The high-latitude ionospheric electric field plays a key role in ionospheric plasma dynamics and energetics. Various ground- and satellite-based observations have been utilized to develop empirical models of the convection electric field. Empirical modeling typically relies on statistical regression techniques in which predefined (and inherently biased) functions are fitted to measurements. In many convection models, it remains common practice to combine data from the Northern and Southern Hemispheres or to disregard differences between the March and September equinoxes. Such approaches make it challenging to identify important input variables and limit their ability to account for equinoctial and hemispheric asymmetries. These asymmetries, which are not fully understood, require further analysis and improved representation in models. In this work, we use nearly ten years of electric field data from the Swarm satellites’ Thermal Ion Imagers (TIIs) together with artificial neural networks (ANNs) to develop a model of high-latitude ionospheric electric potential. The Swarm ‘TII-ANN’ electric potential model explicitly incorporates the day of the year, universal time, solar and geomagnetic activity, 3-D interplanetary magnetic field, and 3-D solar wind velocity. Importantly, it also accounts for equinoctial and hemispheric variations. We describe the new model, validate its performance by comparing corresponding ion drifts to independent measurements from the DMSP satellite, and study the hemispheric and equinoctial asymmetries of high-latitude electric potential. Our results show that the cross-polar cap potential is larger in the Southern Hemisphere than in the Northern Hemisphere during the March equinox, with equinoctial asymmetry being particularly prominent in the south.