调制不稳定性中极端统计量的机器学习预测
Machine learning for prediction of extreme statistics in modulation instability
摘要：
非线性科学研究的一个中心领域是研究驱动极端事件出现的不稳定性。不幸的是，测量这种现象的实验技术往往只能提供部分特征。例如，非线性光纤不稳定性的实时研究通常只使用光谱数据，无法详细预测相关的时间特性。在这里，我们展示了机器学习如何通过仅基于光谱测量来预测调制不稳定性中时间峰值的最大强度的统计数据来克服这一限制。具体来说，我们训练一个基于神经网络的机器学习模型，使用数值模拟的数据将光纤调制不稳定性的光谱和时间特性关联起来，然后我们使用这个模型来预测基于实验的高动态范围光谱数据的时间概率分布。这些结果在所有表现出混沌和不稳定的系统中打开了新的视角，直接的时域观测是困难的。
英文摘要：
A central area of research in nonlinear science is the study of instabilities that drive the emergence of extreme events. Unfortunately, experimental techniques for measuring such phenomena often provide only partial characterization. For example, real-time studies of instabilities in nonlinear fibre optics frequently use only spectral data, precluding detailed predictions about the associated temporal properties. Here, we show how Machine Learning can overcome this limitation by predicting statistics for the maximum intensity of temporal peaks in modulation instability based only on spectral measurements. Specifically, we train a neural network based Machine Learning model to correlate spectral and temporal properties of optical fibre modulation instability using data from numerical simulations, and we then use this model to predict the temporal probability distribution based on high-dynamic range spectral data from experiments. These results open novel perspectives in all systems exhibiting chaos and instability where direct time-domain observations are difficult.
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