RIGNO: A Graph-based framework for robust and accurate operator learning for PDEs on arbitrary domains
This work addresses the problem of accurate and robust operator learning for PDEs on diverse domains, which is crucial for applications in physics and engineering, representing a strong specific gain in the field.
The authors tackled the challenge of learning PDE solution operators on arbitrary domains by proposing RIGNO, a graph neural network-based neural operator that uses a multi-scale approach with a downsampled regional mesh, achieving significantly higher accuracy and robust generalization to unseen spatio-temporal resolutions compared to baselines.
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.