Machine learning has been successfully applied to grid-based PDE modeling in various scientific applications. However, learned PDE solvers based on Lagrangian particle discretizations, which are the preferred approach to problems with free surfaces or complex physics, remain largely unexplored. We present LagrangeBench, the first benchmarking suite for Lagrangian particle problems, focusing on temporal coarse-graining. In particular, our contribution is: (a) seven new fluid mechanics datasets (four in 2D and three in 3D) generated with the Smoothed Particle Hydrodynamics (SPH) method including the Taylor-Green vortex, lid-driven cavity, reverse Poiseuille flow, and dam break, each of which includes different physics like solid wall interactions or free surface, (b) efficient JAX-based API with various recent training strategies and neighbors search routine, and (c) JAX implementation of established Graph Neural Networks (GNNs) like GNS and SEGNN with baseline results. Finally, to measure the performance of learned surrogates we go beyond established position errors and introduce physical metrics like kinetic energy MSE and Sinkhorn distance for the particle distribution. Our codebase is available under the URL: https://github.com/tumaer/lagrangebench

翻译：机器学习已成功应用于基于网格的偏微分方程建模，涉及多种科学应用。然而，基于拉格朗日粒子离散化的学习型偏微分方程求解器——这类方法在处理自由表面或复杂物理问题时具有优势——仍鲜少被探索。我们提出LagrangeBench，这是首个针对拉格朗日粒子问题的基准测试套件，重点关注时间粗粒化。具体而言，我们的贡献包括：(a) 七个新的流体力学数据集（四个二维数据集和三个三维数据集），这些数据集通过光滑粒子流体动力学（SPH）方法生成，涵盖泰勒-格林涡、顶盖驱动腔体、反向泊肃叶流以及溃坝问题，每个数据集均包含固体壁面相互作用或自由表面等不同物理机制；(b) 基于JAX的高效应用编程接口，集成了多种最新训练策略及近邻搜索算法；(c) 基于JAX实现的成熟图神经网络（如GNS和SEGNN）及基准结果。最后，为衡量学习型替代模型的性能，我们超越了传统的位形误差指标，引入了物理度量指标，如动能均方误差和粒子分布上的Sinkhorn距离。我们的代码库可通过以下URL获取：https://github.com/tumaer/lagrangebench