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Multi-Scale Message Passing Neural PDE Solvers

by L. Equer and T. K. Rusch and S. Mishra

(Report number 2023-14)

Abstract
We propose a novel multi-scale message passing neural network algorithm for learning the solutions of time-dependent PDEs. Our algorithm possesses both temporal and spatial multi-scale resolution features by incorporating multi-scale sequence models and graph gating modules in the encoder and processor, respectively. Benchmark numerical experiments are presented to demonstrate that the proposed algorithm outperforms baselines, particularly on a PDE with a range of spatial and temporal scales.

Keywords: Graph neural network (GNN), Partial Differential Equation (PDE), Message-Passing, Multi-scale, Long Expressive Memory (LEM), Gradient Gating (G^2)

@Techreport{ERM23_1051,
  author = {L. Equer and T. K. Rusch and S. Mishra},
  title = {Multi-Scale Message Passing Neural PDE Solvers},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2023-14},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2023/2023-14.pdf },
  year = {2023}
}

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