In this paper, we discuss a general multiscale model reduction framework based on
multiscale finite element methods. We give a brief overview of related multiscale methods …

The objective of this paper is to design novel multi-layer neural networks for multiscale
simulations of flows taking into account the observed fine data and physical modeling …

We present efficient deep learning techniques for approximating flow and transport
equations for both single phase and two-phase flow problems. The proposed methods take …

The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modeling and the …

In this work, we consider a nonlinear strain-limiting elastic model in heterogeneous
domains. We investigate heterogeneous material with soft and stiff inclusions and …

Local multiscale methods often construct multiscale basis functions in the offline stage
without taking into account input parameters, such as source terms, boundary conditions …

Coupled nonlinear system of reaction–diffusion equations describing multi-component
(species) interactions with heterogeneous coefficients is considered. Finite volume method …

In this paper, we present a multiscale method for simulations of the multicontinua
unsaturated flow problems in heterogeneous fractured porous media. The mathematical …

Convection-dominated transport phenomenon is important for many applications. In these
applications, the transport velocity is often a solution of heterogeneous flow problems, which …

In this paper, we investigate neural networks applied to multiscale simulations of porous
media flows and discuss a design of a novel deep neural network model reduction approach …