Physics-Informed Neural Networks (PINNs) have aroused great attention for its ability to address forward and inverse problems of partial differential equations. However, approximating discontinuous functions by neural networks poses a considerable challenge, which results in high computational demands and low accuracy to solve fracture mechanics problems within standard PINNs framework. In this paper, we present a novel method called Discontinuity Embedded Deep Energy Method (DEDEM) for modeling fracture mechanics problems. In this method, interfaces and internal boundaries with weak/strong discontinuities are represented by discontinuous functions constructed by signed distance functions, then the representations are embedded to the input of the neural network so that specific discontinuous features can be imposed to the neural network solution. Results demonstrate that DEDEM can accurately model the mechanical behaviors of cracks on a large variety of fracture problems. Besides, it is also found that DEDEM achieves significantly higher computational efficiency and accuracy than the existing methods based on domain decomposition techniques.

翻译：物理信息神经网络因其处理偏微分方程正反问题的能力而受到广泛关注。然而，神经网络逼近间断函数存在显著挑战，导致在标准PINNs框架下求解断裂力学问题时计算需求高且精度低。本文提出一种称为间断嵌入深度能量法的新方法，用于模拟断裂力学问题。该方法利用符号距离函数构造的间断函数来表示具有弱/强间断性的界面与内部边界，随后将这些表征嵌入神经网络的输入层，从而将特定的间断特征赋予神经网络解。结果表明，DEDEM能够准确模拟多种断裂问题中裂纹的力学行为。此外，研究发现DEDEM相比现有基于区域分解技术的方法，在计算效率与精度上均有显著提升。