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Rare events play a crucial role in many physics, chemistry, and biologyphenomena, when they change the structure of the system, for instance in thecase of multistability, or when they have a huge impact. Rare event algorithmshave been devised to simulate them efficiently, avoiding the computation oflong periods of typical fluctuations. We consider here the family of splittingor cloning algorithms, which are versatile and specifically suited forfar-from-equilibrium dynamics. To be efficient, these algorithms need to use asmart score function during the selection stage. Committor functions are theoptimal score functions. In this work we propose a new approach, based on theanalogue Markov chain, for a data-based learning of approximate committorfunctions. We demonstrate that such learned committor functions are extremelyefficient score functions when used with the Adaptive Multilevel Splittingalgorithm. We illustrate our approach for a gradient dynamics in a three-wellpotential, and for the Charney-DeVore model, which is a paradigmatic toy modelof multistability for atmospheric dynamics. For these two dynamics, we showthat having observed a few transitions is enough to have a very efficientdata-based score function for the rare event algorithm. This new approach ispromising for use for complex dynamics: the rare events can be simulated with aminimal prior knowledge and the results are much more precise than thoseobtained with a user-designed score function.

Coupling rare event algorithms with data-based learned committor functions using the analogue Markov chain