  In this work we demonstrate the efficacy of neural networks in the
characterization of dispersive media. We also develop a neural network to make
predictions for input probe pulses which propagate through a nonlinear
dispersive medium, which may be applied to predicting optimal pulse shapes for
a desired output. The setup requires only a single pulse for the probe,
providing considerable simplification of the current method of dispersion
characterization that requires frequency scanning across the entirety of the
gain and absorption features. We show that the trained networks are able to
predict pulse profiles as well as dispersive features that are nearly identical
to their experimental counterparts. We anticipate that the use of machine
learning in conjunction with optical communication and sensing methods, both
classical and quantum, can provide signal enhancement and experimental
simplifications even in the face of highly complex, layered nonlinear
light-matter interactions.
