  The dynamics of ideal four-wave mixing in optical fiber is reconstructed by
taking advantage of the combination of experimental measurements with
supervised machine learning strategies. The training data consist of
power-dependent spectral phase and amplitude recorded at the output of a short
segment of fiber. The neural network is able to accurately predict the
nonlinear dynamics over tens of kilometers, and to retrieve the main features
of the phase space topology including multiple Fermi-Pasta-Ulam recurrence
cycles and the system separatrix boundary.
