Аннотация:In several areas in computational fluid dynamics, there is a need to solve differential equations of elliptic type. After discretization on a computational grid, the problem is reduced to solving a system of linear algebraic equations (SLAE). The numerical methods widely used for high-fidelity simulations of incompressible turbulent flows require solving a sequence of SLAEs with a constant matrix and changing the right-hand side. A practically important issue is the choice of the parameters of linear solvers, which can have a tangible impact on the SLAE solution time. The paper presents an algorithm for automatic parameters selection for SLAE solving methods. The proposed algorithm finds appropriate parameters for the specified configuration of numerical methods. An approach is based on a genetic algorithm in conjunction with a neural network model. The last one is trained to predict the SLAE solution time with specific parameters. Thus the neural network model acts as a source of knowledge about the influence of each parameter on the linear solver performance. It is shown that optimal parameters set for large SLAE solving can be obtained using solution statistics for smaller SLAEs, which is an important practical aspect. The performance of the algorithm is investigated for both the model SLAEs for the Poisson equation and the SLAEs from the fluid dynamics simulations. The algorithm allows to determine the corresponding optimized parameters of the linear solver and significantly reduce the overall calculations time. The corresponding speedup can reach up to 30% compared to the manually optimized solver parameters.