This paper presents a systematic and comprehensive mathematical model for alkaline water electrolyzer cells, which can be used for simulation and analysis. The model accounts for factors such as gas evolution reactions, dissolution of gases in the electrolyte, bubble formation, and charge transport. It is based on a numerical two-phase model using the Euler-Euler approach, which has been validated against experimental data for various current densities. The study compares the impact of varying potassium hydroxide (KOH) concentration, separator porosity, and electrolyte flow rates on two-phase flow and bubble coverage. Therefore, the electrolyte in the cell consists of a solution of potassium hydroxide in water. The formation of gas bubbles at the electrodes decreases the electrolyte’s ionic conductivity. Additionally, the presence of these bubbles on the electrode surfaces reduces the available surface area for electrochemical reactions, leading to an increase in the overpotential at a given current density. Furthermore, this paper demonstrates how a neural network and ensembled tree model can predict hydrogen production rates in an alkaline water electrolysis process. The trained neural network accurately predicted the hydrogen production rates, indicating the potential of using neural networks for optimization and control of alkaline water electrolysis processes. The model has an average R-squared value of 0.98, indicating a good fit to the data. A new method of describing bubble transfer, “bubble diffusion,” is introduced to improve performance and reduce costs. The model is solved using COMSOL Multi physics 6.0. The machine learning models in this study were built, trained, and tested using MATLAB software R2020a.