Motivated by a computer model calibration problem from the oil and gas industry, involving the design of a honeycomb seal, we develop a new Bayesian methodology to cope with limitations in the canonical apparatus stemming from several factors. We propose a new strategy of on-site design and surrogate modeling for a computer simulator acting on a high-dimensional input space that, although relatively speedy, is prone to numerical instabilities, missing data, and nonstationary dynamics. Our aim is to strike a balance between data-faithful modeling and computational tractability in a calibration framework-tailoring the computer model to a limited field experiment. Situating our on-site surrogates within the canonical calibration apparatus requires updates to that framework. We describe a novel yet intuitive Bayesian setup that carefully decomposes otherwise prohibitively large matrices by exploiting the sparse blockwise structure. Empirical illustrations demonstrate that this approach performs well on toy data and our motivating honeycomb example.
K E Y W O R D SBayesian calibration, big data, computer experiment, local Gaussian process, hierarchical model, uncertainty quantification
INTRODUCTIONWith remarkable advances in computing power, today's complex physical systems can be simulated comparatively cheaply and to high accuracy by using mature libraries. The ability to simulate has dramatically driven down the cost of scientific inquiry in engineering settings, at least at initial proof-of-concept stages. Even so, computer models often idealize the system-they are biased-or require the setting of tuning parameters: inputs unknown or uncontrollable in actual physical processes in the field. An excellent example is the simulation of a free-falling object, which is a potentially involved if well-understood enterprise from a modeling perspective. Acceleration due to gravity might be known, but possibly not precisely. Coefficients of drag may be completely unknown. A model incorporating both factors but not others such as ambient air disturbance or rotational velocity could be biased in consistent but unpredictable ways.Researchers are interested in calibrating such models to experimental data. With a flexible yet sturdy apparatus, a limited number of field observations from physical experiments can provide valuable information to fine tune, improve fidelity, understand uncertainty, and correct bias between simulations and physical phenomena they model. When done right, tuned and bias-corrected simulations are more realistic, forecasts more reliable, and these can inform simulation redevelopment, if necessary.Appl Stochastic Models Bus Ind. 2020;36:283-304.wileyonlinelibrary.com/journal/asmb