We apply generative adversarial network (GAN) technology to build an event generator that simulates particle production in electron-proton scattering that is free of theoretical assumptions about underlying particle dynamics. The difficulty of efficiently training a GAN event simulator lies in learning the complicated patterns of the distributions of the particles physical properties. We develop a GAN that selects a set of transformed features from particle momenta that can be generated easily by the generator, and uses these to produce a set of augmented features that improve the sensitivity of the discriminator. The new Feature-Augmented and Transformed GAN (FAT-GAN) is able to faithfully reproduce the distribution of final state electron momenta in inclusive electron scattering, without the need for input derived from domain-based theoretical assumptions. The developed technology can play a significant role in boosting the science of existing and future accelerator facilities, such as the Electron-Ion Collider.