Abstract: Precondition Conjugate Gradient(PCG) algorithm is an iterativesolving algorithm for solving large-scale sparse matrices which iswidely used in fields such as scientific engineering computing and artificial intelligence.Existing research focuses on using deep learning to generate pre condition operators to improve solving speed.However,fixed preconditioning operators lack generality and are difficult to apply to all sparse matrices because of the spatial complexity of sparse matrices.To address this issue,a preconditioner operator adaptive selection algorithm based on deep learning and its optimization method are proposed.Firstly,a convolutional neural network(PCNN) is designed to capture the spatial structural characteristics of sparse matrices.Secondly,an adaptive classification prediction model combining multi-layer perceptronsis constructed to select the optimal precondition operator.Finally,experimental results on the publicly available dataset in Florida show that the proposed method has a better classification accuracy than deep learning methods such as MLP and SVM,reaching 70.49%;Compared with the PCG algorithm based on Jacobi,ICCG,and SSOR,the proposed method improves performance by 5.5,4.3,and 6.2 times,respectively.

Key words: Conjugate gradient, Precondition method, Deep learning, Large scale sparse matrix, Iterative solution method