material point method

This work addresses the high computational cost and low design iteration efficiency inherent in high-resolution volumetric elastodynamic simulation. We propose the first progressive dynamic level-of-detail (LOD) modeling framework tailored for voxel-based finite element methods. Our core contributions are threefold: (1) a topology-aware prolongation operator construction algorithm that enables efficient interpolation across non-conforming overlapping grids via boundary-binding constraints; (2) seamless integration of multiple coordinate-based deformation methods—including barycentric, biharmonic, and Phong coordinates—as plug-and-play components; and (3) a hierarchical multi-resolution mesh structure to drive coarse-to-fine dynamical coupling. Experiments demonstrate that our method significantly improves dynamic fidelity between low-resolution previews and high-resolution ground truth under challenging scenarios—such as high-speed motion, large deformations, and frictional contact—thereby enabling rapid and reliable animation design iteration.

This work addresses the challenge of high-fidelity, efficient simulation of dynamic behaviors of real-world elastic objects. Methodologically, we propose a continuum-mechanics-based neural simulation framework that employs Gaussian kernels as fundamental continuous material units and introduces a Center-of-Mass System (CMS) hierarchical architecture—explicitly embedding physical constraints such as mass and momentum conservation to enable interpretable, physics-consistent modeling across coarse-to-fine granularities. Our key contributions are: (i) the first integration of Gaussian kernels into continuum-based elastic modeling, and (ii) the introduction of an explicit physics-constrained CMS hierarchical simulation paradigm. Evaluated on our newly established READY benchmark—a real-world video dataset—the method significantly outperforms existing physics-driven approaches in dynamic simulation accuracy. Both source code and trained models will be made publicly available.

This work addresses the computational challenges in real-time implicit hyperelastic solid simulation arising from strong nonlinearity (hyperelasticity) and nonsmoothness (non-penetration contact and Coulomb friction). Methodologically, it introduces a GPU-accelerated local–global splitting framework: (i) contact and friction are unified under a nonlinear complementarity problem (NCP) formulation; (ii) an efficient solver is designed using explicit sparse matrix inverse representations; and (iii) the NCP preconditioner is enhanced to improve convergence rate and friction accuracy. Contributions include: the first real-time, tightly coupled solver achieving high-fidelity friction modeling and mathematically rigorous non-penetration constraints within a unified NCP framework; stable performance exceeding 60 FPS on large-scale systems, under extreme deformations, and across multi-stiffness material configurations; and broad constitutive model compatibility—including Neo-Hookean and St. Venant–Kirchhoff models—ensuring both physical fidelity and engineering practicality.

Reconstructing high-fidelity, topologically closed meshes from sparse or constrained 3D point clouds—especially those acquired from narrow cavities—remains challenging. This paper proposes a novel meshing method based on physically simulated flexible foil deformation. It is the first to integrate dynamic elasticity modeling into point cloud meshing, synergistically combining pressure-driven surface deformation, implicit surface initialization, spatially constrained optimization, and adaptive vertex snapping. This framework unifies geometric fidelity with physical plausibility while automatically generating watertight, topologically consistent surfaces. Extensive evaluation on diverse complex cavity point clouds demonstrates that our method reduces boundary fitting error by 37% compared to Poisson surface reconstruction and ball-pivoting, achieves 100% topological completeness, and significantly improves both accuracy and robustness of closed mesh generation.

This work addresses the limitation of existing physics-based 3D simulation methods—where Gaussian splatting (GS) is coupled with dynamics only via explicit surface meshes (e.g., Marching Cubes)—by proposing the first mesh-free, differentiable physical modeling framework for GS. Methodologically, it treats 3D Gaussian primitives as discrete Newtonian point masses governed by physical dynamics; Gaussian distributions are flattened and deformed via triangle-mesh parameterization, enabling plug-and-play integration with arbitrary black-box physics engines. Key contributions include: (1) the first end-to-end differentiable, mesh-free Gaussian physical model; (2) a novel patch-driven deformation mechanism that jointly preserves geometric fidelity and dynamic consistency; and (3) significant improvements in visual quality and physical plausibility across multiple 3D object rendering benchmarks, while maintaining real-time rendering efficiency.

Existing neural rendering approaches generally overlook the influence of temperature on visual appearance, making it difficult to faithfully simulate thermally coupled phenomena such as melting and solidification. This work introduces thermal phase-change dynamics into 3D Gaussian splatting for the first time by endowing Gaussian points with temperature attributes. It couples a numerical heat conduction–convection solver with Material Point Method (MPM) dynamics and proposes a topology-adaptive rendering strategy to mitigate visual artifacts caused by large deformations. The resulting framework achieves high-fidelity, physically consistent rendering of thermophysical dynamic scenes, demonstrating significantly improved realism and controllability over existing methods in complex phase-transition processes like melting and solidification.

This work investigates whether pretrained image editing models can serve as a universal interface for solving diverse physical equations. The approach encodes both inputs and solutions of physical problems as images, incorporates lightweight adapters to embed scalar parameters, and trains the model under a unified architecture using numerical or analytical solutions across multiple equation types—including elliptic, heat, and Navier-Stokes equations. For the first time, it systematically demonstrates that general-purpose generative models can effectively represent both static and dynamic physical mappings, even capturing shocks and unstable phenomena, thereby expanding their applicability in scientific computing. Experiments across more than ten problem classes yield promising results, yet also reveal limitations of image-based representations in handling wide numerical ranges, enforcing constraints, and simulating long-term chaotic dynamics, such as those in the Kuramoto–Sivashinsky equation.

Traditional simulation of deformable objects relies on mesh-based representations or neural fields requiring per-shape optimization, struggling to balance geometric complexity and computational efficiency. This work proposes a mesh-free reduced-order simulation method that, for the first time, integrates Reproducing Kernel Particle Method (RKPM) with reduced-order elastic dynamics. By employing RKPM to construct a continuous elastic body model and solving the generalized eigenvalue problem of the elastic energy Hessian matrix, the method automatically computes skinning weights without mesh generation or per-shape optimization. The approach achieves a 40× speedup in training compared to neural field–based methods, yields simulation errors lower than those of converged finite element solutions, and demonstrates successful application across diverse geometric representations and robotic simulation tasks.

Efficient simulation of granular media composed of non-convex particles has long been hindered by high computational complexity and challenges in contact modeling. This work proposes a novel approach that, for the first time, integrates geometric contact relationships in configuration space with neural networks to learn a contact mapping. By doing so, it transforms the contact detection problem for rigid non-convex particles into an efficient neural inference process. The method substantially reduces computational overhead, enabling fast, robust, and large-scale dynamic simulations of non-convex particle systems on standard hardware, thereby significantly enhancing both the feasibility and efficiency of such simulations.

This work proposes a novel topology optimization framework that integrates the implicit Material Point Method (MPM) to address numerical instabilities arising from mesh distortion and large rotations in large-deformation problems. For the first time, MPM is incorporated into topology optimization within an end-to-end differentiable pipeline, leveraging automatic differentiation and hyperelastic constitutive models to enable stable and efficient quasi-static optimization of structures undergoing finite deformations. The approach naturally supports both single- and multi-material designs and demonstrates robust performance on complex geometries, including soft robotic grippers. By circumventing the limitations of traditional finite element–based methods, the proposed framework significantly enhances the robustness and applicability of topology optimization in highly nonlinear deformation regimes.