Project: Dynamical measures of uncertainty in neural networks with application to climate dynamics
Supervisors: Kevin Webster (Imperial) & Martin Rasmussen (Imperial)
Project Description:
Neural networks have become a predominant modelling paradigm in many applications, including climate dynamics [1,2]. Standard neural network models do not capture measures of uncertainty, which is problematic since neural networks have been shown to behave sensitively with respect to changes in input data [3]. Traditional approaches to quantify uncertainty use statistical methods. In contrast, we propose to use dynamical systems quantities such as (finite-time) Lyapunov exponents to understand sensitivity with respect to inputs and parameters. Lyapunov exponents are traditionally used to characterise the behaviour of dynamical systems with respect to perturbations. In this project, we first aim to understand this in the context of low-dimensional climate models. The overall aim, however, is to examine how Lyapunov exponents can be learned from data, using a neural network model, so that uncertainty becomes a quantitity that can be understood without the availability of a dynamical systems (climate) model.
We aim to collaborate with the Potsdam Institute for Climate Impact Research (PIK), to apply this to network and machine-learning-based prediction of extreme events, see https://www.pik-potsdam.de/en/institute/departments/complexity-science/research/network-and-machine-learning-based-prediction-of-extreme-events.
