Hybrid algorithms, which combine black-box machine learning methods with experience from traditional numerical methods and domain expertise from diverse application areas, are progressively gaining importance in scientific machine learning and various industrial domains, especially in computational science and engineering. In the present survey, several promising avenues of research will be examined which focus on the combination of machine learning (ML) and domain decomposition methods (DDMs). The aim of this survey is to provide an overview of existing work within this field and to structure it into domain decomposition for machine learning and machine learning-enhanced domain decomposition, including: domain decomposition for classical machine learning, domain decomposition to accelerate the training of physics-aware neural networks, machine learning to enhance the convergence properties or computational efficiency of DDMs, and machine learning as a discretization method in a DDM for the solution of PDEs. In each of these fields, we summarize existing work and key advances within a common framework and, finally, disuss ongoing challenges and opportunities for future research.

翻译：混合算法将黑箱机器学习方法与来自传统数值方法的经验及不同应用领域的专业知识相结合，在科学机器学习及众多工业领域（尤其是计算科学与工程）中日益重要。本综述将重点考察若干具有前景的研究方向，这些方向聚焦于机器学习与区域分解方法的融合。本文旨在梳理该领域现有研究成果，并将其系统划分为：面向机器学习的区域分解方法，以及机器学习增强型区域分解方法，具体包括：面向传统机器学习的区域分解、加速物理感知神经网络训练的区域分解、利用机器学习改善区域分解的收敛性能或计算效率，以及将机器学习作为偏微分方程求解中区域分解的离散化方法。针对每类方法，我们在统一框架下总结现有研究成果与关键进展，最后探讨当前面临的挑战与未来研究机遇。