Том: 15888 , Год издания: 2025

In this paper, we present an attempt to construct a preconditioner based on the machine learning to solve Poisson equation. We use the Conjugate Gradient method. To precondition the algorithm we suggest approximating the inverse Laplace operator with using the U-Net. We consider the supervised learning where the vector of unknowns and right-hand sides are known; thus, we use the relative L² error as the loss function of the network training. We illustrate that U-Net with five convolutional layers provide insuffient accuracy of inverse Laplace operator approximation, so that the constructed conjugate gradient method stabilizes and possesses irreducible residual.