Learning to Select Sparse Linear Solvers with Convolutional Neural Networks

We investigate convolutional-neural-network (CNN) based automatic solver selection for sparse linear systems, a problem of practical importance where solver performance varies dramatically with matrix sparsity structure. A CNN is trained to regress log timing ratios between candidate solvers using spy plot images of matrix nonzero structure as input, achieving strong prediction accuracy on both held-out SuiteSparse matrices and real-world matrices from high-performance simulation codes.