This study develops aGreen hydrogen detailed mathematical model for alkaline water electrolyzer cells to simulate and analyze their performance, incorporating factors such as gas evolution, dissolution, bubble formation, and charge transport through a two-phase Euler-Euler method approach. Validated against experimental data at various current densities, the model assesses the effects of potassium hydroxide concentration, separator porosity, and electrolyte flow on flow dynamics and bubble behavior. Gas bubbles formation at electrodes decreases ionic conductivity and available surface area for reactions, increasing overpotential. The study also highlights the use of neural networks and ensemble tree models for predicting hydrogen production rates, achieving an average R-squared value of 0.98, indicating a strong prediction accuracy and potential for process optimization.