Advances in rare event simulations using data-based estimation of committor functions

Rare events, such as heat waves, floods, or hurricanes, play a crucial role in climate dynamics mainly due to the large impact they have. Predicting the occurrence of such events is thus a major challenge. 

In this talk, we introduce the relevant mathematical object for predicting a future event: the committor function is the probability that an event will occur, conditioned on the current state of the system. Computing this quantity from observations is an extremely difficult task since rare events have a very low probability of occurring and may not even have been observed in measurements made to date. Similarly, direct simulation of such events with comprehensive climate models comes at a prohibitive computational cost. Hence, rare event algorithms have been devised to simulate rare events efficiently, avoiding the computation of long periods of typical fluctuations.

The effectiveness of these algorithms strongly relies on the knowledge of a measure of how close the event of interest is to occur, called the “score function”. The main difficulty is that the optimal score function is the committor function which is exactly the quantity to be computed. Therefore, it is very natural to consider an iterative procedure where the data produced by the algorithm is used to improve the score function, which in turn improves the algorithm, and so on.

In this presentation, we propose a data-driven approach for computing the committor function, based on a Markov chain approximation of the dynamics of the system (the analogue method). We first illustrate this approach for a paradigmatic toy model of multistability for atmospheric dynamics with six variables (the Charney-Devore model). Secondly, we apply this methodology to data generated from a climate model, in order to study and predict the occurrence of extreme heat waves. In both cases, we show that it is possible to obtain fairly precise estimates of the committor function, even when few observations are available.

In the second part of the talk, we show the advantage of coupling the analogue Markov chain with a rare event algorithm. Indeed, the committor learned with the analogue Markov chain can be used as a score function performing better than user-defined score functions, as we show for the Charney-Devore model. 

This new approach is promising for studying rare events in complex dynamics: the rare events can be simulated with a minimal prior knowledge and the results are much more precise than those obtained with a user-designed score function.