The Atlantic Meridional Overturning Circulation (AMOC) is an important component of the global climate, known to be a tipping element, as it could collapse under global warming. The main objective of this study is to compute the probability that the AMOC collapses within a specified time window, using a rare-event algorithm called Trajectory-Adaptive Multilevel Splitting (TAMS). However, the efficiency and accuracy of TAMS depend on the choice of the score function. Although the definition of the optimal score function, called ``committor function" is known, it is impossible in general to compute it a priori. Here, we combine TAMS with a Next-Generation Reservoir Computing technique that estimates the committor function from the data generated by the rare-event algorithm. We test this technique in a stochastic box model of the AMOC for which two types of transition exist, the so-called F(ast)-transitions and S(low)-transitions. Results for the F-transtions compare favorably with those in the literature where a physically-informed score function was used. We show that coupling a rare-event algorithm with machine learning allows for a correct estimation of transition probabilities, transition times, and even transition paths for a wide range of model parameters. We then extend these results to the more difficult problem of S-transitions in the same model. In both cases of F- and S-transitions, we also show how the Next-Generation Reservoir Computing technique can be interpreted to retrieve an analytical estimate of the committor function.

翻译：大西洋经向翻转环流（AMOC）是全球气候的重要组成部分，已知为临界要素，在全球变暖条件下可能发生崩溃。本研究的主要目标是利用名为轨迹自适应多层次分裂（TAMS）的稀有事件算法，计算AMOC在指定时间窗口内崩溃的概率。然而，TAMS的效率和准确性取决于得分函数的选择。尽管最优得分函数（称为“归约函数”）的定义已知，但通常无法先验计算该函数。本文中，我们将TAMS与下一代储层计算技术相结合，该技术根据稀有事件算法生成的数据估计归约函数。我们在AMOC的随机箱式模型中测试了该技术，该模型存在两种转变类型，即所谓的快速转变和慢速转变。快速转变的结果与文献中使用基于物理信息的得分函数的结果相比具有优势。我们表明，将稀有事件算法与机器学习相结合，能够正确估计广泛模型参数下的转变概率、转变时间甚至转变路径。随后，我们将这些结果扩展到同一模型中更困难的慢速转变问题。在快速和慢速两种转变情况下，我们还展示了如何解释下一代储层计算技术以恢复归约函数的解析估计。