Guided experimental design for static nonparametric modeling

Abstract

Sequential or goal-oriented experimental design methods help achieve the target cheaply and quickly. In this work, we exploit Bayesian Optimization to obtain accurate and reliable static models for physical phenomena in cases where parametric models are unavailable. Our Guided Design of Experiments (G-DoE) workflow is proposed with a purely explorative acquisition function and an empirical stopping criterion. Two stopping criteria are proposed, one that is based on convergence rates of the prediction uncertainty and another that is based on a tolerance limit. Stopping criteria thresholds are established by studying factors like noise level and dimension size and their impact on prediction uncertainty convergence. Furthermore, we compare the G-DoE framework with classical Full Factorial and Response Surface strategies in terms of the suggested number of experiments and corresponding accuracy of fit. The proposed algorithm is tested using a methanol synthesis reaction experiment, a vapor pressure experiment, and a synthetic example.