计算机科学

计算机科学 ›› 2026, Vol. 53 ›› Issue (6A): 250900126-6.doi: 10.11896/jsjkx.250900126

• 计算机软件&体系结构 • 上一篇    下一篇

基于深度学习的共轭梯度预条件自适应选择算法

李琴1, 吴思原2, 杨浩原2, 杜沁2, 凌旭1, 肖国庆3   

  1. 1 湖南化工职业技术学院机械工程学院 湖南 株洲 412000
    2 湖南大学信息科学与工程学院 长沙 410082
    3 湖南大学重庆研究院 重庆 401135
  • 出版日期:2026-06-16 发布日期:2026-06-12
  • 通讯作者: 杜沁(seery313@hnu.edu.cn)
  • 作者简介:(805004390@qq.com)
  • 基金资助:
    湖南省自然科学基金(2023JJ60002)

Conjugate Gradient Preconditioner Adaptive Selection Algorithm via Deep Learning

LI Qin1, WU Siyuan2, YANG Haoyuan2, DU Qin2, LING Xu1, XIAO Guoqing3   

  1. 1 College of Mechanical Engineering,Hunan Chemical Vocational Technology College,Zhuzhou,Hunan 412000,China
    2 College of Computer Science and Electronic Engineering,Hunan University,Changsha 410082,China
    3 Research Institute of Hunan University in Chongqing,Chongqing 401135,China
  • Published:2026-06-16 Online:2026-06-12
  • About author:LI Qin,born in 1968,professor.Her main research interests include digital design and manufacturing,and so on.
    DU Qin,born in 2002,Ph.D.His main research interests include high-perfor-mance computing and AI computing.
  • Supported by:
    Natural Science Foundation of Hunan Province,China(2023JJ60002).

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摘要： 预处理共轭梯度(PCG)法作为一种大规模稀疏矩阵迭代求解算法,广泛应用于科学工程计算、人工智能等领域。现有研究聚焦于使用深度学习生成预条件算子,以加快求解速度。然而,由于稀疏矩阵的空间复杂性,固定预条件算子不具备通用性,难以适用于所有的稀疏矩阵。为了解决这个问题,提出了一种基于深度学习的预条件算子自适应选择算法及其优化方法。首先,设计了一种卷积神经网络PCNN来捕获稀疏矩阵的空间结构特性;其次,基于此构建了一种结合多层感知机的自适应分类预测模型以选择最优预条件算子。在佛罗里达公开数据集上的实验结果表明,所提出方法的分类准确率优于MLP和SVM等深度学习方法,可达到70.49%;与基于Jacobi,ICCG和SSOR的PCG算法相比,所提出方法的性能分别提高了5.5,4.3和6.2倍。

关键词: 共轭梯度算法, 预处理算法, 深度学习, 大规模稀疏矩阵, 迭代求解法

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

中图分类号: 

  • O241.6
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