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Multiresolution Mesh Networks For Learning Dynamical Fluid Simulations
Bach Nguyen · Truong Son Hy · Long Tran-Thanh · Risi Kondor

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in AI for Science: Progress and Promises »
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In this paper, we introduce Multiresolution Mesh Networks-enhanced MeshGraphNets (MGN-MeshGraphNet) for learning mesh-based dynamical fluid simulations. The novelty of our proposal comes from the ability to capture multiscale structures of fluid dynamics via a learnable coarse-graining mechanism on meshes (i.e. mesh multiresolution), along with long-range dependencies between multiple timesteps and resolutions for robust prediction. Our proposed method has shown competitive numerical results in comparison with other machine learning approaches based on graph neural networks. Given the flexibility of our data-driven approach for building mesh multiresolution, our method has better generalizability for new fluid dynamical simulations outside of the training data while attaining high accuracies on multiple resolutions and computational speedup compared to the existing PDE numerical solvers of Navier--Stokes equation.

Keywords: graph neural networks · physics · Simulation · Physics simulation · multiresolution

Author Information

Bach Nguyen (University of Texas at Dallas)
Truong Son Hy (The University of Chicago)

Research areas: Kernel methods, Graph kernels, Graph Neural Networks

Long Tran-Thanh (University of Warwick)
Risi Kondor (Flatiron Institute)

Risi Kondor joined the Flatiron Institute in 2019 as a Senior Research Scientist with the Center for Computational Mathematics. Previously, Kondor was an Associate Professor in the Department of Computer Science, Statistics, and the Computational and Applied Mathematics Initiative at the University of Chicago. His research interests include computational harmonic analysis and machine learning. Kondor holds a Ph.D. in Computer Science from Columbia University, an MS in Knowledge Discovery and Data Mining from Carnegie Mellon University, and a BA in Mathematics from the University of Cambridge. He also holds a diploma in Computational Fluid Dynamics from the Von Karman Institute for Fluid Dynamics and a diploma in Physics from Eötvös Loránd University in Budapest.

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