High dimensional model representation (HDMR), a technique useful for reducing the computational burden of complex geophysical models, is applied to a global first principles model of the ionosphere/thermosphere system. HDMR captures the input-output relationship of a model with a series of correlation functions that accurately represents the original model. The resulting Fully Equivalent Operational Model (FEOM) of ionospheric electron density (<e>) described herein is derived from the Integrated Space Weather Prediction Model (ISM). It reproduces ISM <e> with errors of less than 3% over 97% of the three-dimensional ISM grid. The observed factor of 103 speed up in CPU time demonstrates the feasibility of using HDMR to construct a fast and accurate ionospheric model based on first principles model output.