Physics-Informed DeepONet Models Fracture Displacement Fields

This research introduces a novel physics-informed DeepONet framework aimed at creating a fast and physically consistent surrogate model for structural health monitoring, particularly in fractured elastic domains. The model is designed to predict displacement fields based on both boundary conditions and the specific geometry of fractures. A key innovation is its ability to operate without requiring extensive training data generated by traditional finite-element methods. Instead, the framework incorporates physical laws directly into its learning process by weakly imposing the traction-free condition on the fracture boundaries using a localized penalty term. The paper presents a numerical example focusing on a single representative fracture geometry, demonstrating the feasibility of this formulation. This foundational work paves the way for future extensions to surrogate modeling across a wider variety of fracture geometries, offering potential for real-time applications in engineering.