学习区分混沌与噪声的定量准则
Learning a quantitative criterion for distinguishing chaos from noise
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中文总结 AI 辅助
该研究提出一种基于储备池计算与交叉预测方案的纯数据驱动方法，利用皮尔逊相关系数平方作为定量准则，可从时间序列数据中有效区分混沌与噪声，且对经验数据的实际限制具有鲁棒性。
中文摘要 AI 辅助
利用时间序列数据区分混沌与噪声从根本上具有挑战性，因为二者均呈现不规则波动，且共享诸多统计与动力学特性。现有方法面临两项关键局限：时间相关噪声可产生虚假的混沌特征，而对标量时间序列的分析常需明确选择嵌入参数。本文提出一种纯数据驱动的方法，用于区分混沌与噪声，该方法基于具有交叉预测方案的 reservoir-computing（储备池计算）框架。在该方法中，模型被训练为从变量的当前值预测其未来变化，从而将短期可预测性测试与确定性流的平滑性测试相结合。储备池计算的循环结构即使从标量时间序列也能有效预测高维混沌动力学，无需显式延迟坐标重构；而交叉预测框架可强烈抑制由噪声产生的虚假预测相关性。我们将该方法应用于多种合成与经验时间序列。混沌系统始终在真实与预测的未来变化之间呈现强相关性，而噪声过程则明显处于低相关区域。该方法对经验数据中的实际限制也表现出显著鲁棒性，包括测量噪声、有限数据长度以及预测滞后增大。这些结果表明，皮尔逊相关系数平方提供了一种简单的定量准则，可直接从观测时间序列数据区分混沌与噪声。
英文摘要
Distinguishing chaos from noise using time-series data is fundamentally challenging because both exhibit irregular fluctuations and share many statistical and dynamical characteristics. Existing methods face two key limitations: temporally correlated noise can yield spurious signatures of chaos, and analyses of scalar time series often require explicit choices of embedding parameters. Here, we propose a purely data-driven method for distinguishing chaos and noise based on a reservoir-computing framework with a cross-prediction scheme. In the proposed approach, the model is trained to predict the future change of a variable from its current value, thereby combining a short-term predictability test with a test of the smoothness of deterministic flows. The recurrent structure of reservoir computing enables effective prediction of high-dimensional chaotic dynamics even from scalar time series without explicit delay-coordinate reconstruction, while the cross-prediction framework strongly suppresses spurious predictive correlations arising from noise. We apply the proposed method to diverse synthetic and empirical time series. Chaotic systems consistently yield strong correlations between the true and predicted future changes, whereas noise processes remain clearly separated in a low-correlation regime. The method also exhibits substantial robustness to practical limitations in empirical data, including measurement noise, limited data length, and increasing prediction lag. These results demonstrate that the squared Pearson correlation coefficient provides a simple quantitative criterion for distinguishing chaos from noise directly from observed time-series data.
