G-PARC: Graph Neural Network Model for Spatiotemporal Dynamics on Unstructured Meshes

A new neural network architecture called Graph PARC (G-PARC) has been developed to predict nonlinear spatiotemporal dynamics on unstructured meshes. The model addresses limitations in existing physics-aware deep learning methods by using moving least squares kernels to approximate spatial derivatives on irregular graphs. G-PARC embeds derivatives of governing partial differential equations directly into the network's computational graph. This approach achieves better accuracy with 2-3 times fewer parameters than previous methods. The research was announced on arXiv under identifier 2604.16533v1. Physics-aware recurrent convolutional networks (PARC) previously demonstrated strong performance but were restricted to static, uniform Cartesian grids. Graph neural networks naturally handle irregular spatial discretizations but struggle with extreme nonlinear regimes. The proposed method combines strengths from both approaches to efficiently follow evolving localized structures.