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

Technical Report · Thu Apr 02 04:00:00 EDT 2020

DOI:https://doi.org/10.2172/1608084· OSTI ID:1608084

Helmut, Harbrecht ^[1]; Jakeman, John Davis ^[2]; Zaspel, Peter ^[3]

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1. Univ. of Basel (Switzerland)
2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
3. Jacobs Univ. Bremen (Germany)

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.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
• DOE Contract Number: AC04-94AL85000; NA0003525
• OSTI ID: 1608084
• Report Number(s): SAND--2020-3677R; 685101
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Gaussian process
experimental design
modeling
radial basis function
simulation
surrogate
uncertainty quantification