Related papers: Learning macroscopic parameters in nonlinear multi…
Direct pore-scale simulations of fluid flow through porous media are computationally expensive to perform for realistic systems. Previous works have demonstrated using the geometry of the microstructure of porous media to predict the…
We present multiscale graph-based reduction algorithms for upscaling heterogeneous and anisotropic diffusion problems. The proposed coarsening approaches begin by constructing a partitioning of the computational domain into a set of…
The macroscopic properties of materials that we observe and exploit in engineering application result from complex interactions between physics at multiple length and time scales: electronic, atomistic, defects, domains etc. Multiscale…
In this paper we develop a multiscale method to solve problems in complicated porous microstructures with Neumann boundary conditions. By using a coarse-grid quasi-interpolation operator to define a fine detail space and local orthogonal…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum media. The mathematical model contains a coupled system of…
A upscaled lattice Boltzmann method (LBM) for flow simulations in heterogeneous porous media, at both pore and Darcy scales, is proposed in this paper. In the micro-scale simulations, we model flows using LBM with the modified Guo et al.…
This paper extends the author's previous two-dimensional work with Ou and LeVeque to high-resolution finite volume modeling of systems of fluids and poroelastic media in three dimensions, using logically rectangular mapped grids. A method…
This paper introduces an Algebraic MultiScale method for simulation of flow in heterogeneous porous media with embedded discrete Fractures (F-AMS). First, multiscale coarse grids are independently constructed for both porous matrix and…
This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their…
Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…
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…
In this paper, we investigate and design multiscale simulations for stochastic multiscale PDEs. As for the space, we consider a coarse grid and a known multiscale method, the Generalized Multiscale Finite Element Method (GMsFEM). In order…
Multilevel techniques are efficient approaches for solving the large linear systems that arise from discretized partial differential equations and other problems. While geometric multigrid requires detailed knowledge about the underlying…
In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational…
We consider a nonlinear mixed-dimensional model for simulating gas transport in shale formation. The mathematical model consists of a coupled system of nonlinear equations, where flow within fractures is represented using a…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
In this paper, we consider a poroelasticity problem in heterogeneous multicontinuum media that is widely used in simulations of the unconventional hydrocarbon reservoirs and geothermal fields. Mathematical model contains a coupled system of…
In this paper, we present a sparse grid-based Monte Carlo method for solving high-dimensional semi-linear nonlocal diffusion equations with volume constraints. The nonlocal model is governed by a class of semi-linear partial…
Accurately estimating parameters in complex nonlinear systems is crucial across scientific and engineering fields. We present a novel approach for parameter estimation using a neural network with the Huber loss function. This method taps…