Physics-Based Animation

Yi-Lu Chen, Mickaël Ly, Chris Wojtan

The realistic simulation of sand, soil, powders, rubble piles, and large collections of rigid bodies is a common and important problem in the fields of computer graphics, computational physics, and engineering. Direct simulation of these individual bodies quickly becomes expensive, so we often approximate the entire group as a continuum material that can be more easily computed using tools for solving partial differential equations, like the material point method (MPM). In this paper, we present a method for automatically extracting continuum material properties from a collection of rigid bodies. We use numerical homogenization with periodic boundary conditions to simulate an effectively infinite number of rigid bodies in contact. We then record the effective stress-strain relationships from these simulations and convert them into elastic properties and yield criteria for the continuum simulations. Our experiments validate existing theoretical models like the Mohr-Coulomb yield surface by extracting material behaviors from a collection of spheres in contact. We further generalize these existing models to more exotic materials derived from diverse and non-convex shapes. We observe complicated jamming behaviors from non-convex grains, and we introduce a new material model for materials with extremely high levels of internal friction and cohesion. We simulate these new continuum models using MPM with an improved return mapping technique. The end result is a complete system for turning an input rigid body simulation into an efficient continuum simulation with the same effective mechanical properties.

Numerical Homogenization of Sand from Grain-level Simulations

Otman Benchekroun, Eitan Grinspun, Maurizio Chiaramonte, Philip Allen Etter

Designing subspaces for Reduced Order Modeling (ROM) is crucial for accelerating finite element simulations in graphics and engineering. Unfortunately, it’s not always clear which subspace is optimal for arbitrary dynamic simulation. We propose to construct simulation subspaces from force distributions, allowing us to tailor such subspaces to common scene interactions involving constraint penalties, handles-based control, contact and musculoskeletal actuation. To achieve this we adopt a statistical perspective on Reduced Order Modelling, which allows us to push such user-designed force distributions through a linearized simulation to obtain a dual distribution on displacements. To construct our subspace, we then fit a low-rank Gaussian model to this displacement distribution, which we show generalizes Linear Modal Analysis subspaces for uncorrelated unit variance force distributions, as well as Green’s Function subspaces for low rank force distributions. We show our framework allows for the construction of subspaces that are optimal both with respect to physical material properties, as well as arbitrary force distributions as observed in handle-based, contact, and musculoskeletal scene interactions.

Force-Dual Modes: Subspace Design from Stochastic Forces

Jie Chen, Zherong Pan, Bo Ren

We propose a Reinforcement Learning (RL) algorithm that combines several novel techniques to achieve more stable and robust control results for coupled solid-fluid systems. Our method utilizes the twin-delayed actor-critic algorithm to efficiently utilize off-policy data and achieve faster convergence. For more accurate estimations of the value function to guide the search of
optimal policies, we use the Boltzmann softmax operator to reduce the bias of estimation. We further introduce a novel two-step Q-value estimator to reduce the well-known under-estimation issue. Finally, to mitigate the requirement of excessive exploration under sparse rewards, we propose the Fluid Effective Domain Guidance (FEDG) algorithm to guide policy explo- ration, where the policy for an easier task is trained jointly with that for a harder task. Put together, our framework achieves state-of-the-art performance in complex fluid-solid coupling control benchmarks, delivering stable and reliable performance in both 2D and 3D tasks over long horizons.

Fast & Stable Control of Coupled Solid-Fluid Dynamic Systems

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
• Fast Cutting of Cage Based Deformation with Walk on Spheres
• 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
• DiffSurFlow: Efficient and Robust Differentiable Fluid Optimization via
  Surrogate Strategy on Flow Map