Neural network analysis of unstable temporal intensity peaks in continuous wave modulation instability

We report the application of a neural network to correlate spectral and temporal properties for modulation instability excited by a continuous wave field with random quantum noise. Using numerical simulations to generate large ensembles of chaotic modulation instability data, a trained neural network is shown to be able to correlate unstable intensity spectra and associated temporal intensity peaks with correlation coefficients exceeding ρ=0.90 for dynamic ranges exceeding 40 dB. Such excellent correlation is obtained both in the initial evolving phase of modulation instability where spectra typically possess significant sideband structure, as well as in the stationary phase of the instability when distinct sideband structure is not apparent. For both cases, we also test the degree to which a neural network may be able to “forecast” temporal instability peaks based on analyzing spectral intensity at an earlier spatial reference position, but conclude that such forecasting is successful over only within a very localized distance range much less than the characteristic nonlinear length.