RIGNO: A Graph-based Framework For Robust And Accurate Operator Learning For PDEs On Arbitrary Domains

Sepehr Mousavi, Shizheng Wen, Levi Lingsch, Maximilian Herde, Bogdan Raonic, Siddhartha Mishra

Keywords: scientific machine learning, operator learning, partial differential equation, neural operator, graph neural network, AI for science, computational science

TL;DR: We propose a very performant graph-based neural operator architecture for learning the solution operator of PDEs from data on arbitrary domain discretizations, which has been tested on a challenging suite of benchmark datasets.

Abstract: Learning the solution operators of PDEs on arbitrary domains is challenging due to the diversity of possible domain shapes, in addition to the often intricate underlying physics. We propose an end-to-end graph neural network (GNN) based neural operator to learn PDE solution operators from data on point clouds in arbitrary domains. Our multi-scale model maps data between input/output point clouds by passing it through a downsampled regional mesh. The approach includes novel elements aimed at ensuring spatio-temporal resolution invariance. Our model, termed RIGNO, is tested on a challenging suite of benchmarks composed of various time-dependent and steady PDEs defined on a diverse set of domains. We demonstrate that RIGNO is significantly more accurate than neural operator baselines and robustly generalizes to unseen resolutions both in space and in time. Our code is publicly available at github.com/camlab-ethz/rigno.

Primary Area: Machine learning for sciences (e.g. climate, health, life sciences, physics, social sciences)

Submission Number: 12900