We present a novel artificial-neural-network-based computerized ionospheric tomography technique, capable of imaging through time in three-dimensional space. Total electron content (TEC) data collected from a satellite passing over the region of interest are used to train a neural network. The trained network creates estimates of the difference in ionospheric electron density between time steps based on the TEC data. Application of the difference estimate at each time step to the previous electron density image results in a time-varying ionospheric electron density estimate. Experimental results on synthetic data are presented that demonstrate that the algorithm is capable of detecting short-term localized disturbances in the ionosphere.