LagrangeBench: A Lagrangian Fluid Mechanics Benchmarking Suite

Artur Toshev, Gianluca Galletti, Fabian Fritz, Stefan Adami, Nikolaus A. Adams

Keywords: particle-based, Lagrangian, fluid mechanics, benchmark, graph neural networks, smoothed particle hydrodynamics

TL;DR: New 2D and 3D Lagrangian fluid mechanics datasets, training and inference JAX-based codebase with four common graph neural networks, and benchmarking results.

Abstract: 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 three neighbor search routines, 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](https://github.com/tumaer/lagrangebench).

Submission Number: 943