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

arXiv: https://arxiv.org/abs/2607.09382 · HTML: https://mlsanity.com/paper/2607.09382/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 11 references that are in the map.
- First posted on arXiv 10 Jul 2026.

## Builds on (most cited first, 3 of 3)

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Predicting Crack Nucleation and Propagation in Brittle Materials Using Deep Operator Networks with Diverse Trunk Architectures](https://mlsanity.com/paper/2501.00016/) (2024)

## Abstract (arXiv)

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.