# A Hybrid GNN-FEM Framework for Phase-Field Fracture Simulation. Physics-Preserving Hybridization for Generalizable Surrogate Modeling

arXiv: https://arxiv.org/abs/2606.19378 · HTML: https://mlsanity.com/paper/2606.19378/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 45 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Builds on (most cited first, 16 of 16)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning](https://mlsanity.com/paper/2203.16797/) (2022)
- [Hybrid FEM-NN models: Combining artificial neural networks with the finite element method](https://mlsanity.com/paper/2101.00962/) (2021)
- [Modular machine learning-based elastoplasticity: generalization in the context of limited data](https://mlsanity.com/paper/2210.08343/) (2022)
- [Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)](https://mlsanity.com/paper/2503.05617/) (2025)
- [Predicting Crack Nucleation and Propagation in Brittle Materials Using Deep Operator Networks with Diverse Trunk Architectures](https://mlsanity.com/paper/2501.00016/) (2024)
- [Towards out of distribution generalization for problems in mechanics](https://mlsanity.com/paper/2206.14917/) (2022)
- [A physics-augmented neural network framework for finite strain incompressible viscoelasticity](https://mlsanity.com/paper/2511.02959/) (2025)
- [Integrated Finite Element Neural Network (IFENN) for Phase-Field Fracture with Minimal Input and Generalized Geometry-Load Handling](https://mlsanity.com/paper/2505.19566/) (2025)
- [Towards Robust Surrogate Models: Benchmarking Machine Learning Approaches to Expediting Phase Field Simulations of Brittle Fracture](https://mlsanity.com/paper/2507.07237/) (2025)
- [XRePIT: A deep learning-computational fluid dynamics hybrid framework implemented in OpenFOAM for fast, robust, and scalable unsteady simulations](https://mlsanity.com/paper/2510.21804/) (2025)

## Abstract (arXiv)

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.