Reservoir computers rely on an internal network to predict the future state(s) of dynamical processes. To understand how a reservoir's accuracy depends on this network, we study how varying the networ's topology and scaling affects the reservoir's ability to predict the chaotic dynamics on the Lorenz attractor. We define a metric for diversity, the property describing the variety of the responses of the nodes that make up reservoir's internal network. We use Bayesian hyperparameter optimization to find optimal hyperparameters and explore the relationships between diversity, accuracy of model predictions, and model hyperparameters. The content regarding the VPT metric, the effects of network thinning on reservoir computing, and the results from grid search experiments mentioned in this thesis has been done previously. The results regarding the diversity metric, kernel tests, and results from BHO are new and use this previous work as a comparison to the quality and usefulness of these new methods in creating accurate reservoir computers.

This thesis investigates the computer-based modelling and simulation of complex geospatial phenomena. Geospatial systems are real world processes which extend over some meaningful extent of the Earth's surface, such as cities and fisheries. There are many problems that require urgent attention in this domain (for example relating to sustainability) but despite increasing amounts of data and computational power there is a significant gap between the potential for model-based analyses and their actual impact on real world policy and planning. Analytical methods are confounded by the high dimensionality and nonlinearity of spatio-temporal systems and/or are hard to relate to meaningful policy decisions. Simulation-based approaches on the other hand are more heuristic and policy oriented in nature, but they are difficult to validate and almost always over-fit the data: although a given model can be calibrated on a given set of data, it usually performs very poorly on new unseen data sets. The central contribution of this thesis is a framework which is formally grounded and able to be rigourously validated, yet at the same time is interpretable in terms of real world phenomena and thus has a strong connection to domain knowledge. The scope of the thesis spans both theory and practice, and three specific contributions range along this span. Starting at the theoretical end, the first contribution concerns the conceptual and theoretical basis of the framework, which is a technique known as delay reconstruction. The underlying theory is rooted in the rather technical field of dynamical systems (itself largely based on differential topology), which has hindered its wider application and the formation of strong links with other areas. Therefore, the first contribution is an exposition of delay reconstruction in non-technical language, with a focus on explaining how some recent extensions to this theory make the concept far more widely applicable than is often assumed. The second contribution uses this theoretical foundation to develop a practical, unified framework for pattern discovery and hypothesis exploration in geo-spatial data. The central aspect of this framework is the linking of delay reconstruction with domain knowledge. This is done via the notion that determinism is not an on-off quantity, but rather that a given data set may be ascribed a particular 'degree' of determinism, and that that degree may be increased through manipulation of the data set using domain knowledge. This leads to a framework which can handle spatiotemporally complex (including multi-scale) data sets, is sensitive to the amount of data that is available, and is naturally geared to be used interactively with qualitative feedback conveyed to the user via geometry. The framework is complementary to other techniques in that it forms a scaffold within which almost all modelling approaches - including agent-based modelling - can be cast as particular kinds of 'manipulations' of the data, and as such are easily integrated. The third contribution examines the practical efficacy of the framework in a real world case study. This involves a high resolution spatio-temporal record of fishcatch data from trawlers operating in a large fishery. The study is used to test two fundamental capabilities of the framework: (i) whether real world spatio-temporal phenomena can be identified in the degree-of-determinism signature of the data set, (ii) whether the determinism-level can then be increased by manipulating the data in response to this phenomena. One of the main outcomes of this study is a clear identification of the influence of the lunar cycle on the behaviour of Tiger and Endeavour prawns. The framework allows for this to be 'non-destructively subtracted', increasing the detect-ability of further phenomena.