Machine learning for prediction of extreme statistics in modulation instability

TL;DR

This paper demonstrates how machine learning can predict the likelihood of extreme events in nonlinear systems using spectral data alone, bridging the gap between spectral measurements and temporal predictions.

Contribution

It introduces a neural network model that correlates spectral and temporal properties of modulation instability, enabling temporal predictions from spectral data.

Findings

Neural network accurately predicts temporal peak intensities from spectral data.

Model trained on simulations successfully applied to experimental spectral data.

Method extends to other chaotic and unstable systems with limited measurements.

Abstract

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.