Доступ предоставлен для: Guest
Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
International Journal for Uncertainty Quantification
Импакт фактор: 3.259 5-летний Импакт фактор: 2.547 SJR: 0.417 SNIP: 0.8 CiteScore™: 1.52

ISSN Печать: 2152-5080
ISSN Онлайн: 2152-5099

Свободный доступ

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2015007941
pages 375-392

LOW-COST MULTI-DIMENSIONAL GAUSSIAN PROCESS WITH APPLICATION TO UNCERTAINTY QUANTIFICATION

Bledar A. Konomi
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221, USA
Guang Lin
Computational Science & Mathematics Division, Pacific Northwest National Laboratory, Richland, Washington 99352; Department of Mathematics, School of Mechanical Engineering, Purdue University, West Lafayette, Indiana, USA

Краткое описание

Computer codes simulating physical systems often have responses that consist of a set of distinct outputs that evolve in space and time and depend on many uncertain input parameters. The high dimensional nature of these computer codes makes the computations of Gaussian process (GP)-based emulators infeasible, even for a small number of simulation runs. In this paper we develop a covariance function for the GP to explicitly treat the covariance among distinct output variables, input variables, spatial domain, and temporal domain and also allows for Bayesian inference at low computational cost. We base our analysis on a modified version of the linear model of coregionalization (LMC). The proper use of the conditional representation of the multivariate output and the separable model for different domains leads to a Kronecker product representation of the covariance matrix. Moreover, we introduce a nugget to the model which leads to better statistical properties (regarding predictive accuracy) of the multivariate GP without adding to the overall computational complexity. Finally, the prior specification of the LMC parameters allows for an efficient Markov chain Monte Carlo (MCMC) algorithm. Our approach is demonstrated on the Kraichnan-Orszag problem and Flow through randomly heterogeneous porous media.


Articles with similar content:

ANALYSIS OF VARIANCE-BASED MIXED MULTISCALE FINITE ELEMENT METHOD AND APPLICATIONS IN STOCHASTIC TWO-PHASE FLOWS
International Journal for Uncertainty Quantification, Vol.4, 2014, issue 6
Guang Lin, Yalchin Efendiev, Lijian Jiang, Jia Wei
A STOCHASTIC INVERSE PROBLEM FOR MULTISCALE MODELS
International Journal for Multiscale Computational Engineering, Vol.15, 2017, issue 3
N. Panda, Lindley Graham, Clint Dawson, Troy Butler, Donald Estep
TRANSITIONAL ANNEALED ADAPTIVE SLICE SAMPLING FOR GAUSSIAN PROCESS HYPER-PARAMETER ESTIMATION
International Journal for Uncertainty Quantification, Vol.6, 2016, issue 4
Alfredo Garbuno-Inigo, F. A. DiazDelaO, Konstantin M. Zuev
FAST AND FLEXIBLE UNCERTAINTY QUANTIFICATION THROUGH A DATA-DRIVEN SURROGATE MODEL
International Journal for Uncertainty Quantification, Vol.8, 2018, issue 2
Gerta Köster, Hans-Joachim Bungartz, Felix Dietrich, Tobias Neckel, Florian Künzner
MULTIPLE SCENARIOS INTEGRATED UPSCALING WITH FULL TENSOR EFFECTS OF FRACTURED RESERVOIRS
Special Topics & Reviews in Porous Media: An International Journal, Vol.8, 2017, issue 4
Junchao Li, Zhengdong Lei, Shuhong Wu