Related papers: Space-time multiscale model reduction for transpor…
In the paper, we present a strategy for accelerating posterior inference for unknown inputs in time fractional diffusion models. In many inference problems, the posterior may be concentrated in a small portion of the entire prior support.…
The Boltzmann equation, as a model equation in statistical mechanics, is used to describe the statistical behavior of a large number of particles driven by the same physics laws. Depending on the media and the particles to be modeled, the…
Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order…
Numerical treatment of the problem of two-dimensional viscous fluid flow in and around circular porous inclusions is considered. The mathematical model is described by Navier-Stokes equation in the free flow domain $\Omega_f$ and nonlinear…
Motivated by a range of biological applications related to the transport of molecules in cells, we present a modular framework to treat first-passage problems for diffusion in partitioned spaces. The spatial domains can differ with respect…
In this paper, we propose a local-global multiscale mortar mixed finite element method (MMMFEM) for multiphase transport in heterogeneous media. We consider the two-phase flow system, the pressure equation is solved via the multiscale…
Numerical simulations of waves in highly heterogeneous media have important applications, but direct computations are prohibitively expensive. In this paper, we develop a new generalized multiscale finite element method with the aim of…
A projection-based formulation is presented for non-linear model reduction of problems with extreme scale disparity. The approach allows for the selection of an arbitrary, but complete, set of solution variables while preserving the…
In this work, we propose a generalized multiscale inversion algorithm for heterogeneous problems that aims at solving an inverse problem on a computational coarse grid. Previous inversion techniques for multiscale problems seek a…
Multiscale Finite Element Methods (MsFEM) are finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions which generate a specific discretization space, and next…
Motivated by the need for analysing large spatio-temporal panel data, we introduce a novel dimensionality reduction methodology for $n$-dimensional random fields observed across a number $S$ spatial locations and $T$ time periods. We call…
In this paper, we propose a novel iterative multiscale framework for solving high-contrast contact problems of Signorini type. The method integrates the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM)…
In this work, we derived a transport equation based on a generalized equation of time-dependent generator coordinate method (TDGCM) under the Gaussian overlap approximation (GOA). The transport equation is obtained by using…
In this paper, we consider the offline and online Constraint Energy Minimizing Generalized Mul- tiscale Finite Element Method (CEM-GMsFEM) for high-contrast linear elasticity problem. Offline basis construction starts with an auxiliary…
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 adaptive enrichment algorithm for the linear elliptic…
In this work, we employ the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) to solve the problem of linear heterogeneous poroelasticity with coefficients of high contrast. The proposed method makes use…
We propose a new model reduction framework for problems that exhibit transport phenomena. As in the moving finite element method (MFEM), our method employs time-dependent transformation operators and, especially, generalizes MFEM to…
Diffusion models have been widely studied as effective generative tools for solving inverse problems. The main ideas focus on performing the reverse sampling process conditioned on noisy measurements, using well-established numerical…
This paper proposes a non-intrusive, data-driven reduced-order modeling framework for stochastic optimal control problems governed by partial differential equations. The control problem is formulated with a quadratic cost functional and…
Modelling and simulation of mixed-traffic zones is an important tool for transportation planners to assess safety, efficiency, and human-friendliness of future urban areas. This paper addresses problems of calibration and transferability of…