Neural networks for multicontinuum models

Abstract

Neural networks are developed for multicontinuum models. Multicontinuum models [1] assume that processes divided into several continuums and they are connected by some exchange member. In problems connected with PDE not only solution, but also coefficients can depends on time. First we construct LSTM neural network for exchange coefficient that depend on time. We compare the results obtained on the basis of the reference coefficient and on the basis of the neural network. Next we apply same neural network on the solutions. The proposed approach involves the use of a neural network for the approximate generation of a solutions and the further adaptation of the solution of a neural network for generate coarse grid solution based on DG finite elements.