Physics-Based Animation

Yixin Chen, David I.W. Levin, Timothy R. Langlois

We present a physics-based fluid control method utilizing localized spacetime windows, extending force-based fluid control to substantially larger simulation scales. In many practical editing scenarios, user-specified objectives affect only a small region of an otherwise satisfactory simulation, resulting in optimal control force distributions that are highly sparse in both space and time. However, existing optimization-based fluid control methods typically solve for control forces over the entire spacetime domain, leading to unnecessarily high computational cost and poor scalability. Motivated by this observation, we restrict optimization to localized spacetime regions surrounding the edit of interest, significantly reducing the dimensionality of the control problem. Within this framework, control forces are parameterized on a coarse “floating” background grid, decoupling control degrees of freedom from simulation resolution and promoting smooth, physically plausible forces. We further analyze spacetime-window selection as a joint spatial-temporal problem. While the full problem can be formulated as a 2D search over spatial and temporal window extents, practical workflows can often leverage user-specified spatial regions and lightweight temporal-window selection strategies to reduce search cost. Our method enables a range of intuitive editing tasks, where sparse user inputs can induce coherent motion in surrounding fluid structures. We demonstrate the effectiveness and efficiency of our method with various 2D and 3D particle-based free-surface simulation examples.

Fluid Control with Localized Spacetime Windows

Hongcheng Song, Ye Fan, Uri M. Ascher, Dinesh K. Pai

Existing approaches to frictional contact dynamics typically either modify the Coulomb law to improve numerical robustness or solve the exact law in a fully coupled monolithic form. However, in its reduced form, exact Coulomb friction can be written as a cone complementarity problem with an augmented velocity, which reveals a natural split between a cone-constrained linear response and a scalar non-associated coupling induced by tangential velocity. We exploit this structure in the solver design. Our method uses an outer iteration to update the non-associated coupling explicitly, and an inner solve for a strongly convex cone-constrained quadratic program. This separation also makes the inner solver modular, so different numerical schemes can be used without changing the outer iteration. We evaluate the method on rigid-body benchmarks with stick-slip transitions and frictional stacking, and show that it reproduces exact Coulomb complementarity without smoothing or relaxing the friction law.

A Splitting Architecture for Exact Reduced Coulomb Friction

Bernhard Braun, Rene Winchenbach, Jan Bender, Nils Thuerey

We present ST-FLIP, a spatiotemporal extension of the Fluid-Implicit Particle (FLIP) method for incompressible free-surface and two-phase liquid simulation. ST-FLIP enables time steps up to an order of magnitude larger than those typically used in CFL-constrained solvers, while preserving detailed flow structures and visual fidelity. It addresses a common failure mode of large time steps in hybrid particle–grid liquid solvers: temporal under-sampling of particle motion produces aliasing-driven free-surface artifacts after projection. Our key idea is to interpret particles as samples in four-dimensional space-time: in addition to standard spatial jittering, we randomize particle positions along the time axis as well and perform particle-to-grid deposition using a separable 4D kernel. This yields a Monte Carlo estimator of per-step time-slab-integrated particle quantities. Although particles are treated as samples in 4D space-time, our approach works as a lightweight plug-in by collapsing to slab‑integrated 3D grid fields for projection. Building on recent particle‑based phase‑field work, we reuse the particle-to-grid weight accumulators as a conceptual space–time phase field, providing variable‑coefficient projection weights and eliminating the need for per‑step surface reconstruction. The method can be easily integrated into existing FLIP/PIC or APIC solvers with negligible additional computational cost per time step. The effectiveness of our approach is demonstrated through a series of comparisons with state-of-the-art solvers, yielding several-fold speedups for multi-billion-particle simulations at high effective 3D resolutions on a single workstation.

Spatiotemporal FLIP for Fast Free-Surface and Two-Phase Simulation With Very Large Time Steps

Shixun Huang, Siyuan Chen, Yue Chang, Zhecheng Wang, Peter Yichen Chen

Cyclic animation is widely used in computer graphics and interactive content. It supports seamless playback in games, VR, and interactive simulation, where short clips must repeat smoothly over long durations. Achieving physically plausible cyclic synthesis from an input sequence is challenging because the endpoint states of the observed sequence rarely match exactly, and the governing equations of the underlying system are often unavailable.
We therefore propose an equation-free framework that identifies a Koopman surrogate from the observed trajectory and computes a cyclic trajectory by applying a Fourier-parameterized, time-varying control force under a hard temporal periodicity constraint. The resulting formulation reduces cyclic synthesis to a linearly constrained quadratic program that can be solved efficiently through a structured KKT system. Our method is applicable to a diverse range of examples, including N-body systems, cloth, deformable objects, shallow water, etc.

Closing Trajectories: Equation-Free Cyclic Animation via Koopman Surrogates

Rupesh Kumar, Sabhya Khurana, Rahul Narain

We present a technique for simulating detailed cloth dynamics on coarse meshes at interactive rates, by coupling the base mesh simulation with dynamic wrinkles in a physically consistent manner. Building on the wrinkle parameterization introduced by Chen et al. 2021, we introduce a dynamics model for a cloth sheet represented as a superposition of a base surface and a wrinkle distribution parameterized by spatially varying amplitude and frequency. Our model incorporates two-way coupling of the base surface and the wrinkle parameters, allowing the base deformation to drive emergence of wrinkles and permitting compression of the base surface in turn. To deform the mesh using the computed wrinkle parameters, we also introduce a simple phase reconstruction strategy that produces dynamically evolving, temporally coherent wrinkles on the simulated mesh.

Dynamic Wrinkling on Coarsely-Meshed Cloth

Kangrui Zhang, Ruihong Cen, Siyan Zhu, Ruoyan Chen, Bo Ren

We present DIQ-MPM, a novel monolithic two-way coupling framework for simulating interactions between solids modeled with the total Lagrangian formulation and Eulerian incompressible fluids using the Material Point Method (MPM). Our approach combines an implicit TLMPM formulation with a mixed velocity-pressure scheme to robustly simulate compressible solids undergoing large deformations, while eliminating numerical fractures. To enable strong fluid–solid coupling without relying on overlapping grids, we introduce a Dual Interface Quadrature (DIQ) mechanism that maps fluid-solid interface information consistently between the current and reference configurations. This allows us to construct a unified sparse pressure-only system via Schur complement, leading to efficient and stable coupling. We also integrate a particle-based contact force model to resolve solid-solid and solid-boundary contacts within implicit TLMPM. Experimental results demonstrate that our method stably captures free-slip coupling, large deformation phenomena, and complex interactions between compressible solids and incompressible fluids.

DIQ-MPM: Dual Interface Quadrature MPM for Simulating Large Deformation and Fluid-Solid Coupling

Gilles Daviet

We present a family of mixed Material Point Methods well suited to CFL-rate simulation of stiff elastoviscoplastic materials, up to the incompressible limit. Our work builds on the mixed discretization from Daviet and Bertails-Descoubes [2016a] and extends it to handle finite-strain viscoelasticity and more general flow rules, allowing the simulation of a much wider range of materials. Our implicit integration scheme yields a well-posed, symmetric optimization problem with compact stencils, together with an efficient GPU solver. We demonstrate our method on a variety of examples ranging from granular materials and snow to elastic solids, including two-way coupling with rigid-body solvers.

Mixed Material Point Methods for Stiff Elastoplasticity

Li Liao, Pengfei Shen, Yifan Peng

Eigenanalysis of partial differential operators is central to reduced-order physical simulation, but neural shape-space eigenanalysis has largely been limited to natural Neumann boundary conditions. This prevents direct control over supports, openings, heat-exchange boundaries, and other boundary effects that change the underlying operator. We extend neural eigenanalysis for Laplace-type operators to Dirichlet, Robin, and mixed boundary conditions. Boundary placement and Robin coefficients are treated as model inputs, giving a joint shape-boundary space where eigenfunctions and spectra vary continuously with both geometry and boundary configuration. The resulting boundary-aware bases support resonance tuning, reduced-order elastic simulation with changing supports, and transient heat analysis under controllable boundary exchange.

Boundary-aware Neural Model Reduction for PDEs

Lorenzo Diazzi, Jiacheng Dai, Daniele Panozzo, Marco Attene

We present an algorithm that produces high quality tetrahedral meshes conforming with input polyhedra. Our meshing algorithm is based on Ruppert’s Delaunay refinement where convergence is guaranteed thanks to a novel chamfering approach that removes all acute angles from the input. On such a modified input Delaunay refinement produces a Delaunay tetrahedrization where all the faces have bounded angles. The input portions that were removed by the chamfering are re-inserted in this tetrahedrization to achieve exact conformance at the cost of a small number of bad-shaped tetrahedra near the formerly acute input angles. Numerical robustness is guaranteed along all the phases thanks to a clever use of modern indirect geometric predicates and the definition of a new type of implicit point to represent Steiner vertices on the input faces. In practice, our prototype implementation produces meshes having a quality comparable to the state-of-the-art tetgen software: while tetgen fails on 37% of the 3942 valid models in the Thingi10k dataset, our method succeeds on all of them.

Surface chamfering for robust tetrahedral meshing