Physics-Based Animation

Jaehyun Lee, Eftychios Sifakis

Solvers for grid-based discretizations of Partial Differential Equations (PDEs) are ubiquitous in computer graphics. However, efficient implementation of such solvers is contingent on specific design choices for grid data structures (especially for sparse domains), hand-tuned kernels for specific platforms (CPU vs GPU), and typically relies on the lexicon of sparse linear algebra to express its algorithmic building blocks. Meanwhile, modern hardware and software stacks are increasingly optimized around machine learning (ML) workloads, where tensor operators such as convolution, masking, and pooling form the dominant computational vocabulary. We introduce an ML-operator abstraction for discrete PDE solvers on sparse and irregular domains. Our formulation separates solver computation into uniform stencil actions, pointwise coefficient operations, masking, reductions, and localized boundary corrections, yielding a compact operator pipeline that supports practical boundary conditions and matrix-free execution. Unlike neural PDE methods, our approach does not learn a solver. It uses ML operators to express and execute established numerical discretizations. We demonstrate that this abstraction accommodates multigrid, multigrid-preconditioned Krylov solvers, and adjoint differentiation on practical 3D problems, including sparse, irregular, and inverse settings. The same operator-level view also exposes concrete backend optimization targets. Through a sparse domain optimization case study, we show that targeted improvements to a key operator can substantially improve performance over an existing baseline.

Machine Learning Operator Lexicon for Partial Differential Equation Solvers on Irregular and Sparse Domains

Hossam Saeed, Michael Lambiri, Teseo Schneider, Derek Nowrouzezahrai, Paul G. Kry

While cages provide a powerful reduction model to simulate elastic deformations, interactive real-time cutting of cages has been a longstanding challenge. Traditional solvers require costly volumetric re-meshing and global matrix updates after each modification. For mesh-free harmonic weight computation using Walk on Spheres (WoS), we make a key observation: only a small fraction of walks (5-10%) is invalidated by a local cut in most practical cases. We propose a reuse pipeline that efficiently updates only the weights affected by topological modifications. Our approach leverages WoS as an output-sensitive, mesh-free Monte Carlo method for solving Laplacian equations, enabling localized harmonic-weight updates. By identifying and reusing unaffected walks, we minimize re-walking work and preserve statistical accuracy. Our method achieves 10x-40x speedups while remaining statistically identical to full WoS recomputation. This enables real-time interactive cutting on complex 2D and 3D cages, and readily generalizes to other local cage editing operations.

Fast Cutting of Cage Based Deformation with Walk on Spheres

Helge Wrede, Anton R. Wagner, Wojtek Pałubicki, Dominik L. Michels, Sören Pirk

We present a physically based simulation framework for wildland–urban interface (WUI) fires that couples material-aware urban scenes with interactive combustion simulation. Motivated by the dominant WUI exposure pathways of direct flame contact, thermal radiation, and ember transport, our framework combines heterogeneous solid combustion, radiative heat transfer, ember transport, and explicit flame-front propagation. Urban scenes are generated from OpenStreetMap footprints using a procedural pipeline that represents buildings as combustible 3D structures composed of semantic atomic modules with material and fuel annotations. Building on a chemistry-based hybrid Eulerian–Lagrangian fire solver, we model material-dependent heating, conduction, pyrolysis, oxidation, fuel depletion, and ember generation. A hierarchical fuel graph couples semantic scene structure to the solver’s solid fuel grid, enabling subcomponent-level mesh degradation. We demonstrate structure-to-structure ignition, radiative preheating, material-dependent burning, ember-driven spot fires, and validate the method through ablations and comparisons to real-world combustion experiments.

Flamescapes: Simulating the Wildlandfire Urban Interface

Xiaoxuan Ma, Jiashun Wang, Nicolas Ugrinovic, Yehonathan Litman, Kris Kitani

Reconstructing physically stable 3D scenes from a single RGB image enables casual images to be converted into simulation-ready digital assets for applications such as immersive interaction and content creation. However, existing single-image reconstruction methods fall short in capturing the physical structure of a scene. As a result, they often produce geometrically plausible but physically inconsistent results, including object floating and penetration, which lead to unstable behavior in physics simulations. Image-conditioned scene generation methods improve physical plausibility but often rely on strong scene priors, yielding plausible yet inaccurate object arrangements that fail to match the input image. We propose REST3D, a single-image reconstruction framework that can REconstruct physically STable 3D scenes by integrating physical scene understanding with physics-constrained refinement. We first introduce an agentic physical scene understanding technique that constructs a scene-tree representation capturing object physical states and inter-object relationships from a gravity-support perspective, providing a structural prior for reconstruction. Leveraging this structure, we initialize the scene using image-to-3D models, followed by scene-tree-guided alignment and physics-constrained optimization to resolve physical violations while preserving visual consistency with the input image. Experiments show that our method significantly reduces physical errors and improves simulation stability on both synthetic and real-world datasets while maintaining strong reconstruction quality. We further demonstrate the reconstructed scenes in VR-based human-object interaction, showing their potential for immersive applications.

Reconstructing Physically Stable 3D Scenes from a Single Image

Projective dynamics (PD) is a popular framework for efficient physical simulation. However, its factorization-based global solve maps poorly to GPU parallelization, while iterative alternatives often fail to converge effectively for stiff or high-resolution models. This paper reformulates the PD global solve by observing that its primary computational bottleneck lies in vector dot products, which can be reinterpreted as discrete integrations over the deformable body. The resulting integrand exhibits a Yukawa-like kernel structure that peaks sharply at each mesh node and decays exponentially with distance. Exploiting this prior, we partition the domain into near, middle, and far fields around each node, and design a quadrature rule for each that matches the local behavior of the integrand: an anisotropic Gaussian fit with a closed-form integral in the near field, a low-order Gauss-Legendre rule for the smoothed residual in the middle field, and a weighted k-means++ clustering with centroid-based quadrature in the irregular far field. This integration perspective reveals an effective sparsity pattern that enables both excellent parallelism and rapid convergence. Our algorithm also serves as a strong preconditioner for collision-involved PD systems and delivers significant speedup over existing PD solvers across a range of deformable scenarios.

Multi-level Quadrature for Projective Dynamics

Zike Xu, Xuan Zhang, Xiaopei Liu

The simultaneous pursuit of high fidelity, large computational throughput, and a minimal memory footprint has long constituted the central challenge in fluid simulation research. Yet state-of-the-art methods struggle to reconcile all these objectives, and often entail navigating trade-offs among them. We present Kinetic Predicted-Moment Flux Reconstruction (KPM-FR), a high-order kinetic-based scheme for low-Mach-number weakly compressible flows that advances all three fronts within a single framework. KPM-FR is a flux-form fluid flow solver rooted in the principles of the gas-kinetic scheme (GKS), deriving numerical fluxes from the locally evolved Boltzmann-BGK equation to recover Navier-Stokes (NS) solutions. Departing from the GKS and its variants, it carries out kinetic evolution entirely in moment space within the high-order flux reconstruction (FR) framework through a concise predictor-corrector scheme. This translates to two fused GPU kernels per time step, streamlining computation and confining intermediate data to on-chip memory. This design confers several practical advantages. First, compared to conventional high-fidelity lattice Boltzmann methods (LBM), the moment-based formulation reduces the per-point memory footprint by more than fivefold. Second, at matched resolutions, its high-order spatial formulation exhibits markedly lower numerical dissipation, preserving fine-scale vortical structures with greater fidelity. Combining these advantages with a near-saturated throughput exceeding 8 billion solution-point updates per second on a single consumer GPU, KPM-FR delivers large-scale fluid simulation on commodity hardware. Quantitative benchmarks confirm high-order spatial convergence and spectral-like dissipation characteristics, while validation against reference data for flow past solid bodies verifies its practical accuracy. Ultimately, we demonstrate the versatility of KPM-FR across complex geometries and large-scale turbulent flows, capturing multiscale structures with 1.8 billion solution points on a single desktop workstation.

Kinetic Predicted-Moment Flux Reconstruction for High-Order High-Performance Fluid Simul

Zhihao Cen, Chuhua Xian, Hailin Sun, Yuliang Liufu, Zhen Zhang, Xiangyu Chu, Hongmin Cai, Yunbo Zhang, Guoxin Fang

Observing a deformable object reveals its surface motion, but many applications also need its internal stress, material properties, and interaction forces. RealSimLoop combines differentiable physical simulation with vision feedback to keep a simulated object aligned with its real-world behavior. A neural reduced-order model makes both simulation and gradient computation more efficient. Coupled with differentiable 3D Gaussian Splatting, it allows camera observations to guide material-parameter updates within a sliding time window. This continuous adaptation tracks changing stiffness and compensates for simulation mismatch. We demonstrate the framework through robotic manipulation, multi-material structures, temperature-dependent stiffness tracking, force prediction, and stress visualization.

RealSimLoop: Online Real-to-Sim Adaptation via Differentiable Reduced-Order Simulation with Vision Feedback

Xuan Wang, Zhaofeng Luo, Minchen Li, Taku Komura, Kemeng Huang

Implicit time integration is key to robustly simulating stiff materials and large deformations, but its performance is often dominated by repeatedly solving large linear systems. Adaptive coarsening can reduce this cost by concentrating degrees of freedom (DoF) to where it is most needed, yet conventional explicit remeshing changes connectivity (and often vertex ordering), complicating parallel implementations, harming memory locality, and sometimes being disallowed when it may introduce local geometry intersections. Adaptive subspace approaches avoid topological changes, but basis construction and updates incur irregular data access patterns and typically produce dense system matrices, limiting GPU efficiency and keeping many practical systems CPU-centric. We present algebraic adaptive in-solve coarsening, a GPU-oriented method that dynamically reduces DoF within the Newton solve of implicit time integration without explicit topological modification. Starting from a fine mesh, we express adaptivity as a selective edge-collapse process governed by per-edge tags. Collapsible edges are aggregated in parallel using a warp-level hash mapping scheme that groups fine vertices into coarse super-nodes, while protected edges preserve local detail. This defines an implicit coarse mesh whose linear system is assembled algebraically by mapping and reducing fine-scale gradients and Hessians via efficient GPU reduction kernels. We solve the resulting coarse system with a preconditioned conjugate gradient (PCG) method and then prolongate the solution back to the fine mesh. Our approach integrates seamlessly with IPC’s barrier energy and exploits GPU parallelism end-to-end. Across a range of challenging scenarios, we achieve up to 3x speedup over a state-of-the-art GPU IPC solver while producing visually indistinguishable results.

AGIPC: Adaptive In-Solve Algebraic Coarsening for GPU IPC

Chun Yuan, Zixuan Lu, Haoyang Shi, Dewen Guo, Huamin Wang, Chenfanfu Jiang, Zherong Pan, Kui Wu, Yin Yang

While yarn-level garments offer rich dynamic details and compelling visual realism compared to triangle-based models, their wide adoption is hindered by the immense computational cost due to the presence of a large number of degrees of freedom (DOFs). This paper proposes a novel simulation framework designed to enhance the performance and stability for numerical simulation of nonlinear, non-convex, and high-resolution knitwear. Our method generalizes the Douglas-Rachford Splitting (DRS) scheme to resolve the non-convex coupling between stretching, shearing, bending, twisting, and contacting at each yarn thread. A key contribution is a nested decomposition strategy that decouples the non-convex variational energy into independent and convex sub-problems. Such convexification improves solver robustness and removes the necessity for frequent line searches. We provide a theoretically grounded strategy for metric selection for each sub-problem, derived from an analysis of the convergence guarantee of DRS. Consequently, our method achieves close-to-optimal convergence along the nonlinear iterations rather than relying on ad-hoc parameter tuning. The paper also clarifies a formal connection between our generalized DRS and the ADMM (Alternating Direction Method of Multipliers) framework, extending the applicability of our analysis to a broader set of constrained dynamics problems. Experimental results demonstrate that our method robustly handles complex knitwear simulation scenes with superior efficiency, stability, and physical fidelity compared to existing methods. With a matrix-free GPU parallelization, our method allows an interactive simulation rate of knitwear of multi-million DOFs.

Interactive Yarn-level Knitwear with Nested Douglas-Rachford Splitting

Jiafeng Liu, Wenhui Zhou, Xinming Pei, Yifan Peng, Huamin Wang, Yin Yang, Lei Lan, Weiwei Xu

Affine Body Dynamics (ABD) within the Incremental Potential Contact (IPC) framework provides accurate simulation of extremely stiff solids with near-rigid behavior and strict non-penetration guarantees. However, IPC’s globally coupled barrier constraints make it difficult to scale across multiple GPUs and compute nodes. This work introduces a distributed ABD formulation based on adaptive consensus, allowing each compute node to solve a local subproblem in parallel while a global consensus step maintains consistency across shared boundary bodies. The method preserves IPC-level robustness and global consistency under distributed execution, and experiments demonstrate stable convergence, non-penetration, and efficient scaling on large scenes across multiple nodes.

Distributed Affine Body Dynamics with Adaptive Consensus