Learning Physics-Informed Surrogate Model of Linear Elastic Displacement Fields from Geometry

2026-07-10

AI Summary

This work addresses the need for real-time structural health monitoring of cracked elastic bodies by proposing a physics-informed Deep Operator Network (DeepONet) that predicts linear elastic displacement fields directly from boundary conditions and crack geometry without relying on simulation data. The approach introduces a crack-geometry-specific encoding strategy and incorporates a weak-form local penalty term into the loss function to enforce traction-free boundary conditions, enabling unsupervised learning under physically consistent constraints. Validated across diverse crack configurations, the method achieves both high-fidelity predictions and real-time inference, offering a novel paradigm for surrogate modeling of complex cracked systems.

Abstract

This work aims to develop a fast and physically consistent surrogate model for real-time structural health monitoring of fractured elastic domains. We propose a physics-informed DeepONet framework that predicts displacement fields from both boundary conditions and fracture geometry, using a dedicated encoding strategy for the latter and without relying on finite-element-generated training data. The traction-free condition on the fracture boundary is imposed weakly through a localized penalty term. The presented numerical example focuses on one representative fracture geometry, demonstrating the feasibility of the formulation and laying the groundwork for extensions to surrogate modeling across diverse fracture geometries.

Problem

• surrogate model
• linear elasticity
• fracture geometry
• displacement field
• structural health monitoring

Innovation

• Physics-informed DeepONet
• surrogate modeling
• fracture geometry encoding
• traction-free boundary condition
• real-time structural health monitoring