Healthcare companies must submit pharmaceutical drugs or medical device to regulatory bodies before marketing new technology. Regulatory bodies frequently require transparent and interpretable computational modelling to justify a new healthcare technology, but researchers may have several competing models for a biological system and too little data to discriminate between the models. In design of experiments for model discrimination, where the goal is to design maximally informative physical experiments in order to discriminate between rival predictive models, research has focused either on analytical approaches, which cannot manage all functions, or on data-driven approaches, which may have computational difficulties or lack interpretable marginal predictive distributions. We develop a methodology for introducing Gaussian process surrogates in lieu of the original mechanistic models. This allows us to extend existing design and model discrimination methods developed for analytical models to cases of non-analytical models.