  The nonlinear propagation of ultrashort pulses in optical fiber depends
sensitively on both input pulse and fiber parameters. As a result, optimizing
propagation for specific applications generally requires time-consuming
simulations based on sequential integration of the generalized nonlinear
Schr\"odinger equation (GNLSE). Here, we train a feed-forward neural network to
learn the differential propagation dynamics of the GNLSE, allowing emulation of
direct numerical integration of fiber propagation, and particularly the highly
complex case of supercontinuum generation. Comparison with a recurrent neural
network shows that the feed-forward approach yields faster training and
computation, and reduced memory requirements. The approach is generic and can
be extended to other physical systems.
