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Title: Multi-fidelity Gaussian process regression for prediction of random fields

Abstract

We propose a new multi-fidelity Gaussian process regression (GPR) approach for prediction of random fields based on observations of surrogate models or hierarchies of surrogate models. Our method builds upon recent work on recursive Bayesian techniques, in particular recursive co-kriging, and extends it to vector-valued fields and various types of covariances, including separable and non-separable ones. The framework we propose is general and can be used to perform uncertainty propagation and quantification in model-based simulations, multi-fidelity data fusion, and surrogate-based optimization. We demonstrate the effectiveness of the proposed recursive GPR techniques through various examples. Specifically, we study the stochastic Burgers equation and the stochastic Oberbeck–Boussinesq equations describing natural convection within a square enclosure. In both cases we find that the standard deviation of the Gaussian predictors as well as the absolute errors relative to benchmark stochastic solutions are very small, suggesting that the proposed multi-fidelity GPR approaches can yield highly accurate results.

Authors:
 [1];  [2];  [3];  [4]
  1. Department of Engineering and Architecture, University of Trieste (Italy)
  2. Department of Applied Mathematics and Statistics, University of California Santa Cruz (United States)
  3. Department of Mechanical Engineering, Massachusetts Institute of Technology (United States)
  4. Division of Applied Mathematics, Brown University (United States)
Publication Date:
OSTI Identifier:
22622285
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 336; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BENCHMARKS; COMPUTERIZED SIMULATION; ERRORS; FORECASTING; GAUSSIAN PROCESSES; KRIGING; MATHEMATICAL SOLUTIONS; NATURAL CONVECTION; OPTIMIZATION; RANDOMNESS; STOCHASTIC PROCESSES

Citation Formats

Parussini, L., Venturi, D., E-mail: venturi@ucsc.edu, Perdikaris, P., and Karniadakis, G.E. Multi-fidelity Gaussian process regression for prediction of random fields. United States: N. p., 2017. Web. doi:10.1016/J.JCP.2017.01.047.
Parussini, L., Venturi, D., E-mail: venturi@ucsc.edu, Perdikaris, P., & Karniadakis, G.E. Multi-fidelity Gaussian process regression for prediction of random fields. United States. doi:10.1016/J.JCP.2017.01.047.
Parussini, L., Venturi, D., E-mail: venturi@ucsc.edu, Perdikaris, P., and Karniadakis, G.E. Mon . "Multi-fidelity Gaussian process regression for prediction of random fields". United States. doi:10.1016/J.JCP.2017.01.047.
@article{osti_22622285,
title = {Multi-fidelity Gaussian process regression for prediction of random fields},
author = {Parussini, L. and Venturi, D., E-mail: venturi@ucsc.edu and Perdikaris, P. and Karniadakis, G.E.},
abstractNote = {We propose a new multi-fidelity Gaussian process regression (GPR) approach for prediction of random fields based on observations of surrogate models or hierarchies of surrogate models. Our method builds upon recent work on recursive Bayesian techniques, in particular recursive co-kriging, and extends it to vector-valued fields and various types of covariances, including separable and non-separable ones. The framework we propose is general and can be used to perform uncertainty propagation and quantification in model-based simulations, multi-fidelity data fusion, and surrogate-based optimization. We demonstrate the effectiveness of the proposed recursive GPR techniques through various examples. Specifically, we study the stochastic Burgers equation and the stochastic Oberbeck–Boussinesq equations describing natural convection within a square enclosure. In both cases we find that the standard deviation of the Gaussian predictors as well as the absolute errors relative to benchmark stochastic solutions are very small, suggesting that the proposed multi-fidelity GPR approaches can yield highly accurate results.},
doi = {10.1016/J.JCP.2017.01.047},
journal = {Journal of Computational Physics},
number = ,
volume = 336,
place = {United States},
year = {Mon May 01 00:00:00 EDT 2017},
month = {Mon May 01 00:00:00 EDT 2017}
}