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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.

In Germany, 6100 women and 5300 men contract a malignant melanoma of the skin every year. The chances of being cured are good in the early stages of the disease, but the average survival following distant metastasis is only 6 to 9 months. Therefore, early diagnosis is crucial, particularly as the skin is, by nature, a readily accessible organ. The introduction of epiluminescence microscopy has increased diagnostic accuracy significantly. In cases of doubt, complete excision of the suspect pigmented lesion is always advisable. A light skin type, presence of numerous naevi, genetic predisposition (familial history) and increased UV exposure are considered as risk factors. As a rule, adjuvant imunotherapy with interferon-alphais recommended in high-risk patients. A multidisciplinary approach consisting of surgery, radiotherapy, chemotherapy and immunotherapy has proved beneficial in advanced stages of metastasis.