In this paper, we propose a novel data‐driven method that uses a machine learning scheme for formulating fracture simulation with the boundary element method (BEM) as a regression problem. With this method, the crack opening displacement (COD) of every correlation node is predicted at the next frame. In our naive prediction, we design a feature vector directly exploiting stress intensities and toughness at the current frame so that our method predicts the COD at the next frame more reliably. Thus, there is no need to solve the original linear BEM system to calculate displacements. This enables us to propagate crack fronts using the estimated stress intensities. There are existing works that use the machine learning approach to accelerate the speed of traditional physics‐based simulations like smoke and fluid, but our work is the first to incorporate the machine learning scheme into BEM‐based fracture simulations. Our implementation accelerates the acquisition of displacements in linear time over the number of crack fronts at each time step compared with the conventional solution whose time complexity grows exponentially based on the BEM linear system. The databases generated by our method are versatile and can be applied to general situations and different models.

中文翻译：

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从通用数据库预测脆性断裂表面形状

在本文中，我们提出了一种新的数据驱动方法，该方法使用机器学习方案，以边界元法 (BEM) 作为回归问题来制定裂缝模拟。使用这种方法，在下一帧预测每个相关节点的裂纹张开位移（COD）。在我们的天真预测中，我们设计了一个特征向量，直接利用当前帧的应力强度和韧性，以便我们的方法更可靠地预测下一帧的 COD。因此，无需求解原始线性边界元系统来计算位移。这使我们能够使用估计的应力强度扩展裂纹前沿。现有的工作使用机器学习方法来加快传统的基于物理的模拟（如烟雾和流体）的速度，但我们的工作是第一个将机器学习方案纳入基于边界元法的断裂模拟的工作。与基于边界元线性系统的时间复杂度呈指数增长的传统解决方案相比，我们的实现在每个时间步长的裂纹前沿数量上加速了线性时间内位移的获取。我们的方法生成的数据库是通用的，可以应用于一般情况和不同的模型。