Hierarchical Bayesian Emulation of the Expected Net Present Value Utility Function via a Multi-Model Ensemble Member Decomposition

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 establish a hierarchical emulation framework encompassing structured emulators which exploit known constrained and structured behaviour of constituent computer model outputs. This 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. We re-express this as a decision support under uncertainty problem. First, we reduce the computational expense of the analysis by identifying a representative subset of models using an efficient multi-model ensemble subsampling technique. Next we apply our hierarchical emulation methodology to the expected Net Present Value utility function with well control decision parameters as inputs.