Multi-scale graph neural network for physics-informed fluid simulationMulti-scale graph neural network for physics-informed fluid simulationL. Wei, N.M. Freris

Learning-based fluid simulation has proliferated due to its ability to replicate the dynamics with substantial computational savings over traditional numerical solvers. To this end, graph neural networks (GNNs) are a suitable tool to capture fluid dynamics through local particle interactions. Nonetheless, it remains challenging to model the long-range behaviors. To tackle this, this paper models the fluid flow via graphs at different scales in succinct considerability and physical constraints. We propose a novel multi-scale GNN for physics-informed fluid simulation (MSG) by introducing a nonparametric sampling and aggregation method to combine features from graphs with different resolutions. Our design reduces the size of the learnable model and accelerates the model inference time. In addition, zero velocity divergence is explicitly incorporated as a physical constraint through the training loss function. Finally, a fusion mechanism of consecutive predictions is incorporated to alleviate the inductive bias caused by the Markovian assumption. Extensive experiments corroborate the merits over leading particle-based neural network models in terms of both one-step accuracy (+6.7%)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(+ 6.7\%)$$\end{document} and long trajectory prediction (+16.9%)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(+ 16.9\%)$$\end{document}. This comes with a run-time reduction by 2.8%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2.8\%$$\end{document} over the best baseline method.