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Abstract

Phenomena in many fields are described by differential equations where a quantity of interest (for example, depending on the phenomena modelled, a reaction rate, a capacitance, or a subject's cardiac output) appears as a parameter in the differential equation.  We then determine the quantity of interest by choosing parameters in the differential equation so that the computed solution of the differential equation using these parameters matches experimental data as closely as possible.  This may be posed as an optimisation problem that may be tackled by either a classical optimisation approach (as seen in the continuous mathematics course) or a Bayesian optimisation approach.  The aim of this project is to compare these approaches.

Prerequisites: linear algebra, continuous mathematics, probability