I have recently completed a Master of Philosophy (MPhil) in Applied Mathematics at the University of Adelaide, under the wonderful supervision of Associate Professor Sanjeeva Balasuriya and Dr. John Maclean. My research looked at devising practical and computationally efficient methods for characterising uncertainty in geophysical systems, such as the ocean, atmosphere, and climate. Uncertainty can arise from many sources, including measurement error and unresolved process, and directly accounting for this can improve the predictions and forecasts of these models. I combined stochastic processes, dynamical systems, and scientific computing (in Julia, because it’s a cool and fast language) to understand how this uncertainty impacts predictions from a model, without having to resort to computationally expensive simulation. My completed thesis is available here.
Liam Blake. Computable Characterisations of Uncertainty in Differential Equations (2024). MPhil Thesis.
Liam Blake, John Maclean, Sanjeeva Balasuriya (2024). Unifying Lyapunov exponents with probabilistic uncertainty quantification. In review. 10.48550/arXiv.2403.05085.
Liam Blake, John Maclean, Sanjeeva Balasuriya (2023). The convergence of stochastic differential equations to their linearisations in small noise limits. In review. 10.48550/arXiv.2309.16334.