  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 the committor function, is in practice very difficult to
compute. In this paper, we compare different data-based methods (analog 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. Analog 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.
