Deep learning-driven domain decomposition (DLD3): A generalizable AI-driven framework for structural analysis

Abstract

A novel, generalizable Artificial Intelligence (AI)-driven technique, termed Deep Learning-Driven Domain Decomposition (DLD${}^3$), is introduced for simulating two-dimensional linear elasticity problems with arbitrary geometries and boundary conditions (BCs). The DLD${}^3$ framework leverages trained AI models to predict the displacement field within small subdomains, each characterized by varying geometries and BCs. To enforce continuity across the entire domain, the overlapping Schwarz domain decomposition method (DDM) iteratively updates the BCs of each subdomain, thus approximating the overall solution. After evaluating multiple model architectures, the Fourier Neural Operator (FNO) was selected as the AI engine for the DLD${}^3$ method, owing to its data efficiency and high accuracy. We also present a framework that utilizes geometry reconstruction and automated meshing algorithms to generate millions of training data points from high-fidelity finite element (FE) simulations. Several case studies are provided to demonstrate the DLD${}^3$ algorithm’s ability to accurately predict displacement fields in problems involving complex geometries, diverse BCs, and material properties.