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Title: Weighted greedy-optimal design of computer experiments for kernel-based and Gaussian process model emulation and calibration

Abstract

This article is concerned with the approximation of high-dimensional functions by kernel-based methods. Motivated by uncertainty quantification, which often necessitates the construction of approximations that are accurate with respect to a probability density function of random variables, we aim at minimizing the approximation error with respect to a weighted $L^p$-norm. We present a greedy procedure for designing computer experiments based upon a weighted modification of the pivoted Cholesky factorization. The method successively generates nested samples with the goal of minimizing error in regions of high probability. Numerical experiments validate that this new importance sampling strategy is superior to other sampling approaches, especially when used with non-product probability density functions. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data.

Authors:
 [1];  [2];  [3]
  1. Univ. of Basel (Switzerland)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  3. Jacobs Univ. Bremen (Germany)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1608084
Report Number(s):
SAND-2020-3677R
685101
DOE Contract Number:  
AC04-94AL85000; NA0003525
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; uncertainty quantification; radial basis function; modeling; simulation; surrogate; Gaussian process; experimental design

Citation Formats

Helmut, Harbrecht, Jakeman, John Davis, and Zaspel, Peter. Weighted greedy-optimal design of computer experiments for kernel-based and Gaussian process model emulation and calibration. United States: N. p., 2020. Web. doi:10.2172/1608084.
Helmut, Harbrecht, Jakeman, John Davis, & Zaspel, Peter. Weighted greedy-optimal design of computer experiments for kernel-based and Gaussian process model emulation and calibration. United States. https://doi.org/10.2172/1608084
Helmut, Harbrecht, Jakeman, John Davis, and Zaspel, Peter. 2020. "Weighted greedy-optimal design of computer experiments for kernel-based and Gaussian process model emulation and calibration". United States. https://doi.org/10.2172/1608084. https://www.osti.gov/servlets/purl/1608084.
@article{osti_1608084,
title = {Weighted greedy-optimal design of computer experiments for kernel-based and Gaussian process model emulation and calibration},
author = {Helmut, Harbrecht and Jakeman, John Davis and Zaspel, Peter},
abstractNote = {This article is concerned with the approximation of high-dimensional functions by kernel-based methods. Motivated by uncertainty quantification, which often necessitates the construction of approximations that are accurate with respect to a probability density function of random variables, we aim at minimizing the approximation error with respect to a weighted $L^p$-norm. We present a greedy procedure for designing computer experiments based upon a weighted modification of the pivoted Cholesky factorization. The method successively generates nested samples with the goal of minimizing error in regions of high probability. Numerical experiments validate that this new importance sampling strategy is superior to other sampling approaches, especially when used with non-product probability density functions. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data.},
doi = {10.2172/1608084},
url = {https://www.osti.gov/biblio/1608084}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Apr 02 00:00:00 EDT 2020},
month = {Thu Apr 02 00:00:00 EDT 2020}
}