Physics-Based Animation

Zhiyang Dou, Chen Peng, Xinyu Lu, Xiaohan Ye, Lixing Fang, Yuan Liu, Wenping Wang, Chuang Gan, Lingjie Liu, Taku Komura

Humans possess the ability to master a wide range of motor skills, enabling them to quickly and flexibly adapt to the surrounding environment. Despite recent progress in replicating such versatile human motor skills, existing research often oversimplifies or inadequately captures the complex interplay between human body movements and highly dynamic environments, such as interactions with fluids. In this paper, we present a world model for Character-Fluid Coupling (CFC) for simulating human-fluid interactions via two-way coupling. We introduce a two-level world model which consists of a Physics-Informed Neural Network (PINN)-based model for fluid dynamics and a character world model capturing body dynamics under various external forces. This two-level world model adeptly predicts the dynamics of fluid and its influence on rigid bodies via force prediction, sidestepping the computational burden of fluid simulation and providing policy gradients for efficient policy training. Once trained, our system can control characters to complete high-level tasks while adaptively responding to environmental changes. We also present that the fluid initiates emergent behaviors of the characters, enhancing motion diversity and interactivity. Extensive experiments underscore the effectiveness of CFC, demonstrating its ability to produce high-quality, realistic human-fluid interaction animations.

CFC: Simulating Character-Fluid Coupling Using a Two-Level World Model

Jiwei Wang, Wenbin Song, Yicheng Fan, Yang Wang, Xiaopei Liu

Unmanned aerial vehicles (UAVs) have demonstrated remarkable efficacy across diverse fields. Nevertheless, developing flight controllers tailored to a specific UAV design, particularly in environments with strong fluid-interactive dynamics, remains challenging. Conventional controller design experiences often fall short in such cases, rendering it infeasible to apply time-tested practices. Consequently, a simulation test bed becomes indispensable for controller design and evaluation prior to its actual implementation on the physical UAV. This platform should allow for meticulous adjustment of controllers and should be able to transfer to real-world systems without significant performance degradation. Existing simulators predominantly hinge on empirical models due to high efficiency, often overlooking the dynamic interplay between the UAV and the surrounding airflow. This makes it difficult to mimic more complex flight maneuvers, such as an abrupt mid-air halt inside narrow channels, in which the UAV may experience strong fluid-structure interactions. On the other hand, simulators considering the complex surrounding airflow are extremely slow and inadequate to support the design and evaluation of flight controllers. In this paper, we present a novel remedy for highly-efficient UAV flight simulations, which entails a hybrid modeling that deftly combines our novel far-field adaptive block-based fluid simulator with parametric empirical models situated near the boundary of the UAV, with the model parameters automatically calibrated. With this newly devised simulator, a broader spectrum of flight scenarios can be explored for controller design and assessment, encompassing those influenced by potent close-proximity effects, or situations where multiple UAVs operate in close quarters. The practical worth of our simulator has been authenticated through comparisons with actual UAV flight data. We further showcase its utility in designing flight controllers for fixed-wing, multi-rotor,
and hybrid UAVs, and even exemplify its application when multiple UAVs are involved, underlining the unique value of our system for flight controllers.

A Highly-Efficient Hybrid Simulation System for Flight Controller Design and Evaluation of Unmanned Aerial Vehicles

Yibo Liu, Zhixin Fang, Sune Darkner, Noam Aigerman, Kenny Erleben, Paul Kry, Teseo Schneider

We propose mesh-free fluid simulations that exploit a kinematic neural basis for velocity fields represented by an MLP. We design a set of losses that ensures that these neural bases approximate fundamental physical properties such as orthogonality, divergence-free, boundary alignment, and smoothness. Our neural bases can then be used to fit an input sketch of a flow, which will inherit the same fundamental properties from the bases. We then can animate such flow in real-time using standard time integrators. Our neural bases can accommodate different domains, moving boundaries, and naturally extend to three dimensions.

Neural Kinematic Bases for Fluids

Mengfei Liu, Yue Chang, Zhecheng Wang, Peter Yichen Chen, Eitan Grinspun

We introduce a neural field construction that captures gradient discontinuities without baking their location into the network weights. By augmenting input coordinates with a smoothly clamped distance function in a lifting framework, we enable encoding of gradient jumps at evolving interfaces. This design supports discretization-agnostic simulation of parametrized shape families with heterogeneous materials and evolving creases, enabling new reduced-order capabilities such as shape morphing, interactive crease editing, and simulation of soft-rigid hybrid structures. We further demonstrate that our method can be combined with previous lifting techniques to jointly capture both gradient and value discontinuities, supporting simultaneous cuts and creases within a unified model.

Precise Gradient Discontinuities in Neural Fields for Subspace Physics

Jia-Ming Lu, Geng-Chen Cao, Chenfeng Li, Shi-Min Hu

This paper proposes a novel simulation approach that combines implicit integration with the Bonded Discrete Element Method (BDEM) to achieve faster, more stable and more accurate fracture simulation. The new method leverages the eiciency of implicit schemes in dynamic simulation and the versatility of BDEM in fracture modelling. Speciically, an optimization-based integrator for BDEM is introduced and combined with a manifold optimization approach to accelerate the solution process of the quaternion-constrained system. Our comparative experiments indicate that our method ofers better scale consistency and more realistic collision efects than FEM and MPM fragmentation approaches. Additionally, our method achieves a computational speedup of 2.1 ~ 9.8 times over explicit BDEM methods.

Implicit Bonded Discrete Element Method with Manifold Optimization

• Adaptive Optical Layers: Efficient Tall Cell Grids for Liquid Simulation
• A Semi-Analytical Energy Model for Particle-Based Fluid Simulation Involving Complex Moving Boundaries
• Dripping Thin Films for Real-time Digital Painting
• Fluid Composer: Fluid Detail Composition and Rendering Using Video Diffusion Models
• Designing inflatable shells using unstructured meshes
• Convex Primitive Decomposition for Collision Detection
• STAGED: Stress-Tensor Assisted Global-local-global solver for interactive Elastic shape Design
• Interpolated Adaptive Linear Reduced Order Modeling for Deformation Dynamics
• Progressively Projected Newton’s Method
• Affinification: A Fine Approximation of Deformations
• HeatMat: Simulation of City Material Impact on Urban Heat Island Effect

• Fast VEM Fluid Simulation
• Spatiotemporal FLIP for Fast Free-Surface and Two-Phase Simulation With Very Large Time Steps
• Buoyancy-driven Phase Separation in the Material Point Method
• Volume-Preserving LBM-MPM Coupling for Air-Water-Sand Mixtures
• A Nonlocal Monolithic Variational Framework for Free Surface Flows
• Stochastic geomorphological transport for terrain erosion simulation
• Mixwell: Sharp 2D Fluid Brushes for Progressive Physics-Based Mixing
• Curvature Space Editing of Highly-Coiled Hair
• M-ABD: Scalable, Efficient, and Robust Multi-Affine-Body Dynamics
• Heterogeneous Subspace Corrections for GPU Deformable Multibody Dynamics
• Distributed Affine Body Dynamics with Adaptive Consensus
• Better Bending: Analysis, Construction and Verification of Discrete Bending Models for Kirchhoff-Love Shells
• Efficient B-Spline Finite Elements for Cloth Simulation
• Interactive Yarn-level Knitwear with Nested Douglas-Rachford Splitting
• SymX: Energy-based Simulation from Symbolic Expressions
• MeshFEM: A Block-accelerated Solver for Nonlinear Finite Elements
• Fast Sparse Matrix Permutation for Mesh-Based Direct Solvers
• JGS2-GQ: Training-free 2nd Jacobi with Gaussian Quadrature
• Divide and Truncate: A Penetration and Inversion Free Framework for Coupled Multi-physics System
• Robust and Efficient Penetration-Free Elastodynamics without Barriers
• High-Order Continuous Geometrical Validity
• Floating-Point Robustness in Parametric Surface Continuous Collision Detection: From Algorithm to Benchmarking
• AGIPC: Adaptive In-Solve Algebraic Coarsening for GPU IPC
• YASPS: A Symbolic Framework for Extensible, High-Performance IPC Simulation
• Progressing Level-of-Detail Animation for Volumetric Elastodynamics
• Mixed Material Point Methods for Stiff Elastoplasticity
• MPM Lite: Linear Kernels and Integration without Particles
• Tube Maps: Fast SPH Boundary Handling with Tubular Coordinates
• Low-Rank Koopman Deformables with Log-Linear Time Integration
• Physics-Inspired Procedural Texturing of Extremely Deformable Surfaces
• Woodstock: Interactive Modeling of Fungal Wood Decay
• Untangling Surfaces via Shape and Mesh Repulsion
• Surface chamfering for robust tetrahedral meshing
• Boundary-aware Neural Model Reduction for PDEs
• Locality-Aware Automatic Differentiation on the GPU for Mesh-Based Computations

Jia-Ming Lu, Tailing Yuan, Zhe-Han Mo, Shi-Min Hu

This research presents an efficient multigrid solver for deformable body simulations on unstructured tetrahedral meshes. The method combines the Full Approximation Scheme with Galerkin formulation and introduces a matrix-free vertex block Jacobi smoother that eliminates the computational burden of dense coarse matrices. The approach supports both piecewise constant and linear Galerkin formulations and achieves up to 6.9x speedup over traditional methods. Comprehensive GPU optimization techniques address parallel architecture challenges through Morton sorting, grid reduction, and spatial hashing. Extensive experiments demonstrate robust convergence across varying mesh resolutions, material stiffness values, extreme deformations, and complex collision scenarios, enabling practical simulation of million-vertex meshes at interactive frame rates.

Fast Galerkin Multigrid Method for Unstructured Meshes

Jia-Ming Lu, Shi-Min Hu

Simulating stiff materials has long posed formidable challenges for traditional physics-based solvers. Explicit time integration schemes demand prohibitively small time steps, while implicit methods necessitate an excessive number of iterations to converge, often yielding visually objectionable transient configurations in the early iterations, severely limiting their real-time applicability. Position-based dynamics techniques can efficiently simulate stiff constraints but are inherently restricted to constraint-based formulations, curtailing their versatility. We present “Reliable Iterative Dynamics” (RID), a novel iterative solver that introduces a dual descent framework with theoretical guarantees for visual reliability at each iteration, while maintaining fast and stable convergence even for extremely stiff systems. Our core innovation is an iterative method that circumvents the need for numerous iterations or small time steps to handle stiff materials robustly. Experimental evaluations demonstrate our method’s ability to handle a wide range of materials, from soft to infinitely rigid, while producing visually reliable results even with large time steps and minimal iterations. The versatile formulation allows seamless integration with diverse simulation paradigms like the finite element method, material point method, smoothed particle hydrodynamics, and incremental potential contact for applications ranging from elastic body simulations to fluids and collision handling.

Reliable Iterative Dynamics: A Versatile Method for Fast and Robust Simulation

Elie Diaz, Jerry Hsu, Eisen Montalvo-Ruiz, Chris Giles, Cem Yuksel

The efficient simulation of incompressible fluids remains a difficult and open problem. Prior works often make various tradeoffs between incompressibility, stability, and cost. Yet, it is rare to obtain all three. In this paper, we introduce a novel incompressible Smoothed Particle Hydrodynamics (SPH) scheme which uses a second-order implicit descent scheme to optimize a variational energy specially formulated to approach incompressibility. We demonstrate that our method is superior in both incompressibility and stability with a minimal cost to computational budget. Furthermore, we demonstrate that our method is unconditionally stable even under extreme time steps, making it suitable for interactive applications.

Implicit Position-Based Fluids