The propagation of ultrashort pulses in optical fibre plays a central role in the development of light sources and photonic technologies, with applications from fundamental studies of light–matter interactions to high-resolution imaging and remote sensing. However, short pulse dynamics are highly nonlinear, and optimizing pulse propagation for application purposes requires extensive and computationally demanding numerical simulations. This creates a severe bottleneck in designing and optimizing experiments in real time. Here, we present a solution to this problem using a recurrent neural network to model and predict complex nonlinear propagation in optical fibre, solely from the input pulse intensity profile. We highlight particular examples in pulse compression and ultra-broadband supercontinuum generation, and compare neural network predictions with experimental data. We also show how the approach can be generalized to model other propagation scenarios for a wider range of input conditions and fibre systems, including multimode propagation. These results open up novel perspectives in the modelling of nonlinear systems, for the development of future photonic technologies and more generally in physics for studies in Bose–Einstein condensates, plasma physics and hydrodynamics.