Accelerating explicit method for Poisson's equation using machine learning techniques.

We propose a universal approach for acceleration of convergence of numerical methods for diffusion equations. The approach is based on a prediction of the evolution of some low-dimensional representation of the numerical solution. General scheme of the acceleration method employs two key submethods: an autoencoder and a predictor. For both submethods a well-developed techniques from machine learning and data analysis can be used. The proposed approach is applied to a test problem for nonlinear Poisson's equation. Test computations show that speedup up to 10 times can be achieved. [ABSTRACT FROM AUTHOR]