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

翻译：无网格拉格朗日方法因其能够处理大变形与拓扑变化，被广泛应用于流体、固体及其复杂相互作用的模拟。然而，这类物理模拟器需要大量计算资源才能实现精确模拟。为解决此问题，深度学习仿真器虽能实现更快速且可扩展的模拟，但其训练过程通常仍显昂贵且困难，限制了实际应用。受质点法（MPM）启发，我们提出了NeuralMPM——一种用于粒子模拟的神经仿真框架。该框架将拉格朗日粒子插值到固定尺寸的网格上，利用图像到图像神经网络在网格节点上计算状态更新，再插值回粒子空间。与MPM类似，NeuralMPM借助规则体素化表示简化状态动力学计算，同时避免了基于网格的欧拉方法的缺陷。我们在多个数据集（包括流体动力学与流固耦合场景）上验证了NeuralMPM的优势。相较于现有方法，NeuralMPM将训练时间从数天缩短至数小时，同时获得相当或更优的长期精度，使其成为解决实际正反演问题的可行方案。项目页面详见 https://neuralmpm.isach.be