Prior to this, I completed a Master of Philosophy (MPhil) in Applied Mathematics at the University of Adelaide, under the 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) to understand how this uncertainty impacts predictions from a model, without having to resort to computationally expensive simulation. My completed thesis is available here.
Publications & Preprints
2025
Rigorous Convergence Bounds for Stochastic Differential Equations with Application to Uncertainty Quantification
Liam A. A. Blake, John Maclean, and Sanjeeva Balasuriya
Prediction via continuous-time models will always be subject to model error, for example due to unexplainable phenomena, uncertainties in any data driving the model, or discretisation/resolution issues. In this paper, we consider a general class of stochastic differential equations and provide rigorous convergence bounds to an analytically solvable approximation. We provide the explicit convergence rate for all moments of a fully non-autonomous model with both multiplicative noise and uncertain initial conditions. Our second main contribution is to extend stochastic sensitivity, a recently introduced uncertainty quantification tool, to arbitrary dimensions and provide a new calculation method that empowers rapid computation. We demonstrate the power and adaptability of our contributions on a diverse set of numerical examples in 1-, 2-, 3-, and 4-dimensions, including providing stochastic sensitivity calculations for an idealised eddy parameterisation of the Gulf Stream.
2024
Computable Characterisations of Uncertainty in Differential Equations
Liam A. A. Blake
2024
Unifying Lyapunov Exponents with Probabilistic Uncertainty Quantification
Computable Characterisations of Uncertainty in Differential Equations2024