Multi-Scale Message Passing Neural PDE Solvers

TL;DR

This paper introduces a multi-scale message passing neural network for efficiently solving time-dependent PDEs, capturing multiple spatial and temporal scales, and demonstrating superior performance on benchmark problems.

Contribution

The paper presents a novel multi-scale message passing neural network that integrates sequence models and graph gating for solving PDEs across multiple scales.

Findings

Outperforms baseline methods on benchmark PDE problems.

Effectively captures multi-scale spatial and temporal features.

Demonstrates robustness across diverse PDEs.

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.