Dept. of Geosciences Colloquium: Advances in rare event simulations using data-based estimation of committor functions
Dario Lucente, ENS Lyon
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, as a function of the current state of the system. Computing this quantity from observations is an extremely complex task since rare events have a very low probability of occurring and may not even have been observed in measurements made to date. A key difficulty in numerical computation is that rare events can be so rare that simulating them directly is prohibitively expensive. Rare event algorithms have been devised to simulate them efficiently, avoiding the computation of long periods of typical fluctuations. The effectiveness of these algorithms strongly relies on the quality of the score function which is used for the selection stage. 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: a feedback control iterative procedure between the efficient algorithm to produce the data and the learning of the function itself. In the first part of this presentation, we introduce the committor function and we propose a data-driven approach for its computation. This approach aims at learning an effective dynamics by introducing a Markov chain (the analogue Markov chain) on the data. Then, the committor function can be computed using classical methods for computing Markov chain committor functions. We show the effectiveness of this approach in two models. Firstly, we compute the committor function for a paradigmatic toy model of multistability for atmospheric dynamics with six variables (the Charney-Devore model). In this case, the committor function is the probability to observe a transition between two different atmospheric regimes. Secondly, we apply this methodology to a climate data-set, generated from a climate model, in order to study and predict the occurrence of extreme heat waves. In this context, the committor function is the probability that an heat wave will occur within few weeks, as a function of the initial condition. 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 this talk, we provide evidence of the advantage of coupling the analogue Markov chain with a rare event algorithm. Indeed, the learned committor 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.
Event Organizers: Dr. Roy Barkan and Dr. Asaf Inbal