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 …

In this paper, we propose Constraint Energy Minimizing Generalized Multiscale Finite
Element Method (CEM-GMsFEM). The main goal of this paper is to design multiscale basis …

In this paper, we present a mixed generalized multiscale finite element method (GMsFEM)
for solving flow in heterogeneous media. Our approach constructs multiscale basis functions …

In this paper, we propose a rigorous and accurate non-local (in the oversampled region)
upscaling framework based on some recently developed multiscale methods [10]. Our …

In this paper, we derive an a-posteriori error indicator for the Generalized Multiscale Finite
Element Method (GMsFEM) framework. This error indicator is further used to develop an …

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 …

The construction of local reduced-order models via multiscale basis functions has been an
area of active research. In this paper, we propose online multiscale basis functions which …

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 …

Complex processes in perforated domains occur in many real-world applications. These
problems are typically characterized by physical processes in domains with multiple scales …

It is important to develop fast yet accurate numerical methods for seismic wave propagation
to characterize complex geological structures and oil and gas reservoirs. However, the …