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The nonlinear propagation of ultrashort pulses in optical fibers depends sensitively on the input pulse and fiber parameters. As a result, the optimization of propagation for specific applications generally requires time-consuming simulations based on the sequential integration of the generalized nonlinear Schrödinger 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.