Physics-Based Animation

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

We present a novel combustion simulation framework to model fire phenomena across solids, liquids, and gases. Our approach extends traditional fluid solvers by incorporating multi-species thermodynamics and reactive transport for fuel, oxygen, nitrogen, carbon dioxide, water vapor, and residuals. Combustion reactions are governed by stoichiometry-dependent heat release, allowing an accurate simulation of premixed and diffusive flames with varying intensity and composition. We support a wide range of scenarios including jet fires, water suppression (sprays and sprinklers), fuel evaporation, and starvation conditions. Our framework enables interactive heat sources, fire detectors, and realistic rendering of flames (e.g., laminar-to-turbulent transitions and blue-to-orange color shifts). Our key contributions include the tight coupling of species dynamics with thermodynamic feedback, evaporation modeling, and a hybrid SPH-grid representation for the efficient simulation of extinguishing fires. We validate our method through numerous experiments that demonstrate its versatility in both indoor and outdoor fire scenarios.

Fire-X: Extinguishing Fire with Stoichiometric Heat Release

Timna Böttcher, Lukas Westhofen, Stefan Rhys Jeske, Jan Bender

We present a novel implicit porous flow solver using SPH, which maintains fluid incompressibility and is able to model a wide range of scenarios, driven by strongly coupled solid-fluid interaction forces. Many previous SPH porous flow methods reduce particle volumes as they transition across the solid-fluid interface, resulting in significant stability issues. This further allows us to extend SPH pressure solvers to take local porosity into account and results in strict enforcement of incompressibility. As a result, we can simulate porous flow using physically consistent pressure forces between fluid and solid. In contrast to previous SPH porous flow methods, which use explicit forces for internal fluid flow, we employ implicit non-pressure forces. These we solve as a linear system and strongly couple with fluid viscosity and solid elasticity. We capture the most common effects observed in porous flow, namely drag, buoyancy and capillary action due to adhesion. To achieve elastic behavior change based on local fluid saturation, such as bloating or softening, we propose an extension to the elasticity model. We demonstrate the efficacy of our model with various simulations that showcase the different aspects of porous flow behavior. To summarize, our system of strongly coupled non-pressure forces and enforced incompressibility across overlapping phases allows us to naturally model and stably simulate complex porous interactions.

Implicit Incompressible Porous Flow using SPH

Haoxiang Wang, Kui Wu, Hui Qiao, Mattieu Desbrun, Wei Li

Kinetic multiphase flow solvers have recently demonstrated exquisitely complex and turbulent fluid phenomena involving splashing and bubbling. However, they require full simulation of both the liquid phase and the air to capture a large spectrum of fluid behaviors. Moreover, they rely on diffuse interface tracking to properly account for the interfacial forces involved in fluid-air interactions. Consequently, simulating visually appealing fluids is extremely compute intensive given the required resolution to capture small bubbles, and foam simulation is unattainable with this family of methods. While water simulation involves density and viscosity differences between the two phases so large that one can safely ignore the dynamics of air, so-called kinetic free-surface solvers that only consider the liquid motion have been unable to reproduce the full gamut of turbulent fluid behaviors, being often unstable for even moderately complex scenarios. By revisiting kinetic solvers using sharp interfaces and incorporating recent advances in single-phase and multiphase LBM solvers, we propose a free-surface kinetic solver, which we call HOME-FREE LBM, that not only handles turbulence, glugging, and bubbling, but even foam where bubbles stick to each other through surface tension. We demonstrate that our fluid simulator allows for fast and robust bubble growth, breakup, and coalescence, at a fraction of the computational time that existing CG fluid solvers require.

Kinetic Free-Surface Flows and Foams with Sharp Interfaces

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