Dmitry Kuznichov, M.Sc. Thesis Seminar
Thursday, 31.3.2022, 14:00
Advisor: Prof. I. Yavneh and R. Kimmel
During the last decade, Neural Networks (NNs) have proved to be extremely effective tools in many fields of engineering, including autonomous vehicles, medical diagnosis and search engines, and even in art creation. Indeed, NNs often decisively outperform traditional algorithms. One area that is only recently attracting significant interest is using NNs for designing numerical solvers, particularly for discretized partial differential equations. Several recent papers have considered employing NNs for developing multi-grid methods, which are a leading computational tool for solving discretized partial differential equations and other sparse-matrix problems. We extend these new ideas, focusing on so-called relaxation operators (also called smoothers), which are an impor- tant component of the multigrid algorithm that has not yet received much attention in this context. We explore an approach for using NNs to learn relaxation parameters for an ensemble of diffusion operators with random coeﬀicients, for Jacobi-type smoothers and for 4-Color gauss-seidel smoothers. the latter yield exceptionally eﬀicient and easy to parallelize Successive Over Relaxation (SOR) smoothers.