19 Dec 2022
19 Dec 2022
Status: this preprint is open for discussion.

Data-driven methods to estimate the committor function in conceptual ocean models

Valérian Jacques-Dumas1,2, René M. van Westen1, Freddy Bouchet3, and Henk A. Dijkstra1,2 Valérian Jacques-Dumas et al.
  • 1Institute for Marine and Atmospheric research Utrecht, Department of Physics, Utrecht University, Utrecht, the Netherlands
  • 2Centre for Complex Systems Studies, Department of Physics, Utrecht University, Utrecht, the Netherlands
  • 3Univ. Lyon, ENS de Lyon, Univ. Claude Bernard, CNRS, Laboratoire de Physique, Lyon, France

Abstract. In recent years, several climate subsystems have been identified that may undergo a relatively rapid transition compared to the changes in their forcing. Such transitions are rare events in general and simulating long-enough trajectories in order to gather sufficient data to determine transition statistics would be too expensive. Conversely, rare-events algorithms like TAMS (Trajectory-Adaptive Multilevel Sampling) encourage the transition while keeping track of the model statistics. However, this algorithm relies on a score function whose choice is crucial to ensure its efficiency. The optimal score function, called committor function, is in practice very difficult to compute. In this paper, we compare different data-based methods (Analogue Markov Chains, Neural Networks, Reservoir Computing, Dynamical Galerkin Approximation) to estimate the committor from trajectory data. We apply these methods on two models of the Atlantic Ocean circulation featuring very different dynamical behavior. We compare these methods in terms of two measures, evaluating how close the estimate is from the true committor, and in terms of the computational time. We find that all methods are able to extract information from the data in order to provide a good estimate of the committor. Analogue Markov Chains provide a very reliable estimate of the true committor in simple models but prove not so robust when applied to systems with a more complex phase space. Neural network methods clearly stand out by their relatively low testing time, and their training time scales more favorably with the complexity of the model than the other methods. In particular, feedforward neural networks consistently achieve the best performance when trained with enough data, making this method promising for committor estimation in sophisticated climate models.

Valérian Jacques-Dumas et al.

Status: open (until 16 Feb 2023)

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Valérian Jacques-Dumas et al.

Valérian Jacques-Dumas et al.


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Short summary
Computing the probability of occurrence of rare events is relevant because of their high impact, but also difficult due to the lack of data. Rare-event algorithms are designed for that task but their efficiency relies on a score function that is hard to compute. We compare four methods that compute this function from data and measure their performance to assess which one would be best suited to be applied to a climate model. We find neural networks to be most robust and flexible for this task.