Determining optimal factors for chemical synthesis of pharmaceutical products using experimental data
Antony Overstall (University of Glasgow)
Friday 29th January, 2016 15:00-16:00 Maths 522
In a chemical synthesis process to manufacture a pharmaceutical product, an initial set of substances evolve according to chemical reactions, under certain process conditions, into a series of new substances. One of these substances is a target pharmaceutical product and two are unwanted by-products. The aim is to determine the factors (process conditions and amounts of initial substances) that maximise the probability of the amounts of pharmaceutical product and by-products being greater and less than certain levels, respectively. The relationship between the factors and amounts of substances of interest is theoretically described by the intractable solution to a system of ordinary differential equations incorporating temperature dependence. This relationship is refined using observations from an experiment by the fitting of a statistical model. Predictions from this model are used to evaluate the probability of satisfying the constraints and this probability is maximised over the set of factors to provide optimal manufacturing conditions for the pharmaceutical product. To accelerate the model-fitting and the evaluation of the probability of satisfying the constraints, the numerical solution to the differential equations is approximated using statistical emulators.