Robust iterative methods for solving large sparse systems of linear algebraic equations often suffer from the problem of optimizing the corresponding tuning parameters. To improve the performance of the problem of interest, specific parameter tuning is required, which in practice can be a time-consuming and tedious task. This paper proposes an optimization algorithm for tuning the numerical method parameters. The algorithm combines the evolution strategy with the pre-trained neural network used to filter the individuals when constructing the new generation. The proposed coupling of two optimization approaches allows to integrate the adaptivity properties of the evolution strategy with a priori knowledge realized by the neural network. The use of the neural network as a preliminary filter allows for significant weakening of the prediction accuracy requirements and reusing the pre-trained network with a wide range of linear systems. The detailed algorithm efficiency evaluation is performed for a set of model linear systems, including the ones from the SuiteSparse Matrix Collection and the systems from the turbulent flow simulations. The obtained results show that the pre-trained neural network can be effectively reused to optimize parameters for various linear systems, and a significant speedup in the calculations can be achieved at the cost of about 100 trial solves. The hybrid evolution strategy decreases the calculation time by more than 6 times for the black box matrices from the SuiteSparse Matrix Collection and by a factor of 1.4-2 for the sequence of linear systems when modeling turbulent flows. This results in a speedup of up to 1.8 times for the turbulent flow simulations performed in the paper.

翻译：求解大型稀疏线性代数方程组的稳健迭代方法常面临相应调优参数优化的问题。为提升目标问题的性能，需要针对特定参数进行调优，而实际操作中这往往是耗时费力的工作。本文提出一种用于调优数值方法参数的优化算法。该算法将进化策略与预训练神经网络相结合，在构建新一代种群时利用神经网络对个体进行筛选。通过耦合这两种优化方法，既能整合进化策略的自适应特性，又能利用神经网络实现的先验知识。将神经网络作为前置滤波器，可显著降低预测精度要求，并使预训练网络能够复用于各类线性系统。本文针对一组模型线性系统进行了详细的算法效率评估，包括来自SuiteSparse矩阵集合的算例以及湍流模拟中的系统。结果表明：预训练神经网络可有效复用于优化不同线性系统的参数，且通过约100次试验求解即可实现显著的计算加速。对于SuiteSparse矩阵集合中的黑箱矩阵，混合进化策略使计算时间减少6倍以上；对于湍流建模中的线性系统序列，加速比达1.4-2倍。这使得本文进行的湍流模拟获得了最高1.8倍的加速效果。