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：鲁棒的迭代法求解大型稀疏线性代数方程组常面临优化相应调优参数的问题。为提升目标问题的性能，需要针对特定参数进行调优，而在实践中这往往是一项耗时且繁琐的任务。本文提出了一种优化算法，用于调谐数值方法的参数。该算法将进化策略与预训练的神经网络相结合，在构建新一代种群时利用神经网络对个体进行筛选。所提出的两种优化方法的耦合，使得进化策略的自适应特性与神经网络实现的先验知识得以整合。将神经网络作为预筛选器使用，可显著降低对预测精度的要求，并允许预训练网络在广泛的线性系统中重复利用。针对一组模型线性系统（包括来自SuiteSparse矩阵集合的系统以及湍流模拟中的系统）进行了详细的算法效率评估。结果表明，预训练的神经网络可有效重复用于优化不同线性系统的参数，且通过约100次试求解的成本即可实现计算速度的显著提升。混合进化策略使SuiteSparse矩阵集合中的黑箱矩阵计算时间减少超过6倍，而湍流模拟中的线性系统序列计算时间也减少了1.4-2倍。最终，本文所进行的湍流模拟计算速度最高提升至1.8倍。