Despite great progress in simulating multiphysics problems using the numerical
discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate …

Numerical homogenization is a methodology for the computational solution of multiscale
partial differential equations. It aims at reducing complex large-scale problems to simplified …

In this paper, we propose a general approach called Generalized Multiscale Finite Element
Method (GMsFEM) for performing multiscale simulations for problems without scale …

Closed-loop reservoir management is a combination of model-based optimization and data
assimilation (computer-assisted history matching), also referred to as 'real-time reservoir …

We present a general kernel-based framework for learning operators between Banach
spaces along with a priori error analysis and comprehensive numerical comparisons with …

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 …

Numerical homogenization, ie, the finite-dimensional approximation of solution spaces of
PDEs with arbitrary rough coefficients, requires the identification of accurate basis elements …

Although numerical approximation and statistical inference are traditionally covered as
entirely separate subjects, they are intimately connected through the common purpose of …

We introduce a near-linear complexity (geometric and meshless/algebraic) multigrid/
multiresolution method for PDEs with rough (L^∞) coefficients with rigorous a priori …

In this paper we study multiscale finite element methods (MsFEMs) using spectral multiscale
basis functions that are designed for high-contrast problems. Multiscale basis functions are …