Solving spatiotemporal partial differential equations with Physics-informed Graph Neural Network

Zixue Xiang, Wei Peng, Wen Yao, Xu Liu, Xiaoya Zhang

Abstract: Highlights•This study proposes a physics-informed framework (RBF-MGN) based on GNNs and RBF-FD to solve spatio-temporal PDEs. We introduce graph neural networks into a physics-informed learning framework to handle irregular domains better. We choose MeshGraphNets, a graph neural network model with an Encoder-Processor-Decoder architecture, to model the discretized solution.•Radial basis function finite difference, a meshless method, is used to process the node solution maps of model output and construct high-precision difference formats for PDEs. It ensures that the model output fully satisfies the essential boundary conditions and guides the model training by defining a loss function.•We conduct several experiments on heat, wave, and shallow water equations to evaluate the performance of RBF-MGN on irregular domains. The results indicate that RBF-MGN allows for accurate inference with different initial conditions, Gaussian noise, PDE parameters, numbers of collection points, and various types of radial basis functions.