Amortizing Physics-Informed Neural Solvers via Graph Hypernetworks

This paper introduces a graph hypernetwork approach for amortizing Physics-Informed Neural Networks (PINNs) across related PDEs. The method explicitly represents PDE components including fields, derivatives, terms, and residuals as nodes in an operator graph, with coefficients retained as term attributes. A graph hypernetwork generates diagonal initialization codes for meta-trained factorization, enabling efficient knowledge transfer across different PDE configurations.