Modelling from spatiotemporal data: a dynamic systems approach

Several natural phenomena manifest themselves as spatiotemporal evolution processes. The study of these processes, which aims to increase our understanding of the spatiotemporal phenomena for their prediction and control, requires analysis tools to infer models and their parameters from collected data. Whilst several studies exist on how to model from highly complex patterns characteristic of spatiotemporal processes, an approach which may be readily employed in a wide range of scenarios, such as with systems with different forms of observation processes or time-varying systems, is lacking. This work fills this void by providing a systems approach to spatiotemporal modelling which can be used with continuous observations, point process observations, systems exhibiting spatially varying dynamics and time-varying systems.

The developed methodology builds on the stochastic partial differential equation as a suitable class of models for dynamic spatiotemporal modelling which can easily cater for spatially varying dynamics. A dimensionality reduction mechanism employing frequency methods is proposed; this is used to bring the spatiotemporal system, coupled with the observation process, into conventional state-space form. The work also provides a series of joint field-parameter inference methods which can cater for the vast range of problems under study. Variational techniques are found to be particularly amenable to these kinds of problem and hence a novel dual variational filter is developed to cater for time-varying spatiotemporal systems. The filter is seen to compare favourably with other conventional approaches and to work well on real temporal data sets.

The potential of adopting a systems approach to spatiotemporal modelling is shown on the large-scale Wikileaks data set, the Afghan War Diary, where it is found that reliable predictions are possible even in complex scenarios. The encouraging results are a strong indication that the adopted approach may be used for large-scale spatiotemporal systems across several disciplines and thus provide a mechanism by which stochastic models are made available for spatiotemporal control purposes.