Neural networks for predicting the behavior of preconditioned iterative solvers

Abstract

We evaluate the effectiveness of neural networks as a tool for predicting whether a particular combination of preconditioner and iterative method will correctly solve a given sparse linear system Ax = b. We consider several scenarios corresponding to different assumptions about the relationship between the systems used to train the neural network and those for which the neural network is expected to predict behavior. Greater similarity between those two sets leads to better accuracy, but even when the two sets are very different prediction accuracy can be improved by using additional computation. © Springer-Verlag Berlin Heidelberg 2007.