English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We propose a methodology for improving the accuracy of surrogate models ofthe observable response of physical systems as a function of the systems'spatially heterogeneous parameter fields with applications to uncertaintyquantification and parameter estimation in high-dimensional problems.Practitioners often formulate finite-dimensional representations of spatiallyheterogeneous parameter fields using truncated unconditional Karhunen-Lo\'{e}veexpansions (KLEs) for a certain choice of unconditional covariance kernel andconstruct surrogate models of the observable response with respect to therandom variables in the KLE. When direct measurements of the parameter fieldsare available, we propose improving the accuracy of these surrogate models byrepresenting the parameter fields via conditional Karhunen-Lo\'{e}ve expansions(CKLEs). CKLEs are constructed by conditioning the covariance kernel of theunconditional expansion on the direct measurements via Gaussian processregression and then truncating the corresponding KLE. We apply the proposedmethodology to constructing surrogate models via the Basis Adaptation (BA)method of the stationary hydraulic head response, measured at spatiallydiscrete observation locations, of a groundwater flow model of the HanfordSite, as a function of the 1,000-dimensional representation of the model'slog-transmissivity field. We find that BA surrogate models of the hydraulichead based on CKLEs are more accurate than BA surrogate models based onunconditional expansions for forward uncertainty quantification tasks.Furthermore, we find that inverse estimates of the hydraulic transmissivityfield computed using CKLE-based BA surrogate models are more accurate thanthose computed using unconditional BA surrogate models.

Conditional Korhunen-Lo\'{e}ve regression model with Basis Adaptation for high-dimensional problems: uncertainty quantification and inverse modeling