论文标题
基于动态和自适应网格的图形神经网络框架，用于模拟相位场模型中的位移和破裂场
Dynamic and adaptive mesh-based graph neural network framework for simulating displacement and crack fields in phase field models
论文作者
论文摘要
断裂是工程结构失败的主要原因之一。相结合的相结合方法与自适应网格改进（AMR）技术相结合，由于其易于实现和可伸缩性，已广泛用于建模裂纹传播。但是，相位场方法仍然可以在计算上要求，使其对于高通量设计应用程序不可行。与高保真模拟器相比，机器学习（ML）模型（例如图形神经网络（GNN））表明，它们可以通过加速级别的速度更快地模拟复杂的动态问题。在这项工作中，我们提出了一个基于动态网格的GNN框架，用于使用AMR模拟裂纹传播的相位场模拟，以进行不同的裂纹配置。开发的框架 - 基于自适应网格的图形神经网络（Adapt-gnn） - 通过将每个时间步长的图表表示为精制的网格本身来利用ML方法和AMR的好处。使用Adapt-GNN，我们预测与常规相位场断裂模型相比，准确性高的位移场和标量损伤场的演变。我们还使用预测的位移和相位场参数来计算高精度的裂纹应力场。最后，与相位场模型的连续执行相比，我们观察到15-36倍的速度。
Fracture is one of the main causes of failure in engineering structures. Phase field methods coupled with adaptive mesh refinement (AMR) techniques have been widely used to model crack propagation due to their ease of implementation and scalability. However, phase field methods can still be computationally demanding making them unfeasible for high-throughput design applications. Machine learning (ML) models such as Graph Neural Networks (GNNs) have shown their ability to emulate complex dynamic problems with speed-ups orders of magnitude faster compared to high-fidelity simulators. In this work, we present a dynamic mesh-based GNN framework for emulating phase field simulations of crack propagation with AMR for different crack configurations. The developed framework - ADAPTive mesh-based graph neural network (ADAPT-GNN) - exploits the benefits of both ML methods and AMR by describing the graph representation at each time-step as the refined mesh itself. Using ADAPT-GNN, we predict the evolution of displacement fields and scalar damage field (or phase field) with high accuracy compared to conventional phase field fracture model. We also compute crack stress fields with high accuracy using the predicted displacements and phase field parameter. Finally, we observe speed up of 15-36x compared to serial execution of the phase field model.
