A Neural Material Point Method for Particle-based Simulations

2024-08-28

arXiv.org

AI Summary

Existing particle-based simulators (e.g., MPM) handle large deformations and topological changes but incur high computational cost; deep learning surrogates often suffer from expensive training and deteriorating long-horizon accuracy. This work proposes NeuralMPM—the first framework to deeply embed the Material Point Method’s dual-space paradigm (Lagrangian particles ↔ Eulerian grid) into a neural architecture. It integrates bidirectional particle-grid interpolation, CNN- or Transformer-based image-to-image state evolution on the grid, and hybrid representation learning to jointly ensure physical fidelity and efficiency. Training time is reduced from days to hours; long-term simulation error for fluid and fluid–solid coupling tasks decreases by 27%. Moreover, NeuralMPM enables efficient forward simulation and differentiable inverse problem solving—facilitating gradient-based optimization and control.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Sampling/Simulation-based Search
• Multiagent Systems: Multiagent Learning

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

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

Problem

• Reduces computational resources for simulations.
• Improves training efficiency of deep learning emulators.
• Enhances accuracy in fluid and solid interactions.

Innovation

• NeuralMPM framework for particle simulation
• Interpolates particles using image-to-image networks
• Reduces training time significantly with high accuracy