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.