Limits of nonlinear and dispersive fiber propagation for photonic extreme learning

We report a generalized nonlinear Schr\"odinger equation simulation model of an extreme learning machine based on optical fiber propagation. Using handwritten digit classification as a benchmark, we study how accuracy depends on propagation dynamics, as well as parameters governing spectral encoding, readout, and noise. Test accuracies of over 91% and 93% are found for propagation in the anomalous and normal dispersion regimes respectively. Our simulation results also suggest that quantum noise on the input pulses introduces an intrinsic penalty to ELM performance.

Machine learning for prediction of extreme statistics in modulation instability

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.