Physics-Based Animation

Zhiqi Li, Jinjin He, Barnabás Börcsök, Taiyuan Zhang, Duowen Chen, Tao Du, Ming C. Lin, Greg Turk, Bo Zhu

This paper presents a novel adjoint solver for differentiable fluid simulation based on bidirectional flow maps. Our key observation is that the forward fluid solver and its corresponding backward, adjoint solver share the same flow map as the forward simulation. In the forward pass, this map transports fluid impulse variables from the initial frame to the current frame to simulate vortical dynamics. In the backward pass, the same map propagates adjoint variables from the current frame back to the initial frame to compute gradients. This shared long-range map allows the accuracy of gradient computation to benefit directly from improvements in flow map construction. Building on this insight, we introduce a novel adjoint solver that solves the adjoint equations directly on the flow map, enabling long-range and accurate differentiation of incompressible flows without differentiating intermediate numerical steps or storing intermediate variables, as required in conventional adjoint methods. To further improve efficiency, we propose a long-short time-sparse flow map representation for evolving adjoint variables. Our approach has low memory usage, requiring only 6.53GB of data at a resolution of 192^3 while preserving high accuracy in tracking vorticity, enabling new differentiable simulation tasks that require precise identification, prediction, and control of vortex dynamics.

An Adjoint Method for Differentiable Fluid Simulation on Flow Maps

Xiao Sean Zhan, Evan Thompson, Clément Jambon, Kenney Ng, Mina Konaković Luković

Generative models have recently demonstrated impressive capabilities in producing high-quality 3D shapes from a variety of user inputs (e.g., text or images). However, generated objects often lack physical integrity. We introduce PhysiOpt, a differentiable physics optimizer designed to improve the physical behavior of 3D generative outputs, enabling them to transition from virtual designs to physically plausible, real-world objects. While most generative models represent geometry as continuous implicit fields, physics-based approaches often rely on the finite element method (FEM), requiring ad hoc mesh extraction to perform shape optimization. In addition, these methods are typically slow, limiting their integration in fast, iterative generative design workflows. Instead, we bridge the representation gap and propose a fast and effective differentiable simulation pipeline that optimizes shapes directly in the latent space of generative models using an intuitive and easy-to-implement differentiable mapping. This approach enables fast optimization while preserving semantic structure, unlike traditional methods relying on local mesh-based adjustments. We demonstrate the versatility of our optimizer across a range of shape priors, from global and part-based latent models to a state-of-the-art large-scale 3D generator, and compare it to a traditional mesh-based shape optimizer. Our method preserves the native representation and capabilities of the underlying generative model while supporting user-specified materials, loads, and boundary conditions. The resulting designs exhibit improved physical behavior, remain faithful to the learned priors, and are suitable for fabrication. We demonstrate the effectiveness of our approach on both virtual and fabricated objects.

PhysiOpt: Physics-Driven Shape Optimization for 3D Generative Models

Yura Hwang, Jenny Han Lin, Jerry Hsu, Benjamin Mastripolito, James McCann, Cem Yuksel

Lightweight, mesh-level models of knit fabric behavior are useful for both interactive pattern editing and initialization of yarn-level simulations. However, existing mesh-level simulation methods abstract knitting as a homogeneous material, which prevents them from capturing more complicated mixed structures. Furthermore, these methods require different simulation parameters depending on the knit pattern, or arrangement of stitches within the knit. Thus, fitting these parameters to physical examples must be done for each new pattern, even when the same types of stitches are used. To address this, we observe that physical behavior of a stitch is determined not only by its individual structure but also by the stitch types that surround it. In our work, we extend the stitch mesh model to allow for neighbor-aware material properties at the stitch level. Using structural analysis of stitch connections, we derive a finite set of four-way kernels that combine to create general knit-purl patterns for relaxation. From this, we generate a set of reference patterns that can be measured to infer the rest-lengths of the kernels using a linear model. After knitting and measuring these reference patterns, we used the derived kernel rest lengths to run relaxation on our stitch mesh models with mixtures of knits and purls that we then validated against physical examples. Our results show that the 4 neighbors of each stitch is sufficient to account for much of the neighborhood-dependent deformation, while remaining simple enough to directly fit to measured data with a set of 11 basis swatches. This allows our relaxation method to efficiently estimate the rest shape of mixed knit-purl patterns, which enables fast fabric preview and more accurate yarn-level simulation.

Neighbor-Aware Data-Driven Relaxation of Stitch Mesh Models for Knits

J. Andreas Bærentzen, Jonàs Martínez, Jeppe Revall Frisvad, Sylvain Lefebvre

We introduce a divergence-free nD vector noise defined as the n-dimensional cross product of the gradients of n − 1 noise functions. We show that this vector noise function is divergence-free and hence volume preserving for any dimension n. Our method enables precise integration and extends to new settings by substituting noise functions with implicit surfaces, (hyper)surfaces, or custom functions. We demonstrate applications including image warping, surface texturing, noise bounded by implicit surfaces, anisotropic curl-noise, and high-dimensional point jittering up to 7D.

Improving Curl Noise

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