A physics-guided machine learning surrogate, conditioned on hydraulic parameters, that predicts hourly saturation profiles in heap leaching and is trained with a mass-balance penalty on thousands of Richards-equation simulations. Used in a daily predictive controller, it matched a tuned PI controller in tracking a 0.70 saturation target while reaching the target without overshoot and using about 4% less irrigation. Physics guidance cut long-horizon prediction error by about 30% compared with data-only training, and the surrogate ran about 70 times faster than the numerical solver, making large-scale saturation control practical in simulation.