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Recent advances in the field of machine learning open a new era in highperformance computing. Applications of machine learning algorithms for thedevelopment of accurate and cost-efficient surrogates of complex problems havealready attracted major attention from scientists. Despite their powerfulapproximation capabilities, however, surrogates cannot produce the `exact'solution to the problem. To address this issue, this paper exploits up-to-dateML tools and delivers customized iterative solvers of linear equation systems,capable of solving large-scale parametrized problems at any desired level ofaccuracy. Specifically, the proposed approach consists of the following twosteps. At first, a reduced set of model evaluations is performed and thecorresponding solutions are used to establish an approximate mapping from theproblem's parametric space to its solution space using deep feedforward neuralnetworks and convolutional autoencoders. This mapping serves a means to obtainvery accurate initial predictions of the system's response to new query pointsat negligible computational cost. Subsequently, an iterative solver inspired bythe Algebraic Multigrid method in combination with Proper OrthogonalDecomposition, termed POD-2G, is developed that successively refines theinitial predictions towards the exact system solutions. The application ofPOD-2G as a standalone solver or as preconditioner in the context ofpreconditioned conjugate gradient methods is demonstrated on several numericalexamples of large scale systems, with the results indicating its superiorityover conventional iterative solution schemes.

AI-enhanced iterative solvers for accelerating the solution of large scale parametrized systems