Physics-Based Animation

José Antonio Fernández-Fernández, Fabian Löschner, Jan Bender

Newton’s Method is widely used to find the solution of complex non-linear simulation problems. To guarantee a descent direction, it is common practice to clamp the negative eigenvalues of each element Hessian prior to assembly — a strategy known as Projected Newton (PN) — but this perturbation often hinders convergence. In this work, we observe that projecting only a small subset of element Hessians is sufficient to secure a descent direction. Building on this insight, we introduce Progressively Projected Newton (PPN), a novel variant of Newton’s Method that uses the current iterate’s residual to cheaply determine the subset of element Hessians to project. The benefit is twofold: most eigendecompositions are avoided and the global Hessian remains closer to its original form, reducing the number of Newton iterations. We compare PPN with PN and Project-on-Demand Newton (PDN) in a comprehensive set of experiments covering contact-free and contact-rich deformables, co-dimensional and rigid-body simulations, and a range of time step sizes, tolerances and resolutions. PPN reduces the amount of element projections in dynamic simulations by one order of magnitude while simultaneously improving convergence, consistently being the fastest solver in our benchmark.

Progressively Projected Newton’s Method

Alexandre Mercier-Aubin, Teseo Schneider, Paul G. Kry, Sheldon Andrews

We introduce affinification, a novel method for accelerating physics-based animation of elastic solids. During a time-dependent simulation, our method automatically partitions the space into affine and elastic regions depending on the deformation. As such, we capture localized deformations while significantly reducing computational costs with larger regions of model reduction. We design a new clustering method based on deformation rates to capture affinely deforming regions, and explore multiple heuristics for seeding, pattern generation, and the impact of physical parameters on coarsened regions. We compare our method with the ground truth, showing performance increasing with resolution and recorded simulations up to 17 times faster compared to elastic simulations, while retaining similar levels of visual fidelity.

Affinification: A Fine Approximation of Deformations

Liangwang Ruan, Bin Wang, Tiantian Liu, Baoquan Chen

We present an efficient and scalable method for the inverse shape design problem of elastic objects, with broad applicability to diverse materials and interactive editing. The core idea is to decouple material nonlinearity from geometry optimization by introducing the Cauchy stress tensor as an auxiliary variable. We design a three-stage scheme that iteratively optimizes the stress tensors and the rest shape, with each stage being well-posed and efficiently-solvable. To address the lack of a theoretical convergence guarantee arising from the decoupled energy formulation, we incorporate a relaxation method that ensures robust stability in practice. As a result, our method achieves a 3× speedup over the state-of-the-art asymptotic method [Jia21] on a model with 40k vertices and 112k elements (Fig. 2), and exhibits near-linear scalability to large systems (Fig. 8). We demonstrate applications including rest shape design for various materials (ranging from standard models to complex spline-based materials [XSZB15]), interactive material and force editing, and elastic object reconstruction from images.

STAGED: Stress-Tensor Assisted Global-local-global solver for interactive Elastic shape Design

Duowen Chen, Zhiqiang Lao, Yu Guo, Heather Yu

We introduce a hybrid pipeline that combines classical fluid simulation with modern generative video models to produce high- quality, controllable fluid effects without implementationally difficult solvers or costly ray-tracing. First, a lightweight physics- based simulator enforces core properties like incompressibility and lets artists specify layout, boundary conditions, and source positions. Second, we render a simple ‘control video’ via real-time rasterisation (diffuse shading, masks, depth) to capture scene structure and material regions. Third, a text-guided diffusion transformer (e.g., VACE) treats this control video as a canvas, refining it by adding foam, bubbles, splashes, and realistic colour blending for multiple materials. Our method leverages pre- trained video generators’ implicit physical priors, while masking and noise-warping ensure precise, per-material control and seamless mixtures in latent space. Compared to purely simulation-based or generative model based text-only approaches, we avoid implementing specialised multiphase algorithms and expensive rendering passes, yet retain full artistic control over fluid behaviour and appearance. We demonstrate that this training-free strategy delivers photorealistic fluid videos, supports diverse effects (multiphase flows, transparent media and wet foams), and simplifies the artist’s workflow by unifying simulation, shading, and generative rendering in a single, extensible framework.

Fluid Composer: Fluid Detail Composition and Rendering Using Video Diffusion Models

Zoé Herson, Axel Paris, Élie Michel

We present a real-time method to capture and simulate the dynamic behavior of watercolor painting. We develop a physically accurate, grid-based, real-time fluid simulation based on a reparameterized Thin Film model. The equations are rewritten so as to create principled parameters that finely control the length, thickness, and frequency of dripping. Our close connection with physics allows both theoretical and experimental validation of our method. The resulting system can reproduce dripping, fluid-air interface, and pigment advection and diffusion, all controllable by the user in real-time. Our experiments show that artists can use our system to create interesting and varied digital paintings.

Dripping Thin Films for Real-time Digital Painting

Junyuan Liu, Shusen Liu, Yuzhong Guo, Ruikai Liang, Yin Li, Xiaowei He

While semi-analytical boundary handling techniques have proven effective for modeling particle-based fluid-solid interactions, they can become unstable when applied to mesh boundaries undergoing dynamic motion or featuring complex, sharp geometries. We propose a novel semi-analytical energy model for boundary handling that unifies fluid simulation and boundary interactions within a variational framework. The model comprises two key components: a semi-analytical bulk energy formulation that mitigates particle deficiency issues in the evaluation of bulk energy, and a nonlocal contact potential that effectively prevents particle penetration into boundaries. Both energy terms are naturally compatible with the Semi-Implicit SPH (SISPH), and a unified Hessian-free solver combined with reduced-order collision detection enables an efficient and stable GPU-based implementation for both fluid dynamics and nonlinear fluid-solid interactions. Furthermore, the unified treatment of fluid bulk energy and boundary energy via the semi-analytical formulation robustly corrects penetrations in practice, even under severe compression scenarios involving complex moving boundaries. Compared with existing semi-analytical boundary treatments, our method is more robust under fast boundary motion and strong compression. Across challenging benchmarks with sharp features, narrow gaps, and moving meshes, it remains stable and penetration-free where prior methods often fail.

A Semi-Analytical Energy Model for Particle-Based Fluid Simulation Involving Complex Moving Boundaries

Fumiya Narita, Takashi Kanai

Tall cell grids have been proposed as an efficient approach to accelerate large-scale liquid simulation. In this framework, regions near the liquid surface are discretized with regular grids, while regions farther away are represented by elongated rectangular cells. The regular grid region close to the surface is referred to as the optical layer. In previous work, the thickness of this optical layer was uniformly fixed across the entire liquid domain. In this paper, we propose a novel tall cell grid structure in which the thickness of the optical layer is dynamically adjusted according to the motion of the liquid. This adaptive strategy reduces the number of grid cells required in the projection step without compromising visual quality, thereby accelerating the overall simulation. Furthermore, we introduce a two-way coupling scheme between rigid bodies and liquids in regions where the optical layer remains thin. Our algorithm is simple and can be easily integrated into existing tall cell grid frameworks.

Adaptive Optical Layers: Efficient Tall Cell Grids for Liquid Simulation

Xiang Feng, Yunuo Chen, Chang Yu, Hao Su, Demetri Terzopoulos, Yin Yang, Joe Masterjohn, Alejandro Castro, Chenfanfu Jiang

In this paper, we introduce MPM Lite, a new hybrid Lagrangian/Eulerian method that eliminates the need for particle-based quadrature at solve time. Standard MPM practices suffer from a performance bottleneck where expensive implicit solves are proportional to particle-per-cell (PPC) counts due to the the choices of particle-based quadrature and wide-stencil kernels. In contrast, MPM Lite treats particles primarily as carriers of kinematic state and material history. By conceptualizing the background Cartesian grid as a voxel hexahedral mesh, we resample particle states onto fixed-location quadrature points using efficient, compact linear kernels. This architectural shift allows force assembly and the entire time-integration process to proceed without accessing particles, making the solver complexity no longer relate to particles. At the core of our method is a novel stress transfer and stretch reconstruction strategy. To avoid non-physical averaging of deformation gradients, we resample the extensive Kirchhoff stress and derive a rotation-free deformation reference solution, which naturally supports an optimization-based incremental potential formulation. Consequently, MPM Lite can be implemented as modular resampling units coupled with an FEM-style integration module, enabling the direct use of off-the-shelf nonlinear solvers, preconditioners, and unambiguous boundary conditions. We demonstrate through extensive experiments that MPM Lite preserves the robustness and versatility of traditional MPM across diverse materials while delivering significant speedups in implicit settings and improving explicit settings at the same time.

MPM Lite: Linear Kernels and Integration without Particles

Zhanyu Yang, Nikolas Schwarz, Bosheng Li, Dominik Michels, Bedrich Benes, Soren Pirk, Wojtek Palubicki

Fungal wood decay is a complex biophysical phenomenon that involves the degradation of a variety of structural wood components, ranging from lignin and carbohydrates to defensive chemical agents. All these substrates serve as varying resources with different material properties that determine the rate of fungal propagation and the structural integrity and color of decaying wood. We propose a novel approach to simulate the dynamic interactions between the biological and mechanical components of wood decay, including fungal colonization, chemical defense, and moisture-driven fracture. We propose a novel volumetric representation of trees that includes grain-aligned mesh generation, internal moisture dynamics, and tissue-specific health states. Furthermore, we model the anisotropic diffusion, consumption, and resulting material failure caused by white and brown rot fungi. This allows simulating and rendering 3D volumetric decaying trees that realistically capture key aspects of the process, such as the progression of cuboid fracture patterns, the hollowing of trunks, and the effects of environmental moisture on structural stability.

Woodstock: Interactive Modeling of Fungal Wood Decay

Ahmed H. Mahmoud, Rahul Goel, Jonathan Ragan-Kelley, and Justin Solomon

We present a GPU-based system for automatic differentiation (AD) of functions defined on triangle meshes, designed to exploit the locality and sparsity in mesh-based computation. Our system evaluates derivatives using per-element forward-mode AD, confining all computation to registers and shared memory and assembling global gradients, sparse Jacobians, and sparse Hessians directly on the GPU. By avoiding global computation graphs, intermediate buffers, and device-host synchronization, our approach minimizes memory traffic and enables efficient differentiation under both static and dynamically changing sparsity. Our programming model lets users express energy terms over mesh neighborhoods, while our system automatically manages parallel execution, derivative propagation, sparse assembly, and matrix-free operations such as Hessian-vector products. Our system supports both scalar- and vector-valued objectives, dynamic interaction-driven sparsity updates, and seamless integration with external GPU sparse linear solvers. We evaluate our system on applications including elastic and cloth simulation, surface parameterization, mesh smoothing, frame field design, ARAP deformation, and spherical manifold optimization. Across these tasks, our system consistently outperforms state-of-the-art differentiation frameworks, including PyTorch, JAX, Warp, DrJIT, EnzymeAD, and Thallo. We demonstrate speedups across a range of solver types, from Newton and Gauss-Newton for nonlinear least squares to L-BFGS and gradient descent, and across different derivative usage modes, including Hessian-vector products as well as full sparse Hessian and Jacobian construction. Our system is available as open source at this https URL.

Locality-Aware Automatic Differentiation on the GPU for Mesh-Based Computations