Title: A localized ensemble of approximate Gaussian processes for fast sequential emulation

Abstract

More attention has been given to the computational cost associated with the fitting of an emulator. Substantially less attention is given to the computational cost of using that emulator for prediction. This is primarily because the cost of fitting an emulator is usually far greater than that of obtaining a single prediction, and predictions can often be obtained in parallel. In many settings, especially those requiring Markov Chain Monte Carlo, predictions may arrive sequentially and parallelization is not possible. In this case, using an emulator procedure which can produce accurate predictions efficiently can lead to substantial time savings in practice. In this paper, we propose a global model approximate Gaussian process framework via extension of a popular local approximate Gaussian process (laGP) framework. Our proposed emulator can be viewed as a treed Gaussian process where the leaf nodes are laGP models, and the tree structure is learned greedily as a function of the prediction stream. The suggested method (called leapGP) has interpretable tuning parameters which control the time-memory trade-off. One reasonable choice of settings leads to an emulator with a $$\mathscr{O}$$(N²) training cost and makes predictions rapidly with an asymptotic amortized cost of $$\mathscr{O}(\sqrt{N})$$

Authors:

Rumsey, Kellin N.  ^[1];

• Search DOE PAGES for author "Rumsey, Kellin N."
• Search DOE PAGES for ORCID "0000-0002-2989-965X"

Huerta, Gabriel ^[2]; Derek Tucker, J.  ^[2]

• Search DOE PAGES for author "Derek Tucker, J."
• Search DOE PAGES for ORCID "0000-0001-8844-2169"

---

+ Show Author Affiliations

1. Statistical Sciences Los Alamos National Laboratory Los Alamos New Mexico USA
2. Statistical Sciences Sandia National Laboratories Albuquerque New Mexico USA

Publication Date:

Fri May 05 00:00:00 EDT 2023

Research Org.:

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:

USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:

1972761

Alternate Identifier(s):

OSTI ID: 1972762; OSTI ID: 1975649

Report Number(s):

LA-UR-22-30978
Journal ID: ISSN 2049-1573; e576

Grant/Contract Number:  

89233218CNA000001

Resource Type:

Published Article

Journal Name:

Stat

Additional Journal Information:

Journal Name: Stat Journal Volume: 12 Journal Issue: 1; Journal ID: ISSN 2049-1573

Publisher:

Wiley Blackwell (John Wiley & Sons)

Country of Publication:

United Kingdom

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; Mathematics; Gaussian process; approximation; emulation; MCMC; computer models; local approximate GPs