  Diverse domains of science and engineering require and use mechanistic
mathematical models, e.g. systems of differential algebraic equations. Such
models often contain uncertain parameters to be estimated from data. Consider a
dynamic model discrimination setting where we wish to chose: (i) what is the
best mechanistic, time-varying model and (ii) what are the best model parameter
estimates. These tasks are often termed model
discrimination/selection/validation/verification. Typically, several rival
mechanistic models can explain data, so we incorporate available data and also
run new experiments to gather more data. Design of dynamic experiments for
model discrimination helps optimally collect data. For rival mechanistic models
where we have access to gradient information, we extend existing methods to
incorporate a wider range of problem uncertainty and show that our proposed
approach is equivalent to historical approaches when limiting the types of
considered uncertainty. We also consider rival mechanistic models as dynamic
black boxes that we can evaluate, e.g. by running legacy code, but where
gradient or other advanced information is unavailable. We replace these
black-box models with Gaussian process surrogate models and thereby extend the
model discrimination setting to additionally incorporate rival black-box model.
We also explore the consequences of using Gaussian process surrogates to
approximate gradient-based methods.
