Machine Learning Algorithms for Solving Linear Systems of Equations

Abstract

Moving into the fourth industrial revolution and the rapid digital transformation, there is a huge volume of data to be managed in each industry. Industrial simulations commonly produce data including the inputs and outputs of linear systems with several million unknowns. Solving linear systems is one of the fundamental problems in scientific computing, and it requires significant system resources. Determining a suitable method to solve linear systems can be a challenging task, since there is not a certain knowledge about which method is the most suitable for different numerical problems. In this study, the authors demonstrate how machine learning (ML) approach can be used in selecting solvers for linear systems. The chapter includes frequently used ML methods from literature and explain the usage of them to select optimal solvers and preconditioners.