History matching with probabilistic emulators and active learning

Abstract

The scientific understanding of real-world processes has dramatically improved over the years through computer simulations. Such simulators represent complex mathematical models that are implemented as computer codes which are often expensive. The validity of using a particular simulator to draw accurate conclusions relies on the assumption that the computer code is correctly calibrated. This calibration procedure is often pursued under extensive experimentation and comparison with data from a real-world process. The problem is that the data collection may be so expensive that only a handful of experiments are feasible. History matching is a calibration technique that, given a simulator, it iteratively discards regions of the input space using an implausibility measure. When the simulator is computationally expensive, an emulator is used to explore the input space. In this paper, a Gaussian process provides a complete probabilistic output that is incorporated into the implausibility measure. The identification of regions of interest is accomplished with recently developed annealing sampling techniques. Active learning functions are incorporated into the history matching procedure to refocus on the input space and improve the emulator. The efficiency of the proposed framework is tested in well-known examples from the history matching literature, as well as in a proposed testbed of functions of higher dimensions.