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Probabilistic learning inference of boundary value problem with uncertainties based on Kullback-Leibler divergence under implicit constraints - MaRDI portal

Probabilistic learning inference of boundary value problem with uncertainties based on Kullback-Leibler divergence under implicit constraints (Q2142219)

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English	Probabilistic learning inference of boundary value problem with uncertainties based on Kullback-Leibler divergence under implicit constraints	scientific article

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scholarly article

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Probabilistic learning inference of boundary value problem with uncertainties based on Kullback-Leibler divergence under implicit constraints (English)

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Christian Soize

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Computer Methods in Applied Mechanics and Engineering

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publication date

27 May 2022

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full work available at URL

https://arxiv.org/abs/2202.05112

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zbMATH Keywords

probabilistic learning

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statistical inverse problem

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Kullback-Leibler divergence

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implicit constraints

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stochastic homogenization

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uncertainty quantification

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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Bayesian Calibration of Computer Models

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Approximate Bayesian computational methods

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Computational Statistics

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Handbook of Uncertainty Quantification

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Sampling of Bayesian posteriors with a non-Gaussian probabilistic learning on manifolds from a small dataset

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Statistical and computational inverse problems.

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Stochastic spectral methods for efficient Bayesian solution of inverse problems

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Inverse problems: A Bayesian perspective

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A computational inverse method for identification of non-Gaussian random fields using the Bayesian approach in very high dimension

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Bayesian inference with optimal maps

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Itô-SDE MCMC method for Bayesian characterization of errors associated with data limitations in stochastic expansion methods for uncertainty quantification

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Goal-Oriented Optimal Approximations of Bayesian Linear Inverse Problems

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Adaptive method for indirect identification of the statistical properties of random fields in a Bayesian framework

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Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions

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A comparison of variational approximations for fast inference in mixed logit models

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Bayesian Numerical Homogenization

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A Bayesian perspective of statistical machine learning for big data

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On the Brittleness of Bayesian Inference

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A modern maximum-likelihood theory for high-dimensional logistic regression

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A pure Hubbard model with demonstrable pairing adjacent to the Mott-insulating phase

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Maximum likelihood estimation of stochastic chaos representations from experimental data

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Identification of chaos representations of elastic properties of random media using experimental vibration tests

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The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

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Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure

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Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures

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Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems

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Computational Aspects for Constructing Realizations of Polynomial Chaos in High Dimension

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Adaptive sparse polynomial chaos expansion based on least angle regression

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Identification of Polynomial Chaos Representations in High Dimension from a Set of Realizations

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Basis adaptation in homogeneous chaos spaces

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Polynomial Chaos Expansion of a Multimodal Random Vector

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A robust and efficient stepwise regression method for building sparse polynomial chaos expansions

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Reduced Wiener chaos representation of random fields via basis adaptation and projection

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Bayesian adaptation of chaos representations using variational inference and sampling on geodesics

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Compressed Principal Component Analysis of Non-Gaussian Vectors

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Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark

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Hierarchical deep learning neural network (HiDeNN): an artificial intelligence (AI) framework for computational science and engineering

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Projection-based model reduction: formulations for physics-based machine learning

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Clustering discretization methods for generation of material performance databases in machine learning and design optimization

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Machine learning of linear differential equations using Gaussian processes

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DGM: a deep learning algorithm for solving partial differential equations

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Hidden physics models: machine learning of nonlinear partial differential equations

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Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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Sparse regression learning by aggregation and Langevin Monte-Carlo

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An Introduction to Statistical Learning

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Statistical learning and selective inference

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Efficient global optimization of expensive black-box functions

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On the Use of Stochastic Hessian Information in Optimization Methods for Machine Learning

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DESIGN UNDER UNCERTAINTY EMPLOYING STOCHASTIC EXPANSION METHODS

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A neural network-based surrogate model for carbon nanotubes with geometric nonlinearities

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Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold

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On Information and Sufficiency

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Elements of Information Theory

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Computer Vision - ECCV 2004

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Kullback-Leibler upper confidence bounds for optimal sequential allocation

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Probabilistic learning on manifolds constrained by nonlinear partial differential equations for small datasets

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Generalizing the finite element method: Diffuse approximation and diffuse elements

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Meshless methods: An overview and recent developments

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Surface remeshing by local hermite diffuse interpolation

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Meshless methods based on collocation with radial basis functions

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Data-driven probability concentration and sampling on manifold

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Probabilistic learning on manifolds (PLoM) with partition

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A General Convergence Result for a Functional Related to the Theory of Homogenization

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Homogenization and Two-Scale Convergence

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Random field models of heterogeneous materials

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A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites.

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Periodization of random media and representative volume element size for linear composites

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Statistical volume element method for predicting microstructure-constitutive property relations

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Computational stochastic homogenization of heterogeneous media from an elasticity random field having an uncertain spectral measure

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Construction of probability distributions in high dimension using the maximum entropy principle: Applications to stochastic processes, random fields and random matrices

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An algorithm for finding the distribution of maximal entropy

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Solving Nonlinear Equations with Newton's Method

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Calculation of Lagrange Multipliers in the Construction of Maximum Entropy Distributions in High Stochastic Dimension

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Uncertainty quantification. An accelerated course with advanced applications in computational engineering

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Higher-order implicit strong numerical schemes for stochastic differential equations

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Expansion of the global error for numerical schemes solving stochastic differential equations

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Geometric numerical integration illustrated by the Störmer–Verlet method

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Numerical Methods for Second‐Order Stochastic Differential Equations

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Time-domain formulation in computational dynamics for linear viscoelastic media with model uncertainties and stochastic excitation

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Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media

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Stochastic elliptic operators defined by non-Gaussian random fields with uncertain spectrum

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On the statistical dependence for the components of random elasticity tensors exhibiting material symmetry properties

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Random field representations for stochastic elliptic boundary value problems and statistical inverse problems

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Identifiers

10.1016/j.cma.2022.115078

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2142219

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