physics-based particle simulation

This work addresses the limited generalizability of current data-driven physics simulation methods to real-world scenarios, primarily due to the absence of particle-level state annotations in real videos. To overcome this challenge, we propose the first differentiable particle dynamics model that requires no particle-level supervision and can be trained end-to-end directly on unlabeled real videos. Our approach integrates a dense particle representation based on Gaussian splatting, neural dynamics modeling, and rendering-based supervision to jointly learn the evolution of particle positions and orientations, thereby eliminating the need for heuristic sampling strategies. Evaluated on a newly curated dataset comprising approximately 500 diverse real-world videos of object interactions, our method demonstrates robust motion prediction capabilities in complex, realistic settings.

This work proposes a unified Lagrangian particle simulation framework based on a single Transformer architecture, eliminating the need for specialized solvers tailored to distinct physical phenomena such as cloth, fluids, or granular materials. The approach integrates a prediction-correction mechanism: the prediction step models external-force-driven motion, while the correction step efficiently captures complex inter-particle interactions through localized modeling and hierarchical hyper-token attention. For the first time, this method demonstrates cross-domain generalization of a single neural architecture across six physical domains—cloth, elastic solids, Newtonian and non-Newtonian fluids, granular media, and molecular dynamics—significantly reducing computational overhead. Moreover, it enables interactive control, inverse design, and learning from real-world data, thereby diminishing reliance on domain-specific simulators.

This work addresses the high computational cost of Lagrangian particle methods—such as Smoothed Particle Hydrodynamics (SPH) and the Material Point Method (MPM)—in multiscale dynamic simulations. The authors model the state of particle systems as function trajectories in a Hilbert space and propose a linear subspace reduced-order method based on explicit neural basis functions. By eschewing graph structures or nonlinear latent manifolds, this approach unifies classical projection-based model reduction with deep learning frameworks while guaranteeing permutation invariance with respect to particle count. Using only 32 neural basis functions, the method achieves highly accurate dynamic reconstruction and prediction in million-particle SPH simulations, attaining R² > 0.99 and substantially improving computational efficiency.

Existing video generation models produce high-fidelity videos but often lack physical plausibility and 3D controllability. To address this, we propose a physics-anchored image-to-video generation framework. Our method introduces a generative physics network that explicitly models multi-material dynamics—including elastic bodies, granular media (e.g., sand), viscoelastic putty, and rigid bodies—alongside a spatiotemporal attention module to capture inter-particle interactions. We jointly optimize trajectory plausibility and visual quality via a composite loss incorporating physics-based constraints. Furthermore, we employ a diffusion model to synthesize physically consistent 3D point trajectories, which drive controllable video synthesis. Trained on 550K synthetic samples, our approach surpasses state-of-the-art methods in both physical plausibility and visual fidelity. It enables fine-grained dynamic editing guided by physical parameters (e.g., elasticity, friction) and external forces (e.g., gravity, impact), offering unprecedented control over physically grounded video generation.

This work addresses trajectory tracking control for linear time-invariant (LTI) systems. We propose a physics-informed Gaussian process (GP) model predictive control (MPC) framework. Methodologically, we embed the LTI system’s constant-coefficient linear differential equation as a hard constraint into the GP prior—enabling “control-as-inference”—and introduce a virtual setpoint mechanism to explicitly encode and enforce pointwise soft constraints. Theoretically, we prove asymptotic stability of the resulting closed-loop system under the optimal control law. Numerical experiments demonstrate superior constraint satisfaction, tracking accuracy, and robustness compared to baseline methods. Our approach establishes a new paradigm for data-driven control that unifies physical interpretability—through first-principles differential equation constraints—with rigorous stability guarantees.

Reconstructing the dynamics of wind-driven objects from video is highly challenging due to the invisibility of wind fields, their intense spatiotemporal variability, and the complex deformations of the objects. This work proposes the first physics-informed differentiable framework that jointly optimizes spatiotemporal wind forces and object motion by integrating the Material Point Method with the Lattice Boltzmann Method. The approach employs a grid-based wind field representation and models object geometry using 3D Gaussian Splatting, enabling high-fidelity reconstruction and forward simulation through differentiable rendering and physical constraints. Evaluated on our newly introduced WD-Objects dataset, the method significantly outperforms existing techniques in both reconstruction accuracy and simulation fidelity, and further demonstrates its effectiveness and generalization capability by supporting wind field redirection and dynamic generation under novel wind conditions.

Existing methods for modeling the spatiotemporal dynamics of strongly coupled multiphysics systems struggle to balance computational efficiency and fidelity while relying on costly coupled data. This work reframes coupled physics modeling as a probabilistic inference problem and introduces a novel “conditional-to-joint” sampling paradigm by integrating generative modeling with iterative multiphysics coupling mechanisms for the first time. Leveraging operator splitting theory, the approach provides rigorous error controllability guarantees. Notably, it enables training and inference of coupled system behavior using only decoupled data. Experiments on synthetic benchmarks and three complex multiphysics scenarios demonstrate substantial improvements in both simulation efficiency and fidelity, confirming the method’s theoretical advantages and superior performance.

This work proposes a novel framework that generalizes neural cellular automata from static grids to dynamic Lagrangian particle systems, enabling learnable and self-organizing models of cellular behavior. Each particle possesses continuous position coordinates and internal states, updated locally via a shared differentiable neural rule and interacting through differentiable smoothed particle hydrodynamics (SPH) operators to support adaptive neighborhood relations. The approach accommodates heterogeneous dynamics, sparse computation, and end-to-end training, with efficient execution accelerated via CUDA. Demonstrated across tasks including morphogenesis, point cloud classification, and particle-based texture synthesis, the model exhibits self-regeneration capabilities, robustness, and emergent behaviors characteristic of particle systems, thereby validating its effectiveness and scalability.

This work proposes an interpretable neural operator framework for learning the dynamics of partial differential equations (PDEs), addressing key limitations of existing neural operators and Transformers—namely poor interpretability, difficulty in capturing local high-frequency structures, and high computational complexity. The approach leverages a Gaussian basis representation field, where Gaussian particles explicitly encode geometric information to yield a compact, mesh-independent, and directly visualizable state representation. By introducing Petrov–Galerkin projection and a novel PG Gaussian attention mechanism in modal space, the method enables efficient cross-scale coupling and computation. It achieves near-linear complexity, naturally supports irregular geometries, and extends seamlessly to both 2D and 3D settings. Experiments on standard PDE benchmarks and real-world datasets demonstrate state-of-the-art accuracy while offering intrinsic interpretability.

Existing physics-guided video generation methods rely on single-pass predictions of physical parameters, which struggle to accurately capture user intent—particularly in modeling fine-grained dynamics, complex trajectories, and temporally coherent interactions. To address this limitation, this work proposes a reflective agent framework that treats physical programs as executable hypotheses and iteratively refines motion and interaction through a closed-loop “generate–simulate–verify–repair” process. The framework integrates a vision-language model, a physics simulation engine, and a dedicated control API to enable multi-stage user interaction and progressively realize precise event outcomes. Experimental results demonstrate that the generated videos significantly outperform existing approaches in terms of physical plausibility, alignment with input prompts, and generalization across diverse scenarios.