构建复杂断裂模拟数据集,测试机器学习模型加速相场模拟的性能。
Towards Robust Surrogate Models: Benchmarking Machine Learning Approaches to Expediting Phase Field Simulations of Brittle Fracture
- 基于相场法生成6000组复杂断裂仿真数据,含100个时间步
- 对比PINN、FNO和UNet在准确性和鲁棒性上的表现差异
- 适合做固体力学中机器学习加速仿真的研究者参考
数据驱动方法有望显著提升复杂非线性物理现象建模的计算效率。例如,断裂模拟是核心挑战之一,机器学习可带来亟需的速度提升,推动多尺度建模与不确定性量化发展。目前,相场建模(PFM)提供了便捷的变分框架,用于模拟裂纹成核、分叉与扩展。尽管已有研究显示机器学习可近似PFM仿真,但多数依赖过于简单的基准,未能反映PFM在真实断裂过程中的复杂性。为此,我们构建了一个具有挑战性的数据集,基于PFM模拟设计,包含三种能量分解方法、两种边界条件和1000个随机初始裂纹配置,共6000次仿真,每样本包含100个时间步,捕捉裂纹场随时间演化。同时,我们实现并评估了物理信息神经网络(PINN)、傅里叶神经算子(FNO)和UNet作为基线模型,并探索集成策略对预测精度的影响。结合该数据集与文献中的基线模型,旨在为机器学习在固体力学中的应用提供标准化且具挑战性的基准。结果揭示了现有模型的潜力与局限,证明该数据集作为推进断裂力学中机器学习研究的测试平台的实用性。
原文摘要 · Abstract (English)
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.
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