Learning model discrepancy: A Gaussian process and sampling-based approach

Predicting events in the real world with a computer model (simulator) is challenging. Every simulator, to varying extents, has model discrepancy, a mismatch between real world observations and the simulator (given the ‘true’ parameters are known). Model discrepancy occurs for various reasons, including simplified or missing physics in the simulator, numerical approximations that are required to compute the simulator outputs, and the fact that assumptions in the simulator are not generally applicable to all real world contexts. The existence of model discrepancy is problematic for the engineer as performing calibration of the simulator will lead to biased parameter estimates, and the resulting simulator is unlikely to accurately predict (or even be valid for) various contexts of interest. This paper proposes an approach for inferring model discrepancy that overcomes non-identifiability problems associated with jointly inferring the simulator parameters along with the model discrepancy. Instead, the proposed procedure seeks to identify model discrepancy given some parameter distribution, which could come from a ‘likelihood-free’ approach that considers the presence of model discrepancy during calibration, such as Bayesian history matching. In this case, model discrepancy is inferred whilst marginalising out the uncertain simulator outputs via a sampling-based approach, therefore better reflecting the ‘true’ uncertainty associated with the model discrepancy. Verification of the approach is performed before a demonstration on an experiential case study, comprising a representative five storey building structure.