Multi-fidelity Gaussian process regression for prediction of random fields

DOI10.1016/j.jcp.2017.01.047zbMath1419.62272OpenAlexW2586140425MaRDI QIDQ1685592

Paris Perdikaris, Daniele Venturi, George Em. Karniadakis, Lucia Parussini

Publication date: 14 December 2017

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/11368/2903585

zbMATH Keywords

uncertainty quantificationGaussian random fieldsmulti-fidelity modelingrecursive co-kriging

Mathematics Subject Classification ID

Random fields; image analysis (62M40) Gaussian processes (60G15) Bayesian inference (62F15) Numerical solutions to stochastic differential and integral equations (65C30) Prediction theory (aspects of stochastic processes) (60G25)

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Cites Work

• Multi-output local Gaussian process regression: applications to uncertainty quantification
• A fully symmetric nonlinear biorthogonal decomposition theory for random fields
• Multi-element probabilistic collocation method in high dimensions
• Bayesian emulation of complex multi-output and dynamic computer models
• Interpolation of spatial data. Some theory for kriging
• A taxonomy of global optimization methods based on response surfaces
• Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
• High dimensional polynomial interpolation on sparse grids
• Multivariate versus univariate Kriging metamodels for multi-response simulation models
• Bayesian Calibration of Computer Models
• On the convergence of generalized polynomial chaos expansions
• Spectral Methods for Time-Dependent Problems
• Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
• Multi-fidelity optimization via surrogate modelling
• Stochastic bifurcation analysis of Rayleigh–Bénard convection
• Adaptive sampling in hierarchical simulation
• Distribution of Quadratic Forms in Normal Random Variables—Evaluation by Numerical Integration
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Predicting the output from a complex computer code when fast approximations are available
• RECURSIVE CO-KRIGING MODEL FOR DESIGN OF COMPUTER EXPERIMENTS WITH MULTIPLE LEVELS OF FIDELITY
• Wick–Malliavin approximation to nonlinear stochastic partial differential equations: analysis and simulations
• Probabilistic numerics and uncertainty in computations
• Bayesian Analysis of Hierarchical Multifidelity Codes
• On approximating the distribution of indefinite quadratic forms
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
• Unnamed Item