A Graph-Structured, Physics-Informed DeepONet Neural Network for Complex Structural Analysis

This study introduces the Graph-Structured Physics-Informed DeepONet (GS-PI-DeepONet), a novel neural network framework designed to address the challenges of solving parametric Partial Differential Equations (PDEs) in structural analysis, particularly for problems with complex geometries and dynamic boundary conditions. By integrating Graph Neural Networks (GNNs), Deep Operator Networks (DeepONets), and Physics-Informed Neural Networks (PINNs), the proposed method employs graph-structured representations to model unstructured Finite Element (FE) meshes. In this framework, nodes encode physical quantities such as displacements and loads, while edges represent geometric or topological relationships. The framework embeds PDE constraints as soft penalties within the loss function, ensuring adherence to physical laws while reducing reliance on large datasets. Extensive experiments have demonstrated the GS-PI-DeepONet’s superiority over traditional Finite Element Methods (FEMs) and standard DeepONets. For benchmark problems, including cantilever beam bending and Hertz contact, the model achieves high accuracy. In practical applications, such as stiffness analysis of a recliner mechanism and strength analysis of a support bracket, the framework achieves a 7–8 speed-up compared to FEMs, while maintaining fidelity comparable to FEM, with R2 values reaching up to 0.9999 for displacement fields. Consequently, the GS-PI-DeepONet offers a resolution-independent, data-efficient, and physics-consistent approach for real-time simulations, making it ideal for rapid parameter sweeps and design optimizations in engineering applications.