Within high-performance computing (HPC), solving large sparse linear systems efficiently remains paramount, with iterative methods being the predominant choice. However, the performance of these methods is tightly coupled to the aptness of the chosen preconditioner. The multifaceted nature of sparse matrices makes the universal prescription of preconditioners elusive. Notably, the key attribute of sparsity is not precisely captured by scalar metrics such as bandwidth or matrix dimensions. Advancing prior methodologies, this research introduces matrix sparsity depiction via RGB images. Utilizing a convolutional neural network (CNN), the task of preconditioner selection turns into a multi-class classification problem. Extensive tests on 126 SuiteSparse matrices emphasize the enhanced prowess of the CNN model, noting a 32% boost in accuracy and a 25% reduction in computational slowdown.

翻译：在高性能计算领域，高效求解大型稀疏线性系统始终是核心问题，迭代法成为主要选择。然而，这类方法的性能与所选预处理器的适配性密切相关。稀疏矩阵的多面性使得通用型预处理器难以实现普适性配置。值得注意的是，带宽、矩阵维度等标量度量无法精确捕获稀疏性的关键特征。本研究在先前方法基础上，通过RGB图像引入矩阵稀疏性表征。利用卷积神经网络（CNN），将预处理器选择任务转化为多类别分类问题。基于126个SuiteSparse矩阵的广泛测试表明，CNN模型性能显著提升，准确率提高32%，计算耗时降低25%。