论文标题
使用机器学习预测倾斜点并推断出非平稳动力学系统的额化动力学
Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems
论文作者
论文摘要
在本文中，我们考虑了与未知（或部分未知），非平稳性，潜在的嘈杂和混乱的动力学系统相关的机器学习（ML）任务，以预测临界点过渡和长期倾倒点行为。我们专注于特别具有挑战性的情况，在过去的情况下，过去的动态状态时间序列主要是在国家空间的受限区域中，而这种行为会在较大的状态空间集中进化，而在训练过程中未完全观察到ML模型。在这种情况下，要求ML预测系统能够推断出在训练过程中观察到的不同动态。我们研究了ML方法在多大程度上能够为此任务完成有用的结果以及它们失败的条件。通常，我们发现即使在极具挑战性的情况下，ML方法也非常有效，但是（正如人们所期望的那样）在需要````过多'''需要``过多''时会失败。对于后一种情况，我们调查了将ML方法与基于科学知识的常规模型相结合的有效性，因此在综合预测系统中会构成杂种预测，即使是在综合的预测中，我们就会发现ML的效果，即使我们的构成又可以预测，即使是在综合中，我们都会在其基于科学的知识中进行构成。还发现，实现有用的结果可能需要使用非常精心选择的ML超参数，我们提出了一个高参数优化策略来解决该问题，这是本文的主要结论是，基于ML的方法可以预测非固态动力学系统的行为，即使在未来进化的情况下（也许是由于培训点的交叉），也包括在探索数据之外的动态。
In this paper we consider the machine learning (ML) task of predicting tipping point transitions and long-term post-tipping-point behavior associated with the time evolution of an unknown (or partially unknown), non-stationary, potentially noisy and chaotic, dynamical system. We focus on the particularly challenging situation where the past dynamical state time series that is available for ML training predominantly lies in a restricted region of the state space, while the behavior to be predicted evolves on a larger state space set not fully observed by the ML model during training. In this situation, it is required that the ML prediction system have the ability to extrapolate to different dynamics past that which is observed during training. We investigate the extent to which ML methods are capable of accomplishing useful results for this task, as well as conditions under which they fail. In general, we found that the ML methods were surprisingly effective even in situations that were extremely challenging, but do (as one would expect) fail when ``too much" extrapolation is required. For the latter case, we investigate the effectiveness of combining the ML approach with conventional modeling based on scientific knowledge, thus forming a hybrid prediction system which we find can enable useful prediction even when its ML-based and knowledge-based components fail when acting alone. We also found that achieving useful results may require using very carefully selected ML hyperparameters and we propose a hyperparameter optimization strategy to address this problem. The main conclusion of this paper is that ML-based approaches are promising tools for predicting the behavior of non-stationary dynamical systems even in the case where the future evolution (perhaps due to the crossing of a tipping point) includes dynamics on a set outside of that explored by the training data.
