Extreme Events Prediction in Optical Fibre Modulation Instability using Machine Learning

The study of instabilities that drive extreme events is central to nonlinear science. One of the most celebrated example of nonlinear instability is modulation instability (MI) which describes the exponential amplification of noise on top of an input signal. When seeded by noise, MI has been shown to be associated with the emergence of high intensity localized temporal breathers with random statistics and it has also been suggested that MI may be linked to the formation of extreme events or rogue waves [1], Real-time techniques such as the dispersive Fourier transform (DFT) are commonly used to measure ultrafast instabilities [2], Although conceptually simple and easy to implement, the DFT only provides spectral information, limiting the knowledge of associated temporal properties. Here, we show how machine learning can overcome this restriction to study time-domain properties of optical fibre modulation instability based only on spectral intensity measurements. Specifically, we train a supervised neural network (NN) to correlate the spectral and temporal properties of modulation instability using numerical simulations, and then we apply the neural network model to analyse high dynamic range experimental MI spectra to yield the probability distribution for the highest temporal peaks in the instability field [3].