Using Gaussian Processes to Design Dynamic Experiments for Black-Box Model Discrimination under Uncertainty

Abstract

Diverse domains of science and engineering use parameterised mechanistic models. Engineers and scientists can often hypothesise several rival models to explain a specific process or phenomenon. Consider a model discrimination setting where we wish to find the best mechanistic, dynamic model candidate and the best model parameter estimates. Typically, several rival mechanistic models can explain the available data, so design of dynamic experiments for model discrimination helps optimally collect additional data by finding experimental settings that maximise model prediction divergence. We argue there are two main approaches in the literature for solving the optimal design problem: (i) the analytical approach, using linear and Gaussian approximations to find closed-form expressions for the design objective, and (ii) the data-driven approach, which often relies on computationally intensive Monte Carlo techniques. Olofsson et al. (ICML 35, 2018) introduced Gaussian process (GP) surrogate models to hybridise the analytical and data-driven approaches, which allowed for computationally efficient design of experiments for discriminating between black-box models. In this study, we demonstrate that we can extend existing methods for optimal design of dynamic experiments to incorporate a wider range of problem uncertainty. We also extend the Olofsson et al. (2018) method of using GP surrogate models for discriminating between dynamic black-box models. We evaluate our approach on a well-known case study from literature, and explore the consequences of using GP surrogates to approximate gradient-based methods.