Crack is one of the critical factors that degrade the performance of machinery manufacturing equipment. Recently, physics-informed neural networks (PINNs) have received attention due to their strong potential in solving physical problems. For fracture problems, PINNs have been used to predict crack paths by minimizing the variational energy of discrete domains where refined meshes are necessary. To obtain refined meshes, posteriori adaptive refinement techniques are commonly used to perform local refinement of the mesh based on errors in the intermediate calculation process; thus, they require pretest calculations. However, it is computationally expensive to precalculate complex problems, especially crack propagation. To solve this problem, we propose a PointNet-based adaptive refinement method to avoid precalculation when constructing the discrete domain. The proposed method is applied to simulate crack propagation using a PINN. Results show that the proposed method can be used to obtain reliable results efficiently when using the PINN framework.

中文翻译：

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物理信息神经网络集成基于 PointNet 的自适应细化以研究工业应用中的裂纹扩展

裂纹是降低机械制造设备性能的关键因素之一。最近，物理信息神经网络（PINN）因其在解决物理问题方面的强大潜力而受到关注。对于断裂问题，PINN 已用于通过最小化需要细化网格的离散域的变分能量来预测裂纹路径。为了获得细化的网格，通常使用后验自适应细化技术根据中间计算过程中的误差对网格进行局部细化；因此，他们需要进行预测试计算。然而，预先计算复杂问题的计算成本很高，尤其是裂纹扩展。为了解决这个问题，我们提出了一种基于 PointNet 的自适应细化方法，以避免在构建离散域时进行预先计算。所提出的方法适用于使用 PINN 模拟裂纹扩展。结果表明，当使用 PINN 框架时，所提出的方法可以有效地获得可靠的结果。