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Truncated Singular Value Decomposition (SVD) calculates the closest rank-$k$ approximation of a given input matrix. Selecting the appropriate rank $k$ defines a critical model order choice in most applications of SVD. To obtain a principled…

Information Theory · Computer Science 2013-01-08 Mario Frank , Joachim M. Buhmann

We discuss Euclidean covariant vector random fields as the solution of stochastic partial differential equations of the form $DA=\eta$, where $D$ is a covariant (w.r.t. a representation \tau of $SO(d)$) differential operator with "positive…

Mathematical Physics · Physics 2007-05-23 S. Albeverio , H. Gottschalk , J. -L. Wu

In this work, we introduce a Variational Multi-Scale (VMS) method for the numerical approximation of parabolic problems, where sub-grid scales are approximated from the eigenpairs of associated elliptic operator. The abstract method is…

Variational hybrid quantum-classical algorithms are some of the most promising workloads for near-term quantum computers without error correction. The aim of these variational algorithms is to guide the quantum system to a target state that…

Quantum Physics · Physics 2021-03-18 Shavindra P. Premaratne , A. Y. Matsuura

A variationally improved Sturmian approximation for solving time-independent Schr\"odinger equation is developed. This approximation is used to obtain the energy levels of a quartic anharmonic oscillator, a quartic potential, and a Gaussian…

Quantum Physics · Physics 2009-11-07 Ali Mostafazadeh

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction such as Proper Orthogonal Decomposition,…

Numerical Analysis · Mathematics 2023-04-26 Thomas Simpson , Konstantinos Vlachas , Anthony Garland , Nikolaos Dervilis , Eleni Chatzi

Singular Value Decomposition (SVD) is one of the most useful techniques for analyzing data in linear algebra. SVD decomposes a rectangular real or complex matrix into two orthogonal matrices and one diagonal matrix. In this work we…

Quantum Physics · Physics 2012-07-31 Laszlo Gyongyosi , Sandor Imre

We formulate and implement the Variational Quantum Eigensolver Self Consistent Field (VQE-SCF) algorithm in combination with polarizable embedding (PE), thereby extending PE to the regime of quantum computing. We test the resulting…

A new approach to nonperturbative calculations in quantum electrodynamics is proposed. The approach is based on a regular iteration scheme for solution of Schwinger-Dyson equations for generating functional of Green functions. The approach…

High Energy Physics - Phenomenology · Physics 2008-11-26 V. E. Rochev

Variational Bayes (VB) has been used to facilitate the calculation of the posterior distribution in the context of Bayesian inference of the parameters of nonlinear models from data. Previously an analytical formulation of VB has been…

Signal Processing · Electrical Eng. & Systems 2020-07-06 Michael A. Chappell , Martin S. Craig , Mark W. Woolrich

Probabilistic circuits (PCs) enable exact and tractable inference but employ data independent mixture weights that limit their ability to capture local geometry of the data manifold. We propose Voronoi tessellations (VT) as a natural way to…

Machine Learning · Computer Science 2026-03-13 Sahil Sidheekh , Sriraam Natarajan

Conventional variational autoencoders fail in modeling correlations between data points due to their use of factorized priors. Amortized Gaussian process inference through GP-VAEs has led to significant improvements in this regard, but is…

Machine Learning · Statistics 2021-02-25 Metod Jazbec , Matthew Ashman , Vincent Fortuin , Michael Pearce , Stephan Mandt , Gunnar Rätsch

Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to…

Methodology · Statistics 2018-01-17 Jean Daunizeau

Estimating the difference between quantum data is crucial in quantum computing. However, as typical characterizations of quantum data similarity, the trace distance and quantum fidelity are believed to be exponentially-hard to evaluate in…

Quantum Physics · Physics 2021-12-28 Ranyiliu Chen , Zhixin Song , Xuanqiang Zhao , Xin Wang

We pick up a method originally developed by Cheng and Tsai for vacuum perturbation theory which allows to test the consistency of different sets of Feynman rules on a purely diagrammatic level, making explicit loop calculations superfluous.…

High Energy Physics - Theory · Physics 2009-10-09 Marc Achhammer , Ulrich Heinz , Stefan Leupold , Urs Achim Wiedemann

Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…

Machine Learning · Statistics 2021-02-24 Simone Rossi , Markus Heinonen , Edwin V. Bonilla , Zheyang Shen , Maurizio Filippone

In this paper, we present and prove a new truncated $\mathcal{V}$-fractional Taylor's formula using the truncated $\mathcal{V}$-fractional variation of constants formula. In this sense, we present the truncated $\mathcal{V}$-fractional…

Classical Analysis and ODEs · Mathematics 2017-07-10 J. Vanterler da C. Sousa , E. Capelas de Oliveira

In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the…

Numerical Analysis · Mathematics 2022-07-27 Stein K. F. Stoter , Thi-Hoa Nguyen , René R. Hiemstra , Dominik Schillinger

In this paper we study the general minimization vector problem (P), concerning a perturbation mapping, defined in locally convex Hausdorff topological vector spaces where the "WInf" stands for the weak infimum with respect to an ordering…

Optimization and Control · Mathematics 2021-06-01 N. Dinh , D. H. Long

Variational Bayes (VB), also known as independent mean-field approximation, has become a popular method for Bayesian network inference in recent years. Its application is vast, e.g. in neural network, compressed sensing, clustering, etc. to…

Information Theory · Computer Science 2018-03-30 Viet Hung Tran