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

TL;DR

This paper introduces a data-driven method to learn optimal score functions for rare event algorithms using the analogue Markov chain, significantly improving efficiency and precision in simulating rare events in complex systems.

Contribution

The authors propose a novel approach to learn committor functions from data using the analogue Markov chain, enhancing rare event simulation efficiency.

Findings

Learned committor functions are highly effective as score functions in splitting algorithms.

Few observed transitions suffice to create efficient score functions.

The method outperforms user-designed score functions in complex dynamics.

Abstract

Rare events play a crucial role in many physics, chemistry, and biology phenomena, when they change the structure of the system, for instance in the case of multistability, or when they have a huge impact. Rare event algorithms have been devised to simulate them efficiently, avoiding the computation of long periods of typical fluctuations. We consider here the family of splitting or cloning algorithms, which are versatile and specifically suited for far-from-equilibrium dynamics. To be efficient, these algorithms need to use a smart score function during the selection stage. Committor functions are the optimal score functions. In this work we propose a new approach, based on the analogue Markov chain, for a data-based learning of approximate committor functions. We demonstrate that such learned committor functions are extremely efficient score functions when used with the Adaptive Multilevel Splitting algorithm. We illustrate our approach for a gradient dynamics in a three-well potential, and for the Charney-DeVore model, which is a paradigmatic toy model of multistability for atmospheric dynamics. For these two dynamics, we show that having observed a few transitions is enough to have a very efficient data-based score function for the rare event algorithm. This new approach is promising for use for 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.