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Known Boundary Emulation of Complex Computer Models

Vernon, I.R.; Jackson, S.E.; Cumming, J.A.

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Sam Jackson samuel.e.jackson@durham.ac.uk
Assistant Professor



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Abstract

Computer models are now widely used across a range of scientific disciplines to describe various complex physical systems, however to perform full uncertainty quantification we often need to employ emulators. An emulator is a fast statistical construct that mimics the complex computer model, and greatly aids the vastly more computationally intensive uncertainty quantification calculations that a serious scientific analysis often requires. In some cases, the complex model can be solved far more efficiently for certain parameter settings, leading to boundaries or hyperplanes in the input parameter space where the model is essentially known. We show that for a large class of Gaussian process style emulators, multiple boundaries can be formally incorporated into the emulation process, by Bayesian updating of the emulators with respect to the boundaries, for trivial computational cost. The resulting updated emulator equations are given analytically. This leads to emulators that possess increased accuracy across large portions of the input parameter space. We also describe how a user can incorporate such boundaries within standard black box GP emulation packages that are currently available, without altering the core code. Appropriate designs of model runs in the presence of known boundaries are then analysed, with two kinds of general purpose designs proposed. We then apply the improved emulation and design methodology to an important systems biology model of hormonal crosstalk in Arabidopsis Thaliana.

Citation

Vernon, I., Jackson, S., & Cumming, J. (2019). Known Boundary Emulation of Complex Computer Models. SIAM/ASA Journal on Uncertainty Quantification, 7(3), 838-876. https://doi.org/10.1137/18m1164457

Journal Article Type Article
Acceptance Date Feb 26, 2019
Online Publication Date Jul 11, 2019
Publication Date Jan 1, 2019
Deposit Date Jan 10, 2018
Publicly Available Date Mar 29, 2024
Journal SIAM/ASA Journal on Uncertainty Quantification
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 7
Issue 3
Pages 838-876
DOI https://doi.org/10.1137/18m1164457
Related Public URLs http://arxiv.org/abs/1801.03184

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© 2019, Society for Industrial and Applied Mathematics.




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