Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems

Understand

Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications.

• First, most existing PINNs are based on point-wise formulation with fully-connected networks to learn continuous functions, which suffer from poor scalability and hard boundary enforcement.
• Second, the infinite search space over-complicates the non-convex optimization for network training.
• Third, although the convolutional neural network (CNN)-based discrete learning can significantly improve training efficiency, CNNs struggle to handle irregular geometries with unstructured meshes.