Extreme events in weather and climate are among the most detrimental effects of the Climate Crisis. Extreme heatwaves, for instance, have been responsible for significant excess mortality. Moreover, as the climate warms, there is a risk, still unsatisfactorily quantified, that extreme events could make us cross Tipping Points in the Earth System, leading to abrupt changes in the current climate.It is thus of paramount importance to improve our understanding of such extreme events and our ability to forecast them. However, by their nature, extreme events are rare, so there are very few instances in observational data and simulating them with state-of-the-art climate models can be very expensive. To counter this lack of data issue, Rare Event Algorithms can be applied to significantly improve the efficiency in simulating extreme events. Such algorithms need an estimate of the probability of occurrence of the event conditioned on the state of the system, and this is exactly what the prediction task provides.This thesis develops in two main directions. The first is to use Machine Learning (ML) to estimate from long climate model simulations the probabilities of extreme heatwaves over France. In particular, through a hierarchy of increasingly complex ML models, the tradeoffs between amount of data, performance and interpretability of the predictions are investigated. The second is to apply a Rare Event Algorithm to the study of the abrupt collapse of the Atlantic Meridional Overturning Circulation (AMOC). Finally these two pieces are put together to investigate how coupling Machine Learning and Rare Event Algorithms may improve our ability to sample and predict rare events.
