Related papers: A Unified Framework for Multiscale Modeling using …
Lattice Boltzmann Methods (LBM) stand out for their simplicity and computational efficiency while offering the possibility of simulating complex phenomena. While they are optimal for Cartesian meshes, adapted meshes have traditionally been…
We propose a multi-scale hybridized topic modeling method to find hidden topics from transcribed interviews more accurately and efficiently than traditional topic modeling methods. Our multi-scale hybridized topic modeling method (MSHTM)…
In order to decode the human brain, Multivariate Pattern (MVP) classification generates cognitive models by using functional Magnetic Resonance Imaging (fMRI) datasets. As a standard pipeline in the MVP analysis, brain patterns in…
We study the non-Markovian random continuous processes described by the Mori-Zwanzig equation. As a starting point, we use the Markovian Gaussian Ornstein-Uhlenbeck process and introduce an integral memory term depending on the past of the…
This paper presents a multiscale modeling framework (MMF) to model moist atmospheric limited-area weather. The MMF resolves large-scale convection using a coarse grid while simultaneously resolving local features through numerous fine local…
We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media. Some of the methods developed using the framework are already known…
In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response…
The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution…
Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and…
Physical understanding of how the interplay between symmetries and nonlinear effects can control the scaling and multiscaling properties in a coupled driven system, such as magnetohydrodynamic turbulence or turbulent binary fluid mixtures,…
While building machine learning models, Feature selection (FS) stands out as an essential preprocessing step used to handle the uncertainty and vagueness in the data. Recently, the minimum Redundancy and Maximum Relevance (mRMR) approach…
We present the applications of nonlinear local harmonic analysis methods to the modelling of beam-beam interaction. Our approach is based on methods provided the possibility to work with dynamical beam localization in phase space. The…
This paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non immersed fractures. The so called…
We introduce a method to simulate open quantum many-body dynamics by combining time-dependent variational Monte Carlo (tVMC) with quantum trajectory techniques. Our approach unravels the Lindblad master equation into an ensemble of…
Combining multiple modalities carrying complementary information through multimodal learning (MML) has shown considerable benefits for diagnosing multiple pathologies. However, the robustness of multimodal models to missing modalities is…
The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed…
In this paper, we develop a Bayesian multiscale approach based on a multiscale finite element method. Because of scale disparity in many multiscale applications, computational models can not resolve all scales. Various subgrid models are…
Embedding high-dimensional data into resource-limited quantum devices remains a significant challenge for practical quantum machine learning. In multimodal face anti-spoofing, while linear compression methods such as principal component…
In this paper, we propose a unified algorithmic framework for solving many known variants of \mds. Our algorithm is a simple iterative scheme with guaranteed convergence, and is \emph{modular}; by changing the internals of a single…
We introduce a hybrid projection scheme that combines linear Mori projection and conditional Zwanzig projection techniques and use it to derive a Generalized Langevin Equation (GLE) for a general interacting many-body system. The resulting…