Constraint energy minimizing generalized multiscale finite element method
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 …
Element Method (CEM-GMsFEM). The main goal of this paper is to design multiscale basis …
NH-PINN: Neural homogenization-based physics-informed neural network for multiscale problems
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 …
successful in many applications; however, the accuracy of the PINN is not satisfactory when …
Non-local multi-continua upscaling for flows in heterogeneous fractured media
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 …
upscaling framework based on some recently developed multiscale methods [10]. Our …
An adaptive global–local generalized FEM for multiscale advection–diffusion problems
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 …
global–local enrichment (GFEM gl) for transient multiscale PDEs. The adaptive algorithm …
Mitigating spectral bias for the multiscale operator learning
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 …
dimensional parameter and solution spaces of partial differential equations (PDEs). In this …
Multiscale model reduction for shale gas transport in a coupled discrete fracture and dual-continuum porous media
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 …
consisting of fractures that are embedded spatially-distributed in a matrix made of organic …
Deep learning nonlinear multiscale dynamic problems using Koopman operator
M Li, L Jiang - Journal of Computational Physics, 2021 - Elsevier
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 …
nonlinear multiscale dynamical problems. Koopman operator is able to transform a non …
Multicontinuum homogenization and its relation to nonlocal multicontinuum theories
Y Efendiev, WT Leung - Journal of Computational Physics, 2023 - Elsevier
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 …
problems. We present constraint cell problem formulations in a representative volume …
Multiscale model reduction for shale gas transport in poroelastic fractured media
Inherently coupled flow and geomechanics processes in fractured shale media have
implications for shale gas production. The system involves highly complex geo-textures …
implications for shale gas production. The system involves highly complex geo-textures …
Efficient hybrid explicit-implicit learning for multiscale problems
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 …
scales, domain, and so on. Many splitting algorithms have been designed for efficient …