Well-behaved models in data-constrained systems

Abstract

Data comes in many different shapes and forms, but one property that all these types have in common when obtained in real-world scenarios is noise. For simple experiments, this noise can be easily modelled. In more complex scenarios, how this is done is difficult to answer, especially when this noise comes not only from the measurements, but from the system itself. Consequently, how modelling the system is done will not only depend on our assumptions of the data, but also on the constraints that the data impose. However, this thesis will seek models that have, independent of the type data they are being applied to, two desirable properties that make them “well-behaved”: uncertainty propagation, with the distribution of the model’s predictions having to follow that of the data; and smoothness, where similar data points must correspond to similar predictions.

With these two properties specified, this thesis looks into three different types of systems, each constrained in a different way by the data. The first one looks at dimensionality reduction of data sets where the number of data points can be considered large. More specifically, the first part of this thesis evaluates existing models to see if they have the desired properties. The second part of the thesis looks into modelling data that has a clear time-dependence, time-series data. Finally, the last part of this thesis also looks at data that has a time-dependence, but where only the initial and final time-points are available. Furthermore, the evolution of the data between these two points is also constrained in some way by an a priori assumption, with the aim being to find this constrained evolution. For both of these final parts, experiments validating the proposed methods are presented.

Date of Award	26 Jun 2024
Original language	English
Awarding Institution	University of Bath
Sponsors	National Physics Laboratory
Supervisor	Neill Campbell (Supervisor), Tom Fincham Haines (Supervisor) & Carl Henrik Ek (Supervisor)