A proton exchange membrane (PEM) electrolyzer is fed with water and powered by electric power to electrochemically produce hydrogen at low operating temperatures and emits oxygen as a by-product. Due to the complex nature of the performance of PEM electrolyzers, the application of an artificial neural network (ANN) is capable of predicting its dynamic characteristics. A handful of studies have examined and explored ANN in the prediction of the transient characteristics of PEM electrolyzers. This research explores the estimation of the transient behavior of a PEM electrolyzer stack under various operational conditions. Input variables in this study include stack current, oxygen pressure, hydrogen pressure, and stack temperature. ANN models using three differing learning algorithms and time delay structures estimated the hydrogen mass flow rate, which had transient behavior from 0 to 1 kg/h, and forecasted better with a higher count (>5) of hidden layer neurons. A coefficient of determination of 0.84 and a mean squared error of less than 0.005 were recorded. The best-fitting model to predict the dynamic behavior of the hydrogen mass flow rate was an ANN model using the Levenberg–Marquardt algorithm with 40 neurons that had a coefficient of determination of 0.90 and a mean squared error of 0.00337. In conclusion, optimally fit models of hydrogen flow from PEM electrolyzers utilizing artificial neural networks were developed. Such models are useful in establishing an agile flow control system for the electrolyzer system to help decrease power consumption and increase efficiency in hydrogen generation.