Analysing interaction and localization dynamics in modulation instability via data-driven dominant balance

We report the first application of the Machine Learning technique of data-driven dominant balance to optical fiber noise-driven Modulation Instability, with the aim to automatically identify local regions of dispersive and nonlinear interactions governing the dynamics. We first consider the analytical solutions of Nonlinear Schrödinger Equation – solitons on finite background – where it is shown that dominant balance distinguishes two particularly different dynamical regimes: one where the nonlinear process is dominating the dispersive propagation, and one where nonlinearity and second order dispersion act together driving the localization of breathers. By means of numerical simulations, we then analyse the spatio-temporal dynamics of noise-driven Modulation Instability and demonstrate that data-driven dominant balance can successfully identify the associated dominating physical regimes even within the turbulent dynamics.