  Supercontinuum generation is a highly nonlinear process that exhibits
unstable and chaotic characteristics when developing from long pump pulses
injected into the anomalous dispersion regime of an optical fiber. A particular
feature associated with this regime is the long-tailed "rogue wave"-like
statistics of the spectral intensity on the long wavelength edge of the
supercontinuum, linked to the generation of a small number of "rogue solitons"
with extreme red-shifts. Here, we apply machine learning to analyze the
characteristics of these solitons at the edge of the supercontinuum spectrum,
and show how supervised learning can train a neural network to predict the peak
power, duration, and temporal delay of these solitons from only the
supercontinuum spectral intensity without phase information. The network
accurately predicts soliton characteristics for a wide range of scenarios, from
the onset of spectral broadening dominated by pure modulation instability to
near octave-spanning supercontinuum with distinct rogue solitons.
