Abstract

Here, we propose a methodology for improving the accuracy of surrogate models of the observable response of physical systems as a function of the systems’ spatially heterogeneous parameter fields, with applications to uncertainty quantification and parameter estimation in high-dimensional problems. Practitioners often formulate finite-dimensional representations of spatially heterogeneous parameter fields using truncated unconditional Karhunen–Loève expansions (KLEs) for a certain choice of unconditional covariance kernel and construct surrogate models of the observable response with respect to the KLE coefficients. When direct measurements of the parameter fields are available, we propose improving the accuracy of these surrogate models by representing the parameter fields via conditional Karhunen-Loève expansions (CKLEs). CKLEs are constructed by conditioning the covariance kernel of the unconditional expansion on the direct measurements of the parameter field via Gaussian process regression, and then truncating the corresponding KLE. We apply the proposed methodology to constructing surrogate models via the Basis Adaptation (BA) method of the stationary hydraulic head response, measured at spatially discrete observation locations, of a groundwater flow model of the Hanford Site, as a function of the 1000-dimensional representation of the model’s log-transmissivity field. We find that BA surrogate models of the hydraulic head based on CKLEs are more accuratemore » than BA surrogate models based on unconditional expansions for forward uncertainty quantification tasks. Furthermore, we find that inverse estimates of the hydraulic transmissivity field computed using CKLE-based BA surrogate models are more accurate than those computed using unconditional BA surrogate models.« less

Authors:

Yeung, Yu-Hong  ^[1];

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• Search DOE PAGES for ORCID "0000-0003-3210-9898"

Tipireddy, Ramakrishna  ^[2];

• Search DOE PAGES for author "Tipireddy, Ramakrishna"
• Search DOE PAGES for ORCID "0000-0003-2196-2164"

Barajas-Solano, David A.  ^[3];

• Search DOE PAGES for author "Barajas-Solano, David A."
• Search DOE PAGES for ORCID "0000-0003-1442-8086"

Tartakovsky, Alexandre M.  ^[4]

• Search DOE PAGES for author "Tartakovsky, Alexandre M."
• Search DOE PAGES for ORCID "0000-0003-2375-318X"

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+ Show Author Affiliations

1. Univ. of Illinois at Urbana-Champaign, IL (United States)
2. Palo Alto Networks, Santa Clara, CA (United States)
3. Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
4. Univ. of Illinois at Urbana-Champaign, IL (United States); Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Publication Date:

Mon Oct 09 00:00:00 EDT 2023

Research Org.:

Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:

2283182

Alternate Identifier(s):

OSTI ID: 2202516

Report Number(s):

PNNL-SA-186970
Journal ID: ISSN 0045-7825

Grant/Contract Number:  

AC05-76RL01830

Resource Type:

Accepted Manuscript

Journal Name:

Computer Methods in Applied Mechanics and Engineering

Additional Journal Information:

Journal Volume: 418; Journal ID: ISSN 0045-7825

Publisher:

Elsevier

Country of Publication:

United States

Language:

English

Subject:

97 MATHEMATICS AND COMPUTING; model inversion; surrogate modeling; artificial intelligence; conditional Karhunen–Loéve expansion; basis adaptation; uncertainty quantification; inverse modeling; parameter estimation