We develop an empirical dynamic equation for the hourly evolution of 1.8--3.5 MeV energetic electron flux at local noon at geosynchronous altitude. We use a genetic algorithm combined with a neural network to identify the magnetospheric quantities that can be used to model the time evolution of hourly energetic electron fluxes. We then apply a statistical technique to analyze how these quantities modify the evolution of energetic electron flux through phase space. We fit this evolution to an analytical dynamic equation. We show that the ring current index Dst and a Pc 5 ULF wave power index together can produce a meaningful model of the noon energetic electron flux. We also use this model to demonstrate how the magnetosphere would respond to a hypothetical increase in ULF wave power without a storm in Dst. We demonstrate that while the model electrons do respond to any enhancement in ULF wave power, their response is much larger in the presence of a magnetic storm with sustained ULF wave power.