Abstract
Local-nonlocal coupling approaches combine the computational efficiency of local models and the accuracy of nonlocal models. However, the coupling process is challenging, requiring expertise to identify the interface between local and nonlocal regions. This study introduces a machine learning-based approach to automatically detect the regions in which the local and nonlocal models should be used in a coupling approach. This identification process uses the loading functions and provides as output the selected model at the grid points. Training is based on datasets of loading functions for which reference coupling configurations are computed using accurate coupled solutions, where accuracy is measured in terms of the relative error between the solution to the coupling approach and the solution to the nonlocal model. We study two approaches that differ from one another in terms of the data structure. The first approach, referred to as the full-domain input data approach, inputs the full load vector and outputs a full label vector. In this case, the classification process is carried out globally. The second approach consists of a window-based approach, where loads are preprocessed and partitioned into windows and the problem is formulated as a node-wise classification approach in which the central point of each window is treated individually. The classification problems are solved via deep learning algorithms based on convolutional neural networks. The performance of these approaches is studied on one-dimensional numerical examples using F1-scores and accuracy metrics. In particular, it is shown that the windowing approach provides promising results, achieving an accuracy of 0.96 and an F1-score of 0.97. These results underscore the potential of the approach to automate coupling processes, leading to more accurate and computationally efficient solutions for material science applications.
Abstract (translated)
局部非局部耦合方法结合了局部模型的计算效率和全局模型的准确性。然而，耦合过程具有挑战性，需要专业知识和技能来确定局部和全局区域的接口。本研究介绍了一种基于机器学习的方法，用于自动检测在耦合方法中应该使用局部和全局模型的区域。识别过程基于加载函数，并输出网格点上的选定模型。训练基于准确的耦合解决方案计算的数据集，以计算相对于耦合方法和非局部模型的解决方案的相对误差。我们研究了两种不同的数据结构。第一种方法被称为完整域输入数据方法，它输入完整的加载向量并输出完整的标签向量。在这种情况下，分类过程是全局进行的。第二种方法包括一个基于窗口的方法，其中预处理并分隔负载，将问题转化为每个窗口的节点分类方法。分类问题通过基于卷积神经网络的深度学习算法解决。我们研究了这些方法基于F1分数和准确率指标的性能。特别是，证明了窗口方法提供了有前途的结果，实现了0.96的准确性和0.97的F1得分。这些结果强调了这个方法自动耦合过程的潜力，为材料科学应用提供了更准确和计算效率的解决方案。
URL
https://arxiv.org/abs/2404.15388
