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：大西洋经向翻转流（AMOC）是全球气候的重要组成部分，已知其作为气候临界要素，在全球变暖条件下可能发生崩溃。本研究的主要目标是使用名为“轨迹自适应多层分裂（TAMS）”的稀有事件算法，计算AMOC在特定时间窗口内崩溃的概率。然而，TAMS的效率与准确性取决于得分函数的选择。尽管最优得分函数（即“提交函数”）的定义已知，但通常无法先验计算该函数。本文通过将TAMS与下一代储层计算技术相结合，利用稀有事件算法生成的数据估计提交函数。我们在一类存在两种跃迁类型（即快跃迁和慢跃迁）的AMOC随机箱模型中测试该技术。结果显示，对于快跃迁，该方法的计算结果与文献中使用物理驱动得分函数的结果高度吻合。研究表明，将稀有事件算法与机器学习结合，能够在大范围模型参数下正确估计跃迁概率、跃迁时间甚至跃迁路径。随后，我们将这些结果扩展至同一模型中更具挑战性的慢跃迁问题。在快跃迁和慢跃迁两种情况下，我们还展示了如何通过解释下一代储层计算技术来获取提交函数的解析估计值。