cs.LG · 2607.09382 Copy arXiv ID · Jul 10, 2026 Save Learning Physics-Informed Surrogate Model of Linear Elastic Displacement Fields from Geometry Authors: Rodolphe Barlogis , Ferhat Tamssaouet , Quentin Falcoz , Stéphane Grieu
Organizations: PROMES-CNRS, Universit´e Perpignan Via Domitia (UPVD), Perpignan, France · LAAS-CNRS, Universit´e de Toulouse (UT), Toulouse, France
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.
Explore similar work Jun 12, 2026 · Hyeonbin Moon, Yongjin Choi, Seunghwa Ryu Finite Element Method Surrogate Models
May 1, 2026 · Rodolphe Barlogis, Ferhat Tamssaouet, Quentin Falcoz +1
Jun 12, 2026 · cs.LG J/K move · Enter open · S save
Hyeonbin Moon, Yongjin Choi, Seunghwa Ryu
Scientific machine learning (SciML) has emerged as a promising approach for accelerating simulations of complex physical systems, yet achieving physically consistent and generalizable predictions for nonlinear, history-dependent problems remains a central challenge. In this study, we propose a hybrid GNN--FEM framework for efficient and generalizable phase-field fracture modeling. While phase-field approaches provide a robust variational framework for simulating complex crack evolution, their high computational cost limits practical applications because they require solving coupled, nonlinear, and history-dependent systems within an incremental finite element procedure. To address this challenge, a graph neural network surrogate is integrated into the conventional staggered scheme, replacing the phase-field update at each load increment while retaining the FEM-based displacement solver to enforce mechanical equilibrium and boundary conditions. By preserving the incremental solution structure, the framework remains consistent with history-dependent fracture evolution without requiring the surrogate to approximate the full solution trajectory. This selective surrogate strategy emphasizes the identification of a physically meaningful and incrementally structured learning target, rather than relying on brute-force data generation to learn the full fracture process. The proposed framework achieves strong generalization across varying geometries, loading conditions, material properties, and discretizations through dimensionless feature design, a graph-based formulation on mesh-based domains, and a physics-informed loss derived from the governing phase-field equation. Numerical experiments demonstrate that the hybrid approach reduces computational cost while maintaining accuracy compared with conventional FEM, and exhibits robust predictive performance across diverse problem settings.