Towards Robust Surrogate Models: Benchmarking Machine Learning Approaches to Expediting Phase Field Simulations of Brittle Fracture
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Abstract (arXiv)
Data driven approaches have the potential to make modeling complex, nonlinear physical phenomena significantly more computationally tractable. For example, computational modeling of fracture is a core challenge where machine learning techniques have the potential to provide a much needed speedup that would enable progress in areas such as mutli-scale modeling and uncertainty quantification. Currently, phase field modeling (PFM) of fracture is one such approach that offers a convenient variational formulation to model crack nucleation, branching and propagation. To date, machine learning techniques have shown promise in approximating PFM simulations. However, most studies rely on overly simple benchmarks that do not reflect the true complexity of the fracture processes where PFM excels as a method. To address this gap, we introduce a challenging dataset based on PFM simulations designed to benchmark and advance ML methods for fracture modeling. This dataset includes three energy decomposition methods, two boundary conditions, and 1,000 random initial crack configurations for a total of 6,000 simulations. Each sample contains 100 time steps capturing the temporal evolution of the crack field. Alongside this dataset, we also implement and evaluate Physics Informed Neural Networks (PINN), Fourier Neural Operators (FNO) and UNet models as baselines, and explore the impact of ensembling strategies on prediction accuracy. With this combination of our dataset and baseline models drawn from the literature we aim to provide a standardized and challenging benchmark for evaluating machine learning approaches to solid mechanics. Our results highlight both the promise and limitations of popular current models, and demonstrate the utility of this dataset as a testbed for advancing machine learning in fracture mechanics research.
Key facts. Cited by 1 paper in the map (data through 13 Oct 2026). Builds on 59 of its 133 references that are in the map. First posted on arXiv 9 Jul 2025.
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References · 59
- 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,223
- 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,656
- 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,902
- 2022A ConvNet for the 2020scited by 3,563
- 2017Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layercited by 3,463
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,857
- 2018The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networkscited by 2,257
- 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,183
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,989
- 2016Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Networkcited by 1,906
- 2018On the Spectral Bias of Neural Networkscited by 1,329
- 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 728
38 more
- 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 633
- 2019DeepXDE: A deep learning library for solving differential equationscited by 618
- 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 582
- 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 538
- 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 472
- 2019Deep Ensembles: A Loss Landscape Perspectivecited by 441
- 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 406
- 2022Message Passing Neural PDE Solverscited by 378
- 2019Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networkscited by 363
- 2017Snapshot Ensembles: Train 1, get M for freecited by 350
- 2014Identifying and attacking the saddle point problem in high-dimensional non-convex optimizationcited by 288
- 2021Ensemble deep learning: A reviewcited by 284
- 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
- 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solverscited by 212
- 2021Accounting for Variance in Machine Learning Benchmarkscited by 195
- 2022Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisonscited by 170
- 2019Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networkscited by 145
- 2024The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learningcited by 140
- 2019Transfer learning enhanced physics informed neural network for phase-field modeling of fracturecited by 116
- 2022Physics-Informed Deep Neural Operator Networkscited by 112
- 2021A physics-informed variational DeepONet for predicting the crack path in brittle materialscited by 98
- 2023Multiple Physics Pretraining for Physical Surrogate Modelscited by 94
- 2018Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantificationcited by 81
- 2019Physics-Informed Neural Networks for Power Systemscited by 80
- 2020A physics-informed operator regression framework for extracting data-driven continuum modelscited by 60
- 2023Learning Physical Models that Can Respect Conservation Lawscited by 59
- 2018Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous mediacited by 56
- 2025Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraintscited by 48
- 2022Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priorscited by 39
- 2019VarNet: Variational Neural Networks for the Solution of Partial Differential Equationscited by 35
- 2024Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularitycited by 34
- 2025Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systemscited by 29
- 2019Multi-scale Deep Neural Networks for Solving High Dimensional PDEscited by 24
- 2024Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspectivecited by 24
- 2014On the saddle point problem for non-convex optimizationcited by 20
- 2024A review of graph neural network applications in mechanics-related domainscited by 14
- 2024Predicting Crack Nucleation and Propagation in Brittle Materials Using Deep Operator Networks with Diverse Trunk Architecturescited by 12
- 2021Predicting Mechanically Driven Full-Field Quantities of Interest with Deep Learning-Based Metamodelscited by 10
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