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

Abstract

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.

Simple Physics and Integrators Accurately Reproduce Mercury Instability Statistics

“…For example, the data set could be mined to identify system characteristics that predict Mercury instability events and the time horizon for meaningful predictions. Techniques such as this have already been used in oceanatmosphere dynamics (Tantet et al 2015;Chattopadhyay et al 2020;Finkel et al 2020Finkel et al , 2021Finkel et al , 2022Wang et al 2020;Jacques-Dumas et al 2022;Miloshevich et al 2022) and chemistry (Ma & Dinner 2005;Thiede et al 2019).…”

Bringing Statistics to Storylines: Rare Event Sampling for Sudden, Transient Extreme Events

“…Rare event algorithms represent an attractive potential solution to combine the advantages of both approaches, generating both dynamical samples and probabilities of extreme events thanks to careful re‐weighting of cloned trajectories. Inspired by recent successes of rare event algorithms on long‐lasting heat waves (Ragone et al., 2018) and idealized models of regime transitions (Jacques‐Dumas et al., 2023; Lucente, Rolland, et al., 2022), we have investigated the ability of a particular algorithm, adaptive multilevel splitting (AMS) to sample extreme events of a different character: intermittent, short‐lived bursts of energy in the Lorenz‐96 model which have some similar characteristics as extreme daily rain or wind associated with midlatitude cyclones.…”

“…The committor is an optimal score function for AMS in terms of minimizing the variance for $$\widehat{p}(\ell )$$ (Cérou et al., 2019; Lestang et al., 2018; Lucente, Rolland, et al., 2022). Considerable research has recently pursued approximation strategies for the committor in various climate applications (e.g., Finkel et al., 2021; Jacques‐Dumas et al., 2023; Lucente, Herbert, & Bouchet, 2022; Miloshevich et al., 2023; Tantet et al., 2015).…”

Revealing the Statistics of Extreme Events Hidden in Short Weather Forecast Data

“…In this light, viewing Equation as a discretized partial differential equation, the clusters { S t , j } can be seen as members of a finite element basis and P t , t +1 ( i , j ) as stiffness matrices. Indeed, here we use an MSM as a “dynamical Galerkin approximation,” a basis expansion approach to computing forecast quantities like the committor probability from short trajectory data that was originally developed for chemistry applications (Strahan et al., 2021; Thiede et al., 2019) and has recently been applied to climate dynamics (Finkel et al., 2021, 2022; Jacques‐Dumas et al., 2022). Estimate an empirical probability distribution over clusters at the beginning of winter, $$${\pi }_{{T}_{0}}(j)=\mathbb{P}\left\{\mathbf{X}\left({T}_{0}\right)\in {S}_{{T}_{0},j}\right\}$$$ …”

“…Our MSM‐based approximation of the committor probability is similar in spirit to analog forecasting (van den Dool, 1989), which is enjoying a renaissance with novel data‐driven techniques, especially for characterizing extreme weather (Chattopadhyay et al., 2020; Lucente et al., 2022). Dynamical Galerkin approximation (using a basis different than the one used here) and a short trajectory variant of analog forecasting are tested on several benchmark problems in (Jacques‐Dumas et al., 2022). Formally, the transition operator encoded by the matrix in Equation is related to linear inverse models (Penland & Sardeshmukh, 1995), which have also been used to predict subseasonal extremes (Tseng et al., 2021).…”