# Crack Path Prediction with Operator Learning using Discrete Particle System data Generation

arXiv: https://arxiv.org/abs/2506.01976 · HTML: https://mlsanity.com/paper/2506.01976/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 63 references that are in the map.
- First posted on arXiv 15 May 2025.

## Builds on (most cited first, 15 of 15)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions](https://mlsanity.com/paper/2105.09513/) (2021)
- [Optimizing the Optimizer for Physics-Informed Neural Networks and Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2501.16371/) (2025)
- [A review on data-driven constitutive laws for solids](https://mlsanity.com/paper/2405.03658/) (2024)
- [Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularity](https://mlsanity.com/paper/2405.19166/) (2024)
- [On the training and generalization of deep operator networks](https://mlsanity.com/paper/2309.01020/) (2023)
- [Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systems](https://mlsanity.com/paper/2503.13695/) (2025)
- [RiemannONets: Interpretable Neural Operators for Riemann Problems](https://mlsanity.com/paper/2401.08886/) (2024)
- [A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Data](https://mlsanity.com/paper/2305.10706/) (2023)
- [Fusion-DeepONet: A Data-Efficient Neural Operator for Geometry-Dependent Hypersonic and Supersonic Flows](https://mlsanity.com/paper/2501.01934/) (2025)
- [Predicting Crack Nucleation and Propagation in Brittle Materials Using Deep Operator Networks with Diverse Trunk Architectures](https://mlsanity.com/paper/2501.00016/) (2024)
- [Bridging scales in multiscale bubble growth dynamics with correlated fluctuations using neural operator learning](https://mlsanity.com/paper/2403.13299/) (2024)

## Abstract (arXiv)

Accurately modeling crack propagation is critical for predicting failure in engineering materials and structures, where small cracks can rapidly evolve and cause catastrophic damage. The interaction of cracks with discontinuities, such as holes, significantly affects crack deflection and arrest. Recent developments in discrete particle systems with multibody interactions based on constitutive behavior have demonstrated the ability to capture crack nucleation and evolution without relying on continuum assumptions. In this work, we use data from Constitutively Informed Particle Dynamics (CPD) simulations to train operator learning models, specifically Deep Operator Networks (DeepONets), which learn mappings between function spaces instead of finite-dimensional vectors. We explore two DeepONet variants: vanilla and Fusion DeepONet, for predicting time-evolving crack propagation in specimens with varying geometries. Three representative cases are studied: (i) varying notch height without active fracture; and (ii) and (iii) combinations of notch height and hole radius where dynamic fracture occurs on irregular discrete meshes. The models are trained using geometric inputs in the branch network and spatial-temporal coordinates in the trunk network. Results show that Fusion DeepONet consistently outperforms the vanilla variant, with more accurate predictions especially in non-fracturing cases. Fracture-driven scenarios involving displacement and crack evolution remain more challenging. These findings highlight the potential of Fusion DeepONet to generalize across complex, geometry-varying, and time-dependent crack propagation phenomena.