Bayesian Emulation of Grey-Box Multi-Model Ensembles Exploiting Known Interior Structure
Computer models are widely used to study complex real world physical systems. However, there are major limitations to their direct use including: their complex structure; large numbers of inputs and outputs; and long evaluation times. Bayesian emulators are an effective means of addressing these challenges providing fast and efficient statistical approximation for computer model outputs. It is commonly assumed that computer models behave like a ``black-box'' function with no knowledge of the output prior to its evaluation. This ensures that emulators are generalisable but potentially limits their accuracy compared with exploiting such knowledge of constrained or structured output behaviour. We assume a ``grey-box'' computer model and develop a methodological toolkit for its analysis. This includes: multi-model ensemble subsampling to identifying a representative model subset to reduce computational expense; constructing a targeted Bayesian design for optimisation or decision support; a ``divide-and-conquer'' approach to emulating sums of outputs; structured emulators exploiting known constrained and structured behaviour of constituent outputs through splitting the parameter space and imposing truncations; emulation of sums of time series outputs; and emulation of multi-model ensemble outputs. Combining these methods establishes a hierarchical emulation framework which achieves greater physical interpretability and more accurate emulator predictions. This research is motivated by and applied to the commercially important TNO OLYMPUS Well Control Optimisation Challenge from the petroleum industry which we re-express as a decision support under uncertainty problem. We thus encourage users to examine their ``black-box'' simulators to achieve superior emulator accuracy.