Assessing the predictability of nonlinear dynamics under smooth parameter changes
Assessing the predictability of nonlinear dynamics under smooth parameter changes
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DOI：
10.1098/rsif.2019.0627
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发表时间：
2020-01-01
影响因子：
3.9
通讯作者：
Saavedra, Serguei
中科院分区：
文献类型：
--
作者：
Cenci, Simone;Medeiros, Lucas P.;Saavedra, Serguei
非线性动力学的短期预测对于风险评估研究和为物理、生物和金融等问题的可持续决策提供信息非常重要。一般来说，短期预测的准确性取决于两个主要因素：学习算法对未知数据进行良好概括的能力，以及动态的内在可预测性。虽然学习算法的泛化能力可以用成熟的方法进行评估，但从经验时间序列中估计潜在的非线性生成过程的可预测性仍然是一个很大的挑战。在这里，我们表明，在不断变化的环境中，非线性动力学的可预测性可以与系统的时变稳定性相对于模型参数的平滑变化，即其局部结构稳定性。使用合成数据，我们表明，在平稳变化的环境中，从局部结构不稳定状态的预测可以产生显着较大的预测误差，我们提供了一个系统的方法来识别这些状态的数据。最后，我们使用一个经验数据集说明我们的结果的实际适用性。总体而言，这项研究提供了一个框架，在平稳变化的环境中作出的短期预测的不确定性水平相关联。
Short-term forecasts of nonlinear dynamics are important for risk-assessment studies and to inform sustainable decision-making for physical, biological and financial problems, among others. Generally, the accuracy of short-term forecasts depends upon two main factors: the capacity of learning algorithms to generalize well on unseen data and the intrinsic predictability of the dynamics. While generalization skills of learning algorithms can be assessed with well-established methods, estimating the predictability of the underlying nonlinear generating process from empirical time series remains a big challenge. Here, we show that, in changing environments, the predictability of nonlinear dynamics can be associated with the time-varying stability of the system with respect to smooth changes in model parameters, i.e. its local structural stability. Using synthetic data, we demonstrate that forecasts from locally structurally unstable states in smoothly changing environments can produce significantly large prediction errors, and we provide a systematic methodology to identify these states from data. Finally, we illustrate the practical applicability of our results using an empirical dataset. Overall, this study provides a framework to associate an uncertainty level with short-term forecasts made in smoothly changing environments.