A Neural Material Point Method for Particle-based Emulation

TL;DR

NeuralMPM introduces a neural emulation framework inspired by the Material Point Method, enabling faster, scalable, and accurate particle-based simulations for fluids and solids by leveraging grid-based neural computations.

Contribution

The paper presents NeuralMPM, a novel neural emulation approach that combines particle methods with grid-based neural networks to improve simulation speed and accuracy.

Findings

Reduces training time from days to hours.

Achieves comparable or better accuracy than existing methods.

Effective on fluid and fluid-solid interaction datasets.

Abstract

Mesh-free Lagrangian methods are widely used for simulating fluids, solids, and their complex interactions due to their ability to handle large deformations and topological changes. These physics simulators, however, require substantial computational resources for accurate simulations. To address these issues, deep learning emulators promise faster and scalable simulations, yet they often remain expensive and difficult to train, limiting their practical use. Inspired by the Material Point Method (MPM), we present NeuralMPM, a neural emulation framework for particle-based simulations. NeuralMPM interpolates Lagrangian particles onto a fixed-size grid, computes updates on grid nodes using image-to-image neural networks, and interpolates back to the particles. Similarly to MPM, NeuralMPM benefits from the regular voxelized representation to simplify the computation of the state dynamics, while avoiding the drawbacks of mesh-based Eulerian methods. We demonstrate the advantages of NeuralMPM on several datasets, including fluid dynamics and fluid-solid interactions. Compared to existing methods, NeuralMPM reduces training times from days to hours, while achieving comparable or superior long-term accuracy, making it a promising approach for practical forward and inverse problems. A project page is available at https://neuralmpm.isach.be