With the advent of the Square Kilometre Array Observatory (SKAO), scientists will be able to directly observe the Epoch of Reionization by mapping the distribution of neutral hydrogen at different redshifts. While physically motivated results can be simulated with radiative transfer codes, these simulations are computationally expensive and can not readily produce the required scale and resolution simultaneously. Here we introduce the Physics-Informed neural Network for reIONization (PINION), which can accurately and swiftly predict the complete 4-D hydrogen fraction evolution from the smoothed gas and mass density fields from pre-computed N-body simulation. We trained PINION on the C$^2$-Ray simulation outputs and a physics constraint on the reionization chemistry equation is enforced. With only five redshift snapshots and a propagation mask as a simplistic approximation of the ionizing photon mean free path, PINION can accurately predict the entire reionization history between $z=6$ and $12$. We evaluate the accuracy of our predictions by analysing the dimensionless power spectra and morphology statistics estimations against C$^2$-Ray results. We show that while the network's predictions are in good agreement with simulation to redshift $z>7$, the network's accuracy suffers for $z<7$ primarily due to the oversimplified propagation mask. We motivate how PINION performance can be drastically improved and potentially generalized to large-scale simulations.