A Neural Network Based Recommendation System for Solvers and Preconditioners for Systems of Linear Equations

Numerical simulation methods, like the finite element method, lead to large systems of equations. Well-known and highly optimized methods are applied to solve equation systems. Their performance varies depending on the considered simulation (discretization and physics) and the available hardware. Choosing a suitable method includes the selection of a well performing solver and preconditioner which is rarely obvious. Here, a case study is presented, where recommendations are given based on provided training data by feed-forward neural networks. The neural networks compute performance ratings for each reasonable combination of solver and preconditioner, depending on selected properties of the system of linear equations and on the provided hardware. Details about the designed and the applied training methods are given. A statistic as well as a specific evaluation shows the performance of different evaluated neural networks. Results show the effort of using a neural network as recommendation system for solvers and preconditioners for linear equation systems.