Using machine learning to predict statistical properties of non-stationary dynamical processes: System climate,regime transitions, and the effect of stochasticity
Using machine learning to predict statistical properties of non-stationary dynamical processes: System climate,regime transitions, and the effect of stochasticity
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DOI：
10.1063/5.0042598
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发表时间：
2021-03-01
期刊：
影响因子：
2.9
通讯作者：
Ott, Edward
中科院分区：
文献类型：
--
作者：
Patel, Dhruvit;Canaday, Daniel;Ott, Edward
我们开发和测试了机器学习技术，以成功地使用过去的状态时间序列数据和时变系统参数的知识来预测与非平稳动力系统的长期行为相关的“气候”的演变，其中非平稳动力系统本身是未知的。所谓气候，我们指的是轨道的统计特性，而不是它们在时间上的精确轨迹。所谓非平稳，指的是本身随时间变化的系统。我们表明，我们的方法在预测连续渐进气候演变以及相对突然的气候变化(我们称之为“体制转变”)的测试系统上表现良好。我们不仅考虑了无噪声(即确定性)的非平稳动力系统，而且考虑了受随机强迫(即动力噪声)的非平稳动力系统的气候预测，并发展了一种处理后一种情况的方法。本文的主要结论是，机器学习作为一种新的、高效的方法来实现非平稳系统的数据驱动预测，具有广阔的应用前景。
We develop and test machine learning techniques for successfully using past state time series data and knowledge of a time-dependent system parameter to predict the evolution of the "climate" associated with the long-term behavior of a non-stationary dynamical system, where the non-stationary dynamical system is itself unknown. By the term climate, we mean the statistical properties of orbits rather than their precise trajectories in time. By the term non-stationary, we refer to systems that are, themselves, varying with time. We show that our methods perform well on test systems predicting both continuous gradual climate evolution as well as relatively sudden climate changes (which we refer to as "regime transitions"). We consider not only noiseless (i.e., deterministic) non-stationary dynamical systems, but also climate prediction for non-stationary dynamical systems subject to stochastic forcing (i.e., dynamical noise), and we develop a method for handling this latter case. The main conclusion of this paper is that machine learning has great promise as a new and highly effective approach to accomplishing data driven prediction of non-stationary systems.