By combining machine learning methods and the dispersive Fourier transform we demonstrate, to the best of our knowledge, for the first time the possibility to determine the temporal duration of picosecond-scale laser pulses using a nanosecond photodetector. A fiber figure of eight lasers with two amplifiers in a resonator was used to generate pulses with durations varying from 28 to 160 ps and spectral widths varied in the range of 0.75-12 nm. The average power of the pulses was in the range from 40 to 300 mW. The trained artificial neural network makes it possible to predict the pulse duration with the mean agreement of 95%. The proposed technique paves the way to creating compact and low-cost feedback for complex laser systems.