Machine learning and domain decomposition methods -- a survey
Axel Klawonn Martin Lanser Janine Weber
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.