A Sequential Design Approach for Calibrating Dynamic Computer Simulators

摘要

Computer simulators are widely used to describe and explore complex physical processes. The simulator outputs may come in various formats: scalar, multivariate, functional, time series, spatial temporal, to name just a few. This work focuses on computer simulators with time series outputs, which we refer to as dynamic computer simulators. We consider the inverse problem for dynamic computer simulators, that is, to estimate the set of parameters/inputs of the simulator that produces the output matching a prespecified target, or the field observation, as closely as possible. The time series nature of both the field observation and the simulator outputs makes the inverse problem significantly more challenging than in the scalar valued simulator case. In spirit, we follow the popular sequential design framework of computer experiments. However, due to the time series response, a singular value decomposition based Gaussian process model is used for the surrogate model and, subsequently, a new saddle point approximation based expected improvement criterion is developed for choosing the follow-up points. We also propose a new criterion for extracting the optimal inverse problem solution from the final surrogate. Three simulated examples and a real-life two-delay blowfly model have been used to demonstrate higher accuracy of the proposed approach as compared to the popular existing techniques.