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About 10,000 papers for “variational model”
Frederik Van de Steen (13799477), Dimitris Pinotsis (14305308), Wouter Devos (14305311) et al. · Figshare · 2022
<p>This appendix summarizes the variational Bayesian framework used in this paper.</p> <p>(DOCX)</p>
Cited by 0Open access
Leonid Prigozhin · European Journal of Applied Mathematics · 1996
A model describing the evolving shape of a growing pile is considered, and is shown to be equivalent to an evolutionary quasi-variational inequality. If the support surface has no steep slopes, the inequality becomes a variational one. For this case existence and uniqueness of the solution are proved.
Cited by 124
Microelectronics Reliability · 1987
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Jae Mi Suh, Yeongjun Jang, Junsoo Kim et al. · arXiv (Cornell University) · 2026
We develop a variational encrypted model predictive control (VEMPC) protocol whose online execution relies only on encrypted polynomial operations. The proposed approach reformulates the MPC problem into a sampling-based estimator, in which the computation of the quadratic cost is naturally handled by tilting the sampling distribution, thus reducing online encrypted computation. The resulting protocol requires no additional communication rounds or intermediate decryption, and scales efficiently through two complementary levels of parallelism. We analyze the effect of encryption-induced errors on optimality, and simulation results demonstrate the practical applicability of the proposed method.
Cited by 0Open access
Jae Mi Suh, Y.‐R. Jang, Junsoo Kim et al. · ArXiv.org · 2026
We develop a variational encrypted model predictive control (VEMPC) protocol whose online execution relies only on encrypted polynomial operations. The proposed approach reformulates the MPC problem into a sampling-based estimator, in which the computation of the quadratic cost is naturally handled by tilting the sampling distribution, thus reducing online encrypted computation. The resulting protocol requires no additional communication rounds or intermediate decryption, and scales efficiently through two complementary levels of parallelism. We analyze the effect of encryption-induced errors on optimality, and simulation results demonstrate the practical applicability of the proposed method.
Cited by 0Open access
Soni,Som R, Pagano,Nicholas J · Defense Technical Information Center (DTIC) · 1982
The absence of a unified, tractable model to predict the elastic response of a multi-layered laminate (say 100 layers) has foiled attempts to understand the failure modes of practical composite structures. Global models, which follow from an assumed displacement field and lead to the definition of effective (or smeared) laminate moduli, are not sufficiently accurate for stress field computation. On the other hand, local models, in which each layer is represented as a homogeneous anisotropic continuum, become intractable as the number of layers becomes even moderately large (approximately 10). In this work, we blend these concepts into a self-consistent model which can define detailed response functions in a region of interest (local), while representing the remainder of the domain by effective properties (global). In this investigation the laminate thickness is divided into two parts. A variational principle has been used to derive the governing equations of equilibrium. For the global region of the laminate, potential energy has been utilized, while the Reissner functional has been used for the local region. The field equations are based upon an assumed thickness distribution of stress components within each layer of the local region and displacement components in the global region. The derived boundary of the global region and the prescribed tractions (pointwise in an elasticity sense) satisfy the conditions of vanishing resultant force and moment identically. The same conditions are satisfied in the local region.
Cited by 1
Junhong Liu · Applied and Computational Engineering · 2023
Variational autoencoder is one of the deep latent space generation models, which has become increasingly popular in image generation and anomaly detection in recent years. In this paper, we first review the development and research status of traditional variational autoencoders and their variants, and summarize and compare the performance of all variational autoencoders. then give a possible development direction of VAE.
Cited by 4Open access
Miaozhuang Cai (18824100), Yin Zheng (422826), Zhengyang Peng (18824103) et al. · Figshare · 2024
<div><p>Time series data complexity presents new challenges in clustering analysis across fields such as electricity, energy, industry, and finance. Despite advances in representation learning and clustering with Variational Autoencoders (VAE) based deep learning techniques, issues like the absence of discriminative power in feature representation, the disconnect between instance reconstruction and clustering objectives, and scalability challenges with large datasets persist. This paper introduces a novel deep time series clustering approach integrating VAE with metric learning. It leverages a VAE based on Gated Recurrent Units for temporal feature extraction, incorporates metric learning for joint optimization of latent space representation, and employs the sum of log likelihoods as the clustering merging criterion, markedly improving clustering accuracy and interpretability. Experimental findings demonstrate a 27.16% improvement in average clustering accuracy and a 47.15% increase in speed on industrial load data. This study offers novel insights and tools for the thorough analysis and application of time series data, with further exploration of VAE’s potential in time series clustering anticipated in future research.</p></div>
Cited by 0Open access
Coloma Ballester, Vicent Caselles, Joan Verdera · 2004
In this paper we study a variational approach for filling-in regions of missing data in 2D and 3D digital images. Applications of this technique include the restoration of old photographs and removal of superimposed text like dates, subtitles, or publicity, or the zooming of images. The approach presented here, initially introduced in [C. Ballester et al., 2001], is based on a joint interpolation of the image gray-levels and gradient/isophotes directions, smoothly extending the isophote lines into the holes of missing data. The process underlying this approach can be considered as an interpretation of the Gestaltist's principle of good continuation. After discussing the model, we present the numerical algorithm used to minimize it and display some numerical experiments.
Cited by 8
Major, Jan, Łącki, Mateusz, Zakrzewski, Jakub · arXiv (Cornell University) · 2013
For strongly interacting bosons in optical lattices the standard description using Bose-Hubbard model becomes questionable. The role of excited bands becomes important. In such a situation we compare results of simulations using multiband Bose-Hubbard model with a recent proposition based on a time dependent variational approach. It is shown that the latter, in its original formulation, uses too small variational space leading often to spurious effects. Possible expansion of variational approach is discussed.
Cited by 0Open access
F. Anizabalaga, Gm Karadi, Raymond J. Krizek · 1976
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Yair Shapira · 2022
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Jan Henrik Fitschen, Mila Nikolova, Fabien Pierre et al. · HAL (Le Centre pour la Communication Scientifique Directe) · 2015
Color image enhancement is a challenging task in digital imaging with many applications. This paper contributes to image enhancement methods. We propose a new variational model for color improvement in the RGB space based on a desired target intensity image. Our model improves the visual quality of the color image while it preserves the range and takes the hue of the original, badly exposed image into account without amplifying its color artifacts. To approximate the hue of the original image we use the fact that affine transforms are hue preserving. To cope with the noise in the color channels we design a particular coupled TV regularization term. Since the target intensity of the image is unaltered our model respects important image structures. Numerical results demonstrate the very good performance of our method.
Cited by 2
Lokenath Debnath · Birkhäuser Boston eBooks · 2011
This chapter deals with the basic ideas and many major nonlinear model equations which arise in a wide variety of physical problems. Included are one-dimensional wave, Klein–Gordon (KG), sine–Gordon (SG), Burgers, Fisher, Korteweg–de Vries (KdV), Boussinesq, modified KdV, nonlinear Schrödinger (NLS), Benjamin–Ono (BO), Benjamin–Bona–Mahony (BBM), Ginzburg–Landau (GL), Burgers–Huxley (BH), KP, concentric KdV, Whitham, Davey–Stewartson, Toda lattice, Camassa–Holm (CH), and Degasperis–Procesi (DP) equations. This is followed by variational principles and the Euler–Lagrange equations. Also included are Plateau’s problem, Hamilton’s principle, Lagrange’s equations, Hamilton’s equations, the variational principle for nonlinear Klein–Gordon equations, and the variational principle for nonlinear water waves. Special attention is given to the Euler equation of motion, the continuity equation, the associated energy equation and energy flux, linear water wave problems and their solutions, nonlinear finite amplitude waves (the Stokes waves), gravity waves, gravity-capillary waves, and linear and nonlinear dispersion relations. Finally, the modern theory of nonlinear water waves is formulated.
Cited by 1
Jerome Monnier · HAL (Le Centre pour la Communication Scientifique Directe) · 2020
Cited by 0Open access
R. Echegut, L. Piffet · 2009
Cited by 0
Jalil Taghia, Arne Leijon · IEEE Transactions on Pattern Analysis and Machine Intelligence · 2015
This paper addresses modelling data using the Watson distribution. The Watson distribution is one of the simplest distributions for analyzing axially symmetric data. This distribution has gained some attention in recent years due to its modeling capability. However, its Bayesian inference is fairly understudied due to difficulty in handling the normalization factor. Recent development of Markov chain Monte Carlo (MCMC) sampling methods can be applied for this purpose. However, these methods can be prohibitively slow for practical applications. A deterministic alternative is provided by variational methods that convert inference problems into optimization problems. In this paper, we present a variational inference for Watson mixture models. First, the variational framework is used to side-step the intractability arising from the coupling of latent states and parameters. Second, the variational free energy is further lower bounded in order to avoid intractable moment computation. The proposed approach provides a lower bound on the log marginal likelihood and retains distributional information over all parameters. Moreover, we show that it can regulate its own complexity by pruning unnecessary mixture components while avoiding over-fitting. We discuss potential applications of the modeling with Watson distributions in the problem of blind source separation, and clustering gene expression data sets.
Cited by 35
Jiamin Zhang · Communications in Statistics - Simulation and Computation · 2019
In this paper, we propose a variational Bayesian method for estimation of varying-coefficient model. Within the local likelihood framework, we develop variational updates for the approximated posterior and obtain variational lower bound. Mean-field assumption naturally simplifies the estimation procedure, and overcomes the computational burden of traditional Bayesian methods in nonparametric setting. We also propose a Metropolis-Hastings algorithm to select the bandwidth. We conduct simulation study to demonstrate proposed procedure, and apply the proposed estimation method in the analysis of stock return data.
Cited by 1
Charles Yang · 2003
Abstract It is a simple observation that young children’s language is different from that of adults. However, this simple observation raises profound questions: What results in the differences between child language and adult language, and how does the child eventually resolve such differences through exposure to linguistic evidence? These questions are fundamental to language acquisition research. (6) in Chapter 1, repeated below as (14), provides a useful framework within to characterize approaches to language acquisition:Language acquisition can be viewed as a function or algorithm, ℒ, which maps the initial and hence putatively innate state (𝒮0) of the learner to the terminal state (𝒮T), the adult-form language, on the basis of experience, E, in the environment.
Cited by 0
C. Ballester, V. Caselles, J. Verdera et al. · 2004
A variational approach for filling-in regions of missing data in graylevel and color images is introduced in this paper. The approach is based on joint interpolation of the image gray-levels and gradient/isophotes directions, smoothly extending in an automatic fashion the isophote lines into the holes of missing data. This interpolation is computed solving the variational problem via its gradient descent flow, which leads to a set of coupled second order partial differential equations, one for the gray-levels and one for the gradient orientations. The process underlying this approach can be considered as an interpretation of the Gestaltist’s principle of good continuation. No limitations are imposed on the topology of the holes, and all regions of missing data can be simultaneously processed, even if they are surrounded by completely different structures. Applications of this technique include the restoration of old photographs and removal of superimposed text like dates, subtitles, or publicity. Examples of these applications are given. 1.
Cited by 0