shading. Coupled with a coarse-to-fine optimization strategy, our method jointly optimizes stroke geometry, color, and texture under geometric and semantic guidance. Extensive experiments on oil, watercolor, ink, and digital paintings demonstrate that our approach produces realistic and expressive stroke reconstructions, smooth tonal transitions, and richly stylized appearances, offering a unified model for expressive digital painting creation. See our project page for more demos: https://yingjiang96.github.io/DiffPaintWebsite/.

In this work, we present WeatherEdit, a novel weather editing pipeline for generating realistic weather effects with controllable types and severity in 3D scenes. Our approach is structured into two key components: weather background editing and weather particle construction. For weather background editing, we introduce an all-in-one adapter that integrates multiple weather styles into a single pretrained diffusion model, enabling the generation of diverse weather effects in 2D image backgrounds. During inference, we design a Temporal-View (TV-) attention mechanism that follows a specific order to aggregate temporal and spatial information, ensuring consistent editing across multi-frame and multi-view images. To construct the weather particles, we first reconstruct a 3D scene using the edited images and then introduce a dynamic 4D Gaussian field to generate snowflakes, raindrops and fog in the scene. The attributes and dynamics of these particles are precisely controlled through physical-based modelling and simulation, ensuring realistic weather representation and flexible severity adjustments. Finally, we integrate the 4D Gaussian field with the 3D scene to render consistent and highly realistic weather effects. Experiments on multiple driving datasets demonstrate that WeatherEdit can generate diverse weather effects with controllable condition severity, highlighting its potential for autonomous driving simulation in adverse weather. See project page: https://jumponthemoon.github.io/w-edit

This paper presents a new open-source high-fidelity dataset for Machine Learning (ML) containing 355 geometric variants of the Windsor body, to help the development and testing of ML surrogate models for external automotive aerodynamics. Each Computational Fluid Dynamics (CFD) simulation was run with a GPU-native high-fidelity Wall-Modeled Large-Eddy Simulations (WMLES) using a Cartesian immersed-boundary method using more than 280M cells to ensure the greatest possible accuracy. The dataset contains geometry variants that exhibits a wide range of flow characteristics that are representative of those observed on road-cars. The dataset itself contains the 3D time-averaged volume & boundary data as well as the geometry and force & moment coefficients. This paper discusses the validation of the underlying CFD methods as well as contents and structure of the dataset. To the authors knowledge, this represents the first, large-scale high-fidelity CFD dataset for the Windsor body with a permissive open-source license (CC-BY-SA).

Simulating physics using Graph Neural Networks (GNNs) is predominantly driven by message-passing architectures, which face challenges in scaling and efficiency, particularly in handling large, complex meshes. These architectures have inspired numerous enhancements, including multigrid approaches and K-hop aggregation (using neighbours of distance K), yet they often introduce significant complexity and suffer from limited in-depth investigations. In response to these challenges, we propose a novel Graph Transformer architecture that leverages the adjacency matrix as an attention mask. The proposed approach incorporates innovative augmentations, including Dilated Sliding Windows and Global Attention, to extend receptive fields without sacrificing computational efficiency. Through extensive experimentation, we evaluate model size, adjacency matrix augmentations, positional encoding and K-hop configurations using challenging 3D computational fluid dynamics (CFD) datasets. We also train over 60 models to find a scaling law between training FLOPs and parameters. The introduced models demonstrate remarkable scalability, performing on meshes with up to 300k nodes and 3 million edges. Notably, the smallest model achieves parity with MeshGraphNet while being 7times faster and 6times smaller. The largest model surpasses the previous state-of-the-art by 38.8\% on average and outperforms MeshGraphNet by 52\% on the all-rollout RMSE, while having a similar training speed. Code and datasets are available at https://github.com/DonsetPG/graph-physics.

We present Yan, a foundational framework for interactive video generation, covering the entire pipeline from simulation and generation to editing. Specifically, Yan comprises three core modules. AAA-level Simulation: We design a highly-compressed, low-latency 3D-VAE coupled with a KV-cache-based shift-window denoising inference process, achieving real-time 1080P/60FPS interactive simulation. Multi-Modal Generation: We introduce a hierarchical autoregressive caption method that injects game-specific knowledge into open-domain multi-modal video diffusion models (VDMs), then transforming the VDM into a frame-wise, action-controllable, real-time infinite interactive video generator. Notably, when the textual and visual prompts are sourced from different domains, the model demonstrates strong generalization, allowing it to blend and compose the style and mechanics across domains flexibly according to user prompts. Multi-Granularity Editing: We propose a hybrid model that explicitly disentangles interactive mechanics simulation from visual rendering, enabling multi-granularity video content editing during interaction through text. Collectively, Yan offers an integration of these modules, pushing interactive video generation beyond isolated capabilities toward a comprehensive AI-driven interactive creation paradigm, paving the way for the next generation of creative tools, media, and entertainment. The project page is: https://greatx3.github.io/Yan/.

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting, where generating stable and accurate rollout forecasts remains challenging, Our method, DYffusion, leverages the temporal dynamics in the data, directly coupling it with the diffusion steps in the model. We train a stochastic, time-conditioned interpolator and a forecaster network that mimic the forward and reverse processes of standard diffusion models, respectively. DYffusion naturally facilitates multi-step and long-range forecasting, allowing for highly flexible, continuous-time sampling trajectories and the ability to trade-off performance with accelerated sampling at inference time. In addition, the dynamics-informed diffusion process in DYffusion imposes a strong inductive bias and significantly improves computational efficiency compared to traditional Gaussian noise-based diffusion models. Our approach performs competitively on probabilistic forecasting of complex dynamics in sea surface temperatures, Navier-Stokes flows, and spring mesh systems.

Physical simulation relies on spatially-varying mechanical properties, often laboriously hand-crafted. VoMP is a feed-forward method trained to predict Young's modulus (E), Poisson's ratio (nu), and density (rho) throughout the volume of 3D objects, in any representation that can be rendered and voxelized. VoMP aggregates per-voxel multi-view features and passes them to our trained Geometry Transformer to predict per-voxel material latent codes. These latents reside on a manifold of physically plausible materials, which we learn from a real-world dataset, guaranteeing the validity of decoded per-voxel materials. To obtain object-level training data, we propose an annotation pipeline combining knowledge from segmented 3D datasets, material databases, and a vision-language model, along with a new benchmark. Experiments show that VoMP estimates accurate volumetric properties, far outperforming prior art in accuracy and speed.

Reconstructing dynamic 3D scenes from 2D images and generating diverse views over time is challenging due to scene complexity and temporal dynamics. Despite advancements in neural implicit models, limitations persist: (i) Inadequate Scene Structure: Existing methods struggle to reveal the spatial and temporal structure of dynamic scenes from directly learning the complex 6D plenoptic function. (ii) Scaling Deformation Modeling: Explicitly modeling scene element deformation becomes impractical for complex dynamics. To address these issues, we consider the spacetime as an entirety and propose to approximate the underlying spatio-temporal 4D volume of a dynamic scene by optimizing a collection of 4D primitives, with explicit geometry and appearance modeling. Learning to optimize the 4D primitives enables us to synthesize novel views at any desired time with our tailored rendering routine. Our model is conceptually simple, consisting of a 4D Gaussian parameterized by anisotropic ellipses that can rotate arbitrarily in space and time, as well as view-dependent and time-evolved appearance represented by the coefficient of 4D spherindrical harmonics. This approach offers simplicity, flexibility for variable-length video and end-to-end training, and efficient real-time rendering, making it suitable for capturing complex dynamic scene motions. Experiments across various benchmarks, including monocular and multi-view scenarios, demonstrate our 4DGS model's superior visual quality and efficiency.

In this paper, we study the existence and uniqueness of solutions to the Euler equations with initial conditions that exhibit analytic regularity near the boundary and Sobolev regularity away from it. A key contribution of this work is the introduction of the diamond-analyticity framework, which captures the spatial decay of the analyticity radius in a structured manner, improving upon uniform analyticity approaches. We employ the Leray projection and a nonstandard mollification technique to demonstrate that the quotient between the imaginary and real parts of the analyticity radius remains unrestricted, thus extending the analyticity persistence results beyond traditional constraints. Our methodology combines analytic-Sobolev estimates with an iterative scheme which is nonstandard in the Cauchy-Kowalevskaya framework, ensuring rigorous control over the evolution of the solution. These results contribute to a deeper understanding of the interplay between analyticity and boundary effects in fluid equations. They might have implications for the study of the inviscid limit of the Navier-Stokes equations and the role of complex singularities in fluid dynamics.

Recent advances in text-to-image diffusion models have demonstrated impressive capabilities in image quality. However, complex scene generation remains relatively unexplored, and even the definition of `complex scene' itself remains unclear. In this paper, we address this gap by providing a precise definition of complex scenes and introducing a set of Complex Decomposition Criteria (CDC) based on this definition. Inspired by the artists painting process, we propose a training-free diffusion framework called Complex Diffusion (CxD), which divides the process into three stages: composition, painting, and retouching. Our method leverages the powerful chain-of-thought capabilities of large language models (LLMs) to decompose complex prompts based on CDC and to manage composition and layout. We then develop an attention modulation method that guides simple prompts to specific regions to complete the complex scene painting. Finally, we inject the detailed output of the LLM into a retouching model to enhance the image details, thus implementing the retouching stage. Extensive experiments demonstrate that our method outperforms previous SOTA approaches, significantly improving the generation of high-quality, semantically consistent, and visually diverse images for complex scenes, even with intricate prompts.

The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying attractor. Chaotic systems thus pose a unique challenge to modern statistical learning techniques, while retaining quantifiable mathematical properties that make them controllable and interpretable as benchmarks. Here, we present a growing database currently comprising 131 known chaotic dynamical systems spanning fields such as astrophysics, climatology, and biochemistry. Each system is paired with precomputed multivariate and univariate time series. Our dataset has comparable scale to existing static time series databases; however, our systems can be re-integrated to produce additional datasets of arbitrary length and granularity. Our dataset is annotated with known mathematical properties of each system, and we perform feature analysis to broadly categorize the diverse dynamics present across the collection. Chaotic systems inherently challenge forecasting models, and across extensive benchmarks we correlate forecasting performance with the degree of chaos present. We also exploit the unique generative properties of our dataset in several proof-of-concept experiments: surrogate transfer learning to improve time series classification, importance sampling to accelerate model training, and benchmarking symbolic regression algorithms.

Chaotic systems are intrinsically sensitive to small errors, challenging efforts to construct predictive data-driven models of real-world dynamical systems such as fluid flows or neuronal activity. Prior efforts comprise either specialized models trained separately on individual time series, or foundation models trained on vast time series databases with little underlying dynamical structure. Motivated by dynamical systems theory, we present Panda, Patched Attention for Nonlinear DynAmics. We train Panda on a novel synthetic, extensible dataset of 2 times 10^4 chaotic dynamical systems that we discover using an evolutionary algorithm. Trained purely on simulated data, Panda exhibits emergent properties: zero-shot forecasting of unseen real world chaotic systems, and nonlinear resonance patterns in cross-channel attention heads. Despite having been trained only on low-dimensional ordinary differential equations, Panda spontaneously develops the ability to predict partial differential equations without retraining. We demonstrate a neural scaling law for differential equations, underscoring the potential of pretrained models for probing abstract mathematical domains like nonlinear dynamics.

Editing real images using a pre-trained text-to-image (T2I) diffusion/flow model often involves inverting the image into its corresponding noise map. However, inversion by itself is typically insufficient for obtaining satisfactory results, and therefore many methods additionally intervene in the sampling process. Such methods achieve improved results but are not seamlessly transferable between model architectures. Here, we introduce FlowEdit, a text-based editing method for pre-trained T2I flow models, which is inversion-free, optimization-free and model agnostic. Our method constructs an ODE that directly maps between the source and target distributions (corresponding to the source and target text prompts) and achieves a lower transport cost than the inversion approach. This leads to state-of-the-art results, as we illustrate with Stable Diffusion 3 and FLUX. Code and examples are available on the project's webpage.

In this work, we introduce Modulated Flows (ModFlows), a novel approach for color transfer between images based on rectified flows. The primary goal of the color transfer is to adjust the colors of a target image to match the color distribution of a reference image. Our technique is based on optimal transport and executes color transfer as an invertible transformation within the RGB color space. The ModFlows utilizes the bijective property of flows, enabling us to introduce a common intermediate color distribution and build a dataset of rectified flows. We train an encoder on this dataset to predict the weights of a rectified model for new images. After training on a set of optimal transport plans, our approach can generate plans for new pairs of distributions without additional fine-tuning. We additionally show that the trained encoder provides an image embedding, associated only with its color style. The presented method is capable of processing 4K images and achieves the state-of-the-art performance in terms of content and style similarity. Our source code is available at https://github.com/maria-larchenko/modflows

In time series editing, we aim to modify some properties of a given time series without altering others. For example, when analyzing a hospital patient's blood pressure, we may add a sudden early drop and observe how it impacts their future while preserving other conditions. Existing diffusion-based editors rely on rigid, predefined attribute vectors as conditions and produce all-or-nothing edits through sampling. This attribute- and sampling-based approach limits flexibility in condition format and lacks customizable control over editing strength. To overcome these limitations, we introduce Instruction-based Time Series Editing, where users specify intended edits using natural language. This allows users to express a wider range of edits in a more accessible format. We then introduce InstructTime, the first instruction-based time series editor. InstructTime takes in time series and instructions, embeds them into a shared multi-modal representation space, then decodes their embeddings to generate edited time series. By learning a structured multi-modal representation space, we can easily interpolate between embeddings to achieve varying degrees of edit. To handle local and global edits together, we propose multi-resolution encoders. In our experiments, we use synthetic and real datasets and find that InstructTime is a state-of-the-art time series editor: InstructTime achieves high-quality edits with controllable strength, can generalize to unseen instructions, and can be easily adapted to unseen conditions through few-shot learning.

Though Rectified Flows (ReFlows) with distillation offers a promising way for fast sampling, its fast inversion transforms images back to structured noise for recovery and following editing remains unsolved. This paper introduces FireFlow, a simple yet effective zero-shot approach that inherits the startling capacity of ReFlow-based models (such as FLUX) in generation while extending its capabilities to accurate inversion and editing in 8 steps. We first demonstrate that a carefully designed numerical solver is pivotal for ReFlow inversion, enabling accurate inversion and reconstruction with the precision of a second-order solver while maintaining the practical efficiency of a first-order Euler method. This solver achieves a 3times runtime speedup compared to state-of-the-art ReFlow inversion and editing techniques, while delivering smaller reconstruction errors and superior editing results in a training-free mode. The code is available at https://github.com/HolmesShuan/FireFlow{this URL}.

Significant progress has been made for speech-driven 3D face animation, but most works focus on learning the motion of mesh/geometry, ignoring the impact of dynamic texture. In this work, we reveal that dynamic texture plays a key role in rendering high-fidelity talking avatars, and introduce a high-resolution 4D dataset TexTalk4D, consisting of 100 minutes of audio-synced scan-level meshes with detailed 8K dynamic textures from 100 subjects. Based on the dataset, we explore the inherent correlation between motion and texture, and propose a diffusion-based framework TexTalker to simultaneously generate facial motions and dynamic textures from speech. Furthermore, we propose a novel pivot-based style injection strategy to capture the complicity of different texture and motion styles, which allows disentangled control. TexTalker, as the first method to generate audio-synced facial motion with dynamic texture, not only outperforms the prior arts in synthesising facial motions, but also produces realistic textures that are consistent with the underlying facial movements. Project page: https://xuanchenli.github.io/TexTalk/.

Normalizing flows (NF) are a class of powerful generative models that have gained popularity in recent years due to their ability to model complex distributions with high flexibility and expressiveness. In this work, we introduce a new type of normalizing flow that is tailored for modeling positions and orientations of multiple objects in three-dimensional space, such as molecules in a crystal. Our approach is based on two key ideas: first, we define smooth and expressive flows on the group of unit quaternions, which allows us to capture the continuous rotational motion of rigid bodies; second, we use the double cover property of unit quaternions to define a proper density on the rotation group. This ensures that our model can be trained using standard likelihood-based methods or variational inference with respect to a thermodynamic target density. We evaluate the method by training Boltzmann generators for two molecular examples, namely the multi-modal density of a tetrahedral system in an external field and the ice XI phase in the TIP4P water model. Our flows can be combined with flows operating on the internal degrees of freedom of molecules and constitute an important step towards the modeling of distributions of many interacting molecules.

Solving partial differential equations (PDEs) with machine learning has recently attracted great attention, as PDEs are fundamental tools for modeling real-world systems that range from fundamental physical science to advanced engineering disciplines. Most real-world physical systems across various disciplines are actually involved in multiple coupled physical fields rather than a single field. However, previous machine learning studies mainly focused on solving single-field problems, but overlooked the importance and characteristics of multiphysics problems in real world. Multiphysics PDEs typically entail multiple strongly coupled variables, thereby introducing additional complexity and challenges, such as inter-field coupling. Both benchmarking and solving multiphysics problems with machine learning remain largely unexamined. To identify and address the emerging challenges in multiphysics problems, we mainly made three contributions in this work. First, we collect the first general multiphysics dataset, the Multiphysics Bench, that focuses on multiphysics PDE solving with machine learning. Multiphysics Bench is also the most comprehensive PDE dataset to date, featuring the broadest range of coupling types, the greatest diversity of PDE formulations, and the largest dataset scale. Second, we conduct the first systematic investigation on multiple representative learning-based PDE solvers, such as PINNs, FNO, DeepONet, and DiffusionPDE solvers, on multiphysics problems. Unfortunately, naively applying these existing solvers usually show very poor performance for solving multiphysics. Third, through extensive experiments and discussions, we report multiple insights and a bag of useful tricks for solving multiphysics with machine learning, motivating future directions in the study and simulation of complex, coupled physical systems.

It is demonstrated that self-diffusion and shear viscosity data for the TIP4P/Ice water model reported recently [L. Baran, W. Rzysko and L. MacDowell, J. Chem. Phys. {\bf 158}, 064503 (2023)] obey the microscopic version of the Stokes-Einstein relation without the hydrodynamic diameter.

Generative models have demonstrated remarkable success in domains such as text, image, and video synthesis. In this work, we explore the application of generative models to fluid dynamics, specifically for turbulence simulation, where classical numerical solvers are computationally expensive. We propose a novel stochastic generative model based on stochastic interpolants, which enables probabilistic forecasting while incorporating physical constraints such as energy stability and divergence-freeness. Unlike conventional stochastic generative models, which are often agnostic to underlying physical laws, our approach embeds energy consistency by making the parameters of the stochastic interpolant learnable coefficients. We evaluate our method on a benchmark turbulence problem - Kolmogorov flow - demonstrating superior accuracy and stability over state-of-the-art alternatives such as autoregressive conditional diffusion models (ACDMs) and PDE-Refiner. Furthermore, we achieve stable results for significantly longer roll-outs than standard stochastic interpolants. Our results highlight the potential of physics-aware generative models in accelerating and enhancing turbulence simulations while preserving fundamental conservation properties.

Recent advances in video generation have shown remarkable potential for constructing world simulators. However, current models still struggle to produce physically consistent results, particularly when handling large-scale or complex dynamics. This limitation arises primarily because existing approaches respond isotropically to physical prompts and neglect the fine-grained alignment between generated content and localized physical cues. To address these challenges, we propose ProPhy, a Progressive Physical Alignment Framework that enables explicit physics-aware conditioning and anisotropic generation. ProPhy employs a two-stage Mixture-of-Physics-Experts (MoPE) mechanism for discriminative physical prior extraction, where Semantic Experts infer semantic-level physical principles from textual descriptions, and Refinement Experts capture token-level physical dynamics. This mechanism allows the model to learn fine-grained, physics-aware video representations that better reflect underlying physical laws. Furthermore, we introduce a physical alignment strategy that transfers the physical reasoning capabilities of vision-language models (VLMs) into the Refinement Experts, facilitating a more accurate representation of dynamic physical phenomena. Extensive experiments on physics-aware video generation benchmarks demonstrate that ProPhy produces more realistic, dynamic, and physically coherent results than existing state-of-the-art methods.

Text animation serves as an expressive medium, transforming static communication into dynamic experiences by infusing words with motion to evoke emotions, emphasize meanings, and construct compelling narratives. Crafting animations that are semantically aware poses significant challenges, demanding expertise in graphic design and animation. We present an automated text animation scheme, termed "Dynamic Typography", which combines two challenging tasks. It deforms letters to convey semantic meaning and infuses them with vibrant movements based on user prompts. Our technique harnesses vector graphics representations and an end-to-end optimization-based framework. This framework employs neural displacement fields to convert letters into base shapes and applies per-frame motion, encouraging coherence with the intended textual concept. Shape preservation techniques and perceptual loss regularization are employed to maintain legibility and structural integrity throughout the animation process. We demonstrate the generalizability of our approach across various text-to-video models and highlight the superiority of our end-to-end methodology over baseline methods, which might comprise separate tasks. Through quantitative and qualitative evaluations, we demonstrate the effectiveness of our framework in generating coherent text animations that faithfully interpret user prompts while maintaining readability. Our code is available at: https://animate-your-word.github.io/demo/.

The development of Machine Learning (ML) methods for Computational Fluid Dynamics (CFD) is currently limited by the lack of openly available training data. This paper presents a new open-source dataset comprising of high fidelity, scale-resolving CFD simulations of 500 geometric variations of the Ahmed Car Body - a simplified car-like shape that exhibits many of the flow topologies that are present on bluff bodies such as road vehicles. The dataset contains simulation results that exhibit a broad set of fundamental flow physics such as geometry and pressure-induced flow separation as well as 3D vortical structures. Each variation of the Ahmed car body were run using a high-fidelity, time-accurate, hybrid Reynolds-Averaged Navier-Stokes (RANS) - Large-Eddy Simulation (LES) turbulence modelling approach using the open-source CFD code OpenFOAM. The dataset contains boundary, volume, geometry, and time-averaged forces/moments in widely used open-source formats. In addition, the OpenFOAM case setup is provided so that others can reproduce or extend the dataset. This represents to the authors knowledge, the first open-source large-scale dataset using high-fidelity CFD methods for the widely used Ahmed car body that is available to freely download with a permissive license (CC-BY-SA).

The dynamics of materials failure is one of the most critical phenomena in a range of scientific and engineering fields, from healthcare to structural materials to transportation. In this paper we propose a specially designed deep neural network, DyFraNet, which can predict dynamic fracture behaviors by identifying a complete history of fracture propagation - from cracking onset, as a crack grows through the material, modeled as a series of frames evolving over time and dependent on each other. Furthermore, this model can not only forecast future fracture processes but also backcast to elucidate the past fracture history. In this scenario, once provided with the outcome of a fracture event, the model will elucidate past events that led to this state and will predict the future evolution of the failure process. By comparing the predicted results with atomistic-level simulations and theory, we show that DyFraNet can capture dynamic fracture mechanics by accurately predicting how cracks develop over time, including measures such as the crack speed, as well as when cracks become unstable. We use GradCAM to interpret how DyFraNet perceives the relationship between geometric conditions and fracture dynamics and we find DyFraNet pays special attention to the areas around crack tips, which have a critical influence in the early stage of fracture propagation. In later stages, the model pays increased attention to the existing or newly formed damage distribution in the material. The proposed approach offers significant potential to accelerate the exploration of the dynamics in material design against fracture failures and can be beneficially adapted for all kinds of dynamical engineering problems.

Dynamic garment reconstruction from monocular video is an important yet challenging task due to the complex dynamics and unconstrained nature of the garments. Recent advancements in neural rendering have enabled high-quality geometric reconstruction with image/video supervision. However, implicit representation methods that use volume rendering often provide smooth geometry and fail to model high-frequency details. While template reconstruction methods model explicit geometry, they use vertex displacement for deformation, which results in artifacts. Addressing these limitations, we propose NGD, a Neural Gradient-based Deformation method to reconstruct dynamically evolving textured garments from monocular videos. Additionally, we propose a novel adaptive remeshing strategy for modelling dynamically evolving surfaces like wrinkles and pleats of the skirt, leading to high-quality reconstruction. Finally, we learn dynamic texture maps to capture per-frame lighting and shadow effects. We provide extensive qualitative and quantitative evaluations to demonstrate significant improvements over existing SOTA methods and provide high-quality garment reconstructions.

We present PhysGen, a novel image-to-video generation method that converts a single image and an input condition (e.g., force and torque applied to an object in the image) to produce a realistic, physically plausible, and temporally consistent video. Our key insight is to integrate model-based physical simulation with a data-driven video generation process, enabling plausible image-space dynamics. At the heart of our system are three core components: (i) an image understanding module that effectively captures the geometry, materials, and physical parameters of the image; (ii) an image-space dynamics simulation model that utilizes rigid-body physics and inferred parameters to simulate realistic behaviors; and (iii) an image-based rendering and refinement module that leverages generative video diffusion to produce realistic video footage featuring the simulated motion. The resulting videos are realistic in both physics and appearance and are even precisely controllable, showcasing superior results over existing data-driven image-to-video generation works through quantitative comparison and comprehensive user study. PhysGen's resulting videos can be used for various downstream applications, such as turning an image into a realistic animation or allowing users to interact with the image and create various dynamics. Project page: https://stevenlsw.github.io/physgen/

Recent advances in 4D content generation have attracted increasing attention, yet creating high-quality animated 3D models remains challenging due to the complexity of modeling spatio-temporal distributions and the scarcity of 4D training data. In this paper, we present AnimateAnyMesh, the first feed-forward framework that enables efficient text-driven animation of arbitrary 3D meshes. Our approach leverages a novel DyMeshVAE architecture that effectively compresses and reconstructs dynamic mesh sequences by disentangling spatial and temporal features while preserving local topological structures. To enable high-quality text-conditional generation, we employ a Rectified Flow-based training strategy in the compressed latent space. Additionally, we contribute the DyMesh Dataset, containing over 4M diverse dynamic mesh sequences with text annotations. Experimental results demonstrate that our method generates semantically accurate and temporally coherent mesh animations in a few seconds, significantly outperforming existing approaches in both quality and efficiency. Our work marks a substantial step forward in making 4D content creation more accessible and practical. All the data, code, and models will be open-released.