Towards Robust Surrogate Models: Benchmarking Machine Learning Approaches to Expediting Phase Field Simulations of Brittle Fracture

2025-07-09

AI Summary

Existing machine learning methods for phase-field fracture modeling (PFM) are predominantly evaluated on oversimplified benchmarks, failing to capture realistic, complex fracture behaviors. Method: We introduce the first standardized, high-complexity benchmark dataset for brittle fracture—comprising 6,000 samples—featuring diverse energy decomposition schemes, heterogeneous boundary conditions, and stochastic initial crack configurations, enabling multiscale and uncertainty-aware evaluation. Using this dataset, we systematically assess three representative architectures—physics-informed neural networks (PINNs), Fourier neural operators (FNOs), and U-Net—and enhance their generalization and robustness via ensemble learning. Contribution/Results: Experiments uncover shared limitations of current models in capturing strongly nonlinear fracture evolution, validating the dataset’s efficacy for rigorous reliability assessment. This work establishes a scalable, multiphysics-coupled testbed for trustworthy, mechanics-driven AI research.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

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.

Problem

• Benchmarking ML models for accelerating phase field fracture simulations
• Addressing lack of complex datasets for fracture process modeling
• Evaluating ML approaches to improve solid mechanics simulation accuracy

Innovation

• Physics Informed Neural Networks for fracture modeling
• Fourier Neural Operators as baseline benchmarks
• UNet models with ensembling strategies