Gaussian processes for hybridisation of analytical and data-driven approaches for design of experiments

Abstract

In many areas of science and engineering, gathering data and making measurements of a system is costly and time-consuming. Whether the data comes from real-life experiments or computer models, we wish to maximally utilise already existing data to make informed and optimal decisions. The decisions might have to do with where next to evaluate the system, or how to control the system. Our focus is on design of experiments to aid model discrimination, i.e. discarding inadequate members of a set of rival models.

Many models are too complex to analyse to the extent we sometimes wish. To discriminate between parametric models, we often wish to compute function gradients. However, if our function involves evaluating complex legacy code or stochastic simulations, then function gradients are not readily available to us. The function is effectively a black box, where we can input variable values and collect the output function value, without knowing exactly what happens inside the box.

For situations involving black-box functions or models, we turn to black-box methods. Our approach is to construct probabilistic surrogate models using Gaussian process regression. A Gaussian process is a distribution over functions, yielding a Gaussian distribution at each test point, with a mean and variance conditioned on previous function or model evaluations.

We use the surrogate model method to tackle design of experiments for model discrimination. Given our surrogate models, we can utilise existing analytical methods to solve our problems, taking the inherent uncertainty in variables and about our surrogate models into account. Using literature case studies, we demonstrate how our method balances accuracy and computational complexity in solving both the design of experiments and model discrimination problems. We do this for both static and dynamic models. Open-source Python packages GPdoemd and doepy implement our methods.