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Sensitivity of Chaotic Dynamics Prediction to Observation Noise

机译：混沌动力学预测观察噪声的敏感性

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Recent advances in nonlinear time-series prediction demonstrated the ability of recurrent neural network to forecast chaotic time series on a multi-step horizon, outperforming previous approaches. Researches considered chaotic systems with different degree of complexity, but the analysis was mainly limited to the noise-free case. In this work, we extend the analysis to a noisy environment, in order to fill the gap between deterministic and real-world time series. We consider four archetypal deterministic chaotic systems each with different levels of additive noise, representing the observation uncertainty always affecting practical applications. A time series of solar irradiance is also taken into account as a real-world case study. Various neural architectures, including feed-forward and recurrent networks, are adopted as predictors. LSTM cells are used as recurrent neurons, with a special focus on the training approach. As in the noise-free case, LSTM trained without the traditional teacher forcing, i.e., with a training that replicates the forecasting conditions, proved to be the best architecture. The experiments on the archetypal systems also shows that the error due to the model identification is negligible if compared to the one caused by a small observation noise. In other words, system identification and predictions are well distinct tasks.
机译：在非线性时间序列预测的最新进展证明递归神经网络来预测混沌时间序列上一个多步骤的地平线的能力，超越以前的方法。研究认为具有不同程度的复杂的混沌系统，但分析主要限于无噪声的情况下。在这项工作中，我们分析扩展到一个嘈杂的环境中，为了填补确定性和现实世界的时间序列之间的差距。我们考虑四个典型的确定性混沌每个系统有不同程度的加性噪声​​，代表观察的不确定性总是影响实际应用。时间序列的太阳辐射也考虑到作为一个真实的案例研究。各种神经结构，包括前馈和复发性网络中，采用作为预测。 LSTM细胞作为神经元反复发作，特别注重人才的培养途径。正如在无噪声的情况下，训练有素的LSTM没有传统的以教师强迫，即与复制预测条件下的训练，被证明是最好的架构。在典型的系统还示出了实验，如果相对于一个引起的小观测噪声由于模型识别误差是可以忽略的。换句话说，系统识别和预测非常不同的任务。

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