# ML-based identification of the interface regions for coupling local and nonlocal models

arXiv: https://arxiv.org/abs/2404.15388 · HTML: https://mlsanity.com/paper/2404.15388/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 56 references that are in the map.
- First posted on arXiv 23 Apr 2024.

## Builds on (most cited first, 14 of 14)

- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospects](https://mlsanity.com/paper/2004.02806/) (2020)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [Model Evaluation, Model Selection, and Algorithm Selection in Machine Learning](https://mlsanity.com/paper/1811.12808/) (2018)
- [A nonlocal physics-informed deep learning framework using the peridynamic differential operator](https://mlsanity.com/paper/2006.00446/) (2020)
- [A data-driven peridynamic continuum model for upscaling molecular dynamics](https://mlsanity.com/paper/2108.04883/) (2021)
- [Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws](https://mlsanity.com/paper/2012.04157/) (2020)
- [What machine learning can do for computational solid mechanics](https://mlsanity.com/paper/2109.08419/) (2021)
- [GNN-based physics solver for time-independent PDEs](https://mlsanity.com/paper/2303.15681/) (2023)
- [Nonlocal Neural Networks, Nonlocal Diffusion and Nonlocal Modeling](https://mlsanity.com/paper/1806.00681/) (2018)
- [Bilevel parameter learning for nonlocal image denoising models](https://mlsanity.com/paper/1912.02347/) (2019)
- [On the treatment of boundary conditions for bond-based peridynamic models](https://mlsanity.com/paper/2008.09725/) (2020)
- [Coupling approaches for classical linear elasticity and bond-based peridynamic models](https://mlsanity.com/paper/2203.09934/) (2022)

## Abstract (arXiv)

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.