mlsanityData to 14 Oct 2026

Predicting Crack Nucleation and Propagation in Brittle Materials Using Deep Operator Networks with Diverse Trunk Architectures

arXiv 2501.00016 ↗First posted 15 Dec 2024physics.comp-ph cs.AIcited by 12

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Abstract (arXiv)

Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merging, and branching, without relying on ad-hoc assumptions. However, the numerical solution of phase-field fracture problems is characterized by a high computational cost. To address this challenge, in this paper, we employ a deep neural operator (DeepONet) consisting of a branch network and a trunk network to solve brittle fracture problems. We explore three distinct approaches that vary in their trunk network configurations. In the first approach, we demonstrate the effectiveness of a two-step DeepONet, which results in a simplification of the learning task. In the second approach, we employ a physics-informed DeepONet, whereby the mathematical expression of the energy is integrated into the trunk network's loss to enforce physical consistency. The integration of physics also results in a substantially smaller data size needed for training. In the third approach, we replace the neural network in the trunk with a Kolmogorov-Arnold Network and train it without the physics loss. Using these methods, we model crack nucleation in a one-dimensional homogeneous bar under prescribed end displacements, as well as crack propagation and branching in single edge-notched specimens with varying notch lengths subjected to tensile and shear loading. We show that the networks predict the solution fields accurately, and the error in the predicted fields is localized near the crack.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 20 of its 47 references that are in the map. First posted on arXiv 15 Dec 2024.

Builds on

20 of 47 references.

References · 20

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  3. 2017Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semanticscited by 1,358
  4. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
  5. 2024Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximationcited by 118
  6. 2019Transfer learning enhanced physics informed neural network for phase-field modeling of fracturecited by 116
  7. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 104
  8. 2021A physics-informed variational DeepONet for predicting the crack path in brittle materialscited by 98
  9. 2024On the expressiveness and spectral bias of KANscited by 37
  10. 2024Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modelingcited by 36
  11. 2024A review on data-driven constitutive laws for solidscited by 35
  12. 2024Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularitycited by 34
8 more
  1. 2023On the training and generalization of deep operator networkscited by 31
  2. 2024RiemannONets: Interpretable Neural Operators for Riemann Problemscited by 28
  3. 2021Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential trainingcited by 26
  4. 2023Phase-Field DeepONet: Physics-informed deep operator neural network for fast simulations of pattern formation governed by gradient flows of free-energy functionalscited by 26
  5. 2024Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networkscited by 20
  6. 2023A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Datacited by 18
  7. 2022Revisiting PINNs: Generative Adversarial Physics-informed Neural Networks and Point-weighting Methodcited by 10
  8. 2023Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNscited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 10; 2026: 2.

12 papers.

  1. 2025Optimizing the Optimizer for Physics-Informed Neural Networks and Kolmogorov-Arnold Networkscited by 42
  2. 2025Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systemscited by 31
  3. 2025A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learningcited by 6
  4. 2025Probabilistic Predictions of Process-Induced Deformation in Carbon/Epoxy Composites Using a Deep Operator Networkcited by 3
  5. 2025AMORE: Adaptive Multi-Output Operator Network for Stiff Chemical Kineticscited by 2
  6. 2025Learning Physical Systems: Symplectification via Gauge Fixing in Dirac Structurescited by 1
  7. 2025Towards Robust Surrogate Models: Benchmarking Machine Learning Approaches to Expediting Phase Field Simulations of Brittle Fracturecited by 1
  8. 2025MINPO: Memory-Informed Neural Pseudo-Operator to Resolve Nonlocal Spatiotemporal Dynamicscited by 1
  9. 2025Crack Path Prediction with Operator Learning using Discrete Particle System data Generationcited by 0
  10. 2025From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systemscited by 0
  11. 2026A Hybrid GNN-FEM Framework for Phase-Field Fracture Simulation. Physics-Preserving Hybridization for Generalizable Surrogate Modelingcited by 0
  12. 2026Learning Physics-Informed Surrogate Model of Linear Elastic Displacement Fields from Geometrycited by 0