PI-GEFN: A Physics-Informed Graph Edge Filter Network inspired by finite element formulation

Abstract

This work introduces PI-GEFN, a Physics-Informed Graph Edge Filter Network inspired by finite element methods (FEM), designed to solve both forward and inverse problems in linear elasticity. Unlike conventional graph neural networks (GNNs) that abstract physical relationships, PI-GEFN integrates physically meaningful stiffness contributions as edge features and incorporates residual-based loss functions derived from the FEM system. This architecture enables the surrogate model to preserve the equilibrium characteristics of the physical system while remaining scalable and data-efficient. We demonstrate the model’s effectiveness across various parametric regimes including geometry variations, material properties, and Neumann boundary conditions achieving high accuracy in displacement predictions and parameter identification. The model performs robustly even under sparse supervision and demonstrates competitive accuracy and convergence with PINN-based methods. These qualities position PI-GEFN as a versatile and physically grounded surrogate modeling tool for real-time simulation, design, and inverse identification tasks in computational mechanics.