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Projection-Based Dimensional Reduction of Adaptively Refined Nonlinear Models
Adaptive mesh refinement (AMR) is fairly practiced in the context of high-dimensional, mesh-based computational models. However, it is in its infancy...
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On the Symmetry Reduction of the (1+3)-Dimensional Inhomogeneous Monge–Ampère Equation to Algebraic Equations
We perform the procedure of symmetry reduction of (1+3)-dimensional inhomogeneous Monge–Ampère equation to algebraic equations. Some results obtained...
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Finite-Dimensional Reduction of Systems of Nonlinear Diffusion Equations
AbstractWe present a class of one-dimensional systems of nonlinear parabolic equations for which the phase dynamics at large time can be described...
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Federated Sufficient Dimension Reduction Through High-Dimensional Sparse Sliced Inverse Regression
Federated learning has become a popular tool in the big data era nowadays. It trains a centralized model based on data from different clients while...
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Reduction of the (1 + 3)-Dimensional Inhomogeneous Monge–Ampère Equation to First-Order Partial Differential Equations
We study the relationships between the structural properties of two-dimensional nonconjugate subalgebras of the Lie algebra of the generalized...
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Dimensional Reduction by Fourier Analysis of a Stokes-Darcy Fracture Model
We consider a Stokes flow along a thin fracture coupled to a Darcy flow in the surrounding matrix domain. In order to derive a dimensionally reduced...
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Dimensional Reduction for the Ferroelectric Smectic A-Type Phase of Bent-Core Liquid Crystals
We analytically derive and numerically simulate a two-dimensional energy functional modelling the effects of a constant electric field on a thin...
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Nonlinear Representation and Dimensionality Reduction
Digital medical images can be viewed as digital representations of real physical tissue properties that are convenient for handling, storing,...
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Reduction Techniques
We review nonautonomous versions of centre manifolds, namely centre fibre bundles, their Taylor approximation and the use of the Reduction Principle...
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Reduction Techniques
We review nonautonomous versions of the two classical methods to simplify bifurcation problems: (1) centre integral manifolds allow a reduction in...
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Complexity Reduction for Parametric High Dimensional Models in the Analysis of Financial Risk
This paper presents a parametric model order reduction (pMOR) approach for financial risk analysis based on the proper orthogonal decomposition...
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Reduction of the Two-Dimensional Thermoelasticity Problems for Solids with Corner Points to Key Integrodifferential Equations
We propose a generalization of the method of direct integration of the original equations of two-dimensional problems of thermoelasticity for solids...
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Front Transport Reduction for Complex Moving Fronts
This work addresses model order reduction for complex moving fronts, which are transported by advection or through a reaction–diffusion process. Such...
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Nonlinear Schemes: Clustering, Feature Extraction and Dimension Reduction
Often data seem to sit in some high-dimensional space, because of the way they are recorded and presented. But intrinsically, they may be...
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On reduction numbers and Castelnuovo–Mumford regularity of blowup rings and modules
We prove new results on the interplay between reduction numbers and the Castelnuovo–Mumford regularity of blowup algebras and blowup modules, the key...
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A Dynamical System-Based Framework for Dimension Reduction
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call the dynamical...
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Nonlinear Model Reduction for Slow–Fast Stochastic Systems Near Unknown Invariant Manifolds
We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant...
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A Local Approach to Parameter Space Reduction for Regression and Classification Tasks
Parameter space reduction has been proved to be a crucial tool to speed-up the execution of many numerical tasks such as optimization, inverse...
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Algorithmic Feature Selection and Dimensionality Reduction in Signal Classification Tasks
This paper presents a research endeavour addressing the recognition of acoustic emission signals, aiming to enhance their utilisation in...