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 …

Physics-informed neural network (PINN) is a data-driven approach to solving equations. It is
successful in many applications; however, the accuracy of the PINN is not satisfactory when …

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 …

This paper develops an adaptive algorithm for the Generalized Finite Element Method with
global–local enrichment (GFEM gl) for transient multiscale PDEs. The adaptive algorithm …

Neural operators have emerged as a powerful tool for learning the mapping between infinite-
dimensional parameter and solution spaces of partial differential equations (PDEs). In this …

Natural gas production from shale formations involves highly complex geological features
consisting of fractures that are embedded spatially-distributed in a matrix made of organic …

In this paper, a deep learning method using Koopman operator is presented for modeling
nonlinear multiscale dynamical problems. Koopman operator is able to transform a non …

In this paper, we present a general derivation of multicontinuum equations and discuss cell
problems. We present constraint cell problem formulations in a representative volume …

Inherently coupled flow and geomechanics processes in fractured shale media have
implications for shale gas production. The system involves highly complex geo-textures …

Splitting method is a powerful method to handle application problems by splitting physics,
scales, domain, and so on. Many splitting algorithms have been designed for efficient …