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.

翻译：局部-非局部耦合方法结合了局部模型的计算效率与非局部模型的准确性。然而，耦合过程具有挑战性，需要专业知识来识别局部区域与非局部区域之间的界面。本研究引入一种基于机器学习的方法，可自动检测耦合过程中应使用局部和非局部模型的区域。该识别过程利用载荷函数作为输入，输出网格点上选定的模型。训练基于载荷函数数据集，其中参考耦合配置通过精确耦合解计算得出，精度通过耦合方法解与非局部模型解之间的相对误差来衡量。我们研究了两种数据结构不同的方法。第一种方法称为全域输入数据法，输入完整载荷向量并输出完整标签向量，此时分类过程全局执行。第二种方法采用基于窗口的方法，将载荷预处理并划分为窗口，问题被公式化为节点级分类方法，每个窗口的中心点被单独处理。分类问题通过基于卷积神经网络的深度学习算法求解。采用F1分数和准确率指标在一维数值算例中研究了这些方法的性能。结果表明，窗口法尤其展现了令人瞩目的效果，准确率达到0.96，F1分数达到0.97。这些结果凸显了该方法在自动化耦合过程中的潜力，可为材料科学应用提供更精确且计算高效的解决方案。