A neural network based recommendation system for solvers and preconditioners for systems of linear equations

摘要

Numerical simulation methods like the finite element method lead to large systems of linear equations solved with well-known methods. Their performance varies depending on the considered simulation (discretization and physics) and the available hardware. To predict a suitable method including the solver and a well performing preconditioner, a feed-forward neural network is used. It computes 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 show the performance of different neural networks as recommendation systems.