PhyGNNet: Solving spatiotemporal PDEs with Physics-informed Graph Neural Network
This work addresses a bottleneck in PDE solving for fields like physics and chemistry, though it is incremental as it builds on existing PINN methods with a graph-based approach.
The paper tackles the limited fitting and extrapolation ability of Physics-informed Neural Networks (PINNs) for solving spatiotemporal PDEs by proposing PhyGNNet, a physics-informed graph neural network, which shows better performance on Burgers and heat equations compared to PINN.
Solving partial differential equations (PDEs) is an important research means in the fields of physics, biology, and chemistry. As an approximate alternative to numerical methods, PINN has received extensive attention and played an important role in many fields. However, PINN uses a fully connected network as its model, which has limited fitting ability and limited extrapolation ability in both time and space. In this paper, we propose PhyGNNet for solving partial differential equations on the basics of a graph neural network which consists of encoder, processer, and decoder blocks. In particular, we divide the computing area into regular grids, define partial differential operators on the grids, then construct pde loss for the network to optimize to build PhyGNNet model. What's more, we conduct comparative experiments on Burgers equation and heat equation to validate our approach, the results show that our method has better fit ability and extrapolation ability both in time and spatial areas compared with PINN.