Related papers: E($3$) Equivariant Graph Neural Networks for Particle-Based Fluid Mechanics

E($3$) Equivariant Graph Neural Networks for Particle-Based Fluid Mechanics

URL: http://arxiv.org/abs/2304.00150v1
Date: Fri, 31 Mar 2023 21:56:35 GMT
Title: E($3$) Equivariant Graph Neural Networks for Particle-Based Fluid Mechanics
Authors: Artur P. Toshev, Gianluca Galletti, Johannes Brandstetter, Stefan Adami and Nikolaus A. Adams
Abstract summary: We demonstrate that equivariant graph neural networks have the potential to learn more accurate dynamic-interaction models. We benchmark two well-studied fluid flow systems, namely the 3D decaying Taylor-Green vortex and the 3D reverse Poiseuille flow.
Score: 2.1401663582288144
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We contribute to the vastly growing field of machine learning for engineering systems by demonstrating that equivariant graph neural networks have the potential to learn more accurate dynamic-interaction models than their non-equivariant counterparts. We benchmark two well-studied fluid flow systems, namely the 3D decaying Taylor-Green vortex and the 3D reverse Poiseuille flow, and compare equivariant graph neural networks to their non-equivariant counterparts on different performance measures, such as kinetic energy or Sinkhorn distance. Such measures are typically used in engineering to validate numerical solvers. Our main findings are that while being rather slow to train and evaluate, equivariant models learn more physically accurate interactions. This indicates opportunities for future work towards coarse-grained models for turbulent flows, and generalization across system dynamics and parameters.

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