Cholesky-based experimental design for Gaussian process and kernel-based emulation and calibration.
- Univ. of Basel (Switzerland)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Jacobs Univ., Bremen (Germany)
Gaussian processes and other kernel-based methods are used extensively to construct approximations of multivariate data sets. The accuracy of these approximations is dependent on the data used. This paper presents a computationally efficient algorithm to greedily select training samples that minimize the weighted Lp error of kernel-based approximations for a given number of data. The method successively generates nested samples, with the goal of minimizing the error in high probability regions of densities specified by users. The algorithm presented is extremely simple and can be implemented using existing pivoted Cholesky factorization methods. Training samples are generated in batches which allows training data to be evaluated (labeled) in parallel. For smooth kernels, the algorithm performs comparably with the greedy integrated variance design but has significantly lower complexity. Numerical experiments demonstrate the efficacy of the approach for bounded, unbounded, multi-modal and non-tensor product densities. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data using Bayesian inference.
- Research Organization:
- Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- Grant/Contract Number:
- AC04-94AL85000
- OSTI ID:
- 1770338
- Report Number(s):
- SAND--2020-12052J; 691942
- Journal Information:
- Communications in Computational Physics, Journal Name: Communications in Computational Physics Journal Issue: 4 Vol. 29; ISSN 1815-2406
- Publisher:
- Global Science PressCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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