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This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…

Machine Learning · Computer Science 2019-05-31 Mauro Maggioni , James M. Murphy

In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…

Numerical Analysis · Mathematics 2020-12-16 Barbara Verfürth

Simulating reactive dissolution of solid minerals in porous media has many subsurface applications, including carbon capture and storage (CCS), geothermal systems and oil & gas recovery. As traditional direct numerical simulators are…

Machine Learning · Computer Science 2025-12-16 Marcos Cirne , Hannah Menke , Alhasan Abdellatif , Julien Maes , Florian Doster , Ahmed H. Elsheikh

We present a new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which simultaneously gives an approximation of the solution and of its gradient. In the case of simplicial meshes, the…

Numerical Analysis · Mathematics 2016-08-16 Jérôme Droniou , Robert Eymard

Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…

Computational Physics · Physics 2020-08-26 Sebastian Kaltenbach , Phaedon-Stelios Koutsourelakis

The properties of constrained fluids have increasingly gained relevance for applications ranging from materials to biology. In this work, we propose a multiscale model using twin neural networks to investigate the properties of a fluid…

Chemical Physics · Physics 2024-08-07 Peiyuan Gao , George Em Karniadakis , Panos Stinis

The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…

Numerical Analysis · Mathematics 2025-05-06 Surendra Nepal , Vishnu Raveendran , Michael Eden , Rainey Lyons , Adrian Muntean

We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…

Methodology · Statistics 2018-04-19 David A. Barajas-Solano , Alexandre M. Tartakovsky

Pore-scale simulations accurately describe transport properties of fluids in the subsurface. These simulations enhance our understanding of applications such as assessing hydrogen storage efficiency and forecasting CO$_2$ sequestration…

Deep Learning research is advancing at a fantastic rate, and there is much to gain from transferring this knowledge to older fields like Computational Fluid Dynamics in practical engineering contexts. This work compares state-of-the-art…

Computational Physics · Physics 2020-10-01 Pierre Jacquier , Azzedine Abdedou , Vincent Delmas , Azzeddine Soulaimani

In Computational Fluid Dynamics (CFD), coarse mesh simulations offer computational efficiency but often lack precision. Applying conventional super-resolution to these simulations poses a significant challenge due to the fundamental…

Anomalous behavior is ubiquitous in subsurface solute transport due to the presence of high degrees of heterogeneity at different scales in the media. Although fractional models have been extensively used to describe the anomalous transport…

Numerical Analysis · Mathematics 2022-02-01 Xiao Xu , Marta D'Elia , Christian Glusa , John T. Foster

Subgrid processes in global climate models are represented by parameterizations which are a major source of uncertainties in simulations of climate. In recent years, it has been suggested that machine-learning (ML) parameterizations based…

Atmospheric and Oceanic Physics · Physics 2022-12-27 Peidong Wang , Janni Yuval , Paul A. O'Gorman

Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…

Optimization and Control · Mathematics 2021-07-08 Morteza Boroun , Afrooz Jalilzadeh

We discuss Coarse Grid Projection (CGP) methodology as a guide for partial mesh refinement of incompressible flow computations for the first time. Based on it, if for a given spatial resolution the numerical simulation diverges or the…

Computational Physics · Physics 2018-03-29 Ali Kashefi

When simulating multiscale stochastic differential equations (SDEs) in high-dimensions, separation of timescales, stochastic noise and high-dimensionality can make simulations prohibitively expensive. The computational cost is dictated by…

Dynamical Systems · Mathematics 2015-10-13 Miles Crosskey , Mauro Maggioni

The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…

Numerical Analysis · Mathematics 2022-02-11 Vladimír Lukeš , Eduard Rohan

Contactless and non-invasive estimation of mechanical properties of physical media from optical observations is of interest for manifold engineering and biomedical applications, where direct physical measurements are not possible.…

Computer Vision and Pattern Recognition · Computer Science 2026-02-10 A. N. Maria Antony , T. Richter , E. Gladilin

Efficient simulation of Darcy flow in highly heterogeneous porous media requires iterative solvers that remain robust under large permeability contrasts and mixed boundary conditions. Spectral coarse spaces in two-level overlapping Schwarz…

Numerical Analysis · Mathematics 2026-03-30 Yucheng Liu , Tak Shing Au Yeung , Eric T. Chung , Simon See

Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…

Numerical Analysis · Mathematics 2021-08-10 Fabrizio Greco , Lorenzo Leonetti , Paolo Lonetti , Raimondo Luciano , Andrea Pranno