We explore the potential of the deep Ritz method to learn complex fracture processes such as quasistatic crack nucleation, propagation, kinking, branching, and coalescence within the unified variational framework of phase-field modeling of brittle fracture. We elucidate the challenges related to the neural-network-based approximation of the energy landscape, and the ability of an optimization approach to reach the correct energy minimum, and we discuss the choices in the construction and training of the neural network which prove to be critical to accurately and efficiently capture all the relevant fracture phenomena. The developed method is applied to several benchmark problems and the results are shown to be in qualitative and quantitative agreement with the finite element solution. The robustness of the approach is tested by using neural networks with different initializations.

中文翻译：

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利用基于物理的深度学习进行断裂相场建模


我们探索了深度 Ritz 方法在脆性断裂相场建模的统一变分框架内学习复杂断裂过程的潜力，例如准静态裂纹成核、扩展、扭结、分支和合并。我们阐明了与基于神经网络的能源景观近似相关的挑战，以及优化方法达到正确能量最小值的能力，并讨论了神经网络的构建和训练中的选择，这些选择被证明是对于准确有效地捕获所有相关的断裂现象至关重要。所开发的方法应用于几个基准问题，结果显示与有限元解在定性和定量上一致。通过使用具有不同初始化的神经网络来测试该方法的鲁棒性。