Sparse Matrix Reordering Method Selection with Parallel Computing and Deep Learning

Sparse matrix reordering is an important step in Cholesky decomposition. By reordering the rows and columns of the matrix, the time of computation and storage cost can be greatly reduced. With the proposal of various reordering algorithms, the selection of suitable reordering methods for various matrices has become an important research topic. In this paper, we propose a method to predict the optimal reordering method by visualizing sparse matrices in chunks in a parallel manner and feeding them into a deep convolutional neural network. The results show that the theoretical performance can reach 95% of the optimal performance, the prediction accuracy of the method can reach up to 85%, the parallel framework achieves an average speedup ratio of 11.35 times over the serial framework, and the performance is greatly improved compared with the traversal selection method on large sparse matrices.