Message Passing is all you need!

This study presents a novel approach to deepening the physical understanding of message passing architectures within simulations of physical systems. By tailoring the design to the underlying nature of hyperbolic, parabolic, and elliptic partial differential equations (PDEs), the method ensures effective information propagation throughout the computational domain. This alignment between Graph Neural Network (GNN) architecture and the governing physical principles enhances both the accuracy and robustness of simulations, enabling more efficient and high-fidelity modeling across diverse physical regimes.