This literature review extends and contributes to research on the development of data-driven optimal control. Previous reviews have documented the development of model-based and data-driven control in isolation and have not critically reviewed reinforcement learning approaches for adaptive data-driven optimal control frameworks. The presented review discusses the development of model-based to model-free adaptive controllers, highlighting the use of data in control frameworks. In data-driven control frameworks, reinforcement learning methods may be used to derive the optimal policy for dynamical systems. Attractive characteristics of these methods include not requiring a mathematical model of complex systems, their inherent adaptive control capabilities, being an unsupervised learning technique and their decision-making abilities, which are both an advantage and motivation behind this approach. This review considers previous reviews on these topics, including recent work on data-driven control methods. In addition, this review shows the use of data to derive system dynamics, determine the control policy using feedback information, and tune fixed controllers. Furthermore, the review summarises various data-driven methods and their corresponding characteristics. Finally, the review provides a taxonomy, a timeline and a concise narrative of the development of model-based to model-free data-driven adaptive control and underlines the limitations of these techniques due to the lack of theoretical analysis. Areas of further work include theoretical analysis on stability and robustness for data-driven control systems, explainability of black-box policy learning techniques and an evaluation of the impact of the extension of system simulators to include digital twins.

Galaxy morphology characterisation is an important area of study, as the type and formation of galaxies offer insights into the origin and evolution of the universe. Owing to the increased availability of images of galaxies, scientists have turned to crowd-sourcing to automate the process of instance labelling. However, research has shown that using crowd-sourced labels for galaxy classification comes with many pitfalls. An alternative approach to galaxy classification is metric learning. Metric learning allows for improved representations for classification, anomaly detection, information retrieval, clustering and dimensionality reduction. Understanding the implications of this approach regarding crowd-sourced labels is of paramount importance if scientists intend to continue using them. This paper compares metric learning and classification models trained or fine-tuned on both the crowd-sourced Galaxy Zoo 2 (GZ2-H) dataset and expertly labelled EFIGI catalogue. The study uses the Revised Shapley-Ames (RSA) catalogue of bright galaxies, also labelled by experts, as an unseen test set. The RSA catalogue allows for an accurate comparison of the performance of the models at predicting the Hubble types of galaxies. The classification accuracy for the crowd-sourced and expert models indicated that the models are comparable on the surface. However, using alternative metrics, the results show that the models trained on the expert dataset outperformed the model trained on the crowd-sourced data in terms of actual vs predicted labels. Further, the results show that fine-tuning a model pre-trained on crowd-sourced data can outperform the state-of-the-art in galaxy characterisation. The models trained to predict the Hubble types of galaxies are better when fine-tuned using the Proxy-NCA and Normalised-Softmax loss functions than with other pairwise losses. The Normalised-Softmax loss yielded the best overall 9-class models with accuracies at 30.88% (GZ2-H) and 30.05% (EFIGI) and MAP values of 0.3483 (GZ2-H) and 0.3889. The Proxy-NCA loss produced the second-best overall 9-class models with accuracies at 30.33% (GZ2-H) and 20.03% (EFIGI) and MAP values of 0.3577 (GZ2-H) and 0.3917 (EFIGI). Finally, the paper highlights the need for caution when utilising crowd-sourced labels; however, it argues that transfer learning from crowd-sourced labelled data to expert-labelled data can still lead to significant improvements.

This work investigates the convergence dynamics of a numerical scheme employed for the approximation and solution of the Frank–Kamenetskii partial differential equation. A framework for computing the critical Frank–Kamenetskii parameter to arbitrary accuracy is presented and used in the subsequent numerical simulations. The numerical method employed is a Crank–Nicolson type implicit scheme coupled with a fourth order spatial discretisation as well as a Newton–Raphson update step which allows for the nonlinear source term to be treated implicitly. This numerical implementation allows for the analysis of the convergence of the transient solution toward the steady-state solution. The choice of termination criteria, numerically dictating this convergence, is interrogated and it is found that the traditional choice for termination is insufficient in the case of the Frank–Kamenetskii partial differential equation which exhibits slow transience as the solution approaches the steady-state. Four measures of convergence are proposed, compared and discussed herein.