Hydrogen is a clean energy carrier with broad application potential. This study focuses on improving hydrogen production efficiency in a proton exchange membrane (PEM) electrolyzer system that integrates a photovoltaic (PV) array, a battery energy storage system, and the electrolyzer. The PV array is interfaced with the electrolyzer through a buck converter using a maximum power point tracking (MPPT) algorithm to ensure maximum energy harvesting. A key contribution of this work is the integration of a battery system through a dual-active-bridge (DAB) converter. The DAB converter employs a multilayer perceptron (MLP) model to dynamically regulate the electrolyzer current and maintain optimal operating efficiency. An adaptive energy management strategy is further proposed to address solar irradiance fluctuations and enhance long-term operational stability. The MLP model is developed in Python and embedded into a PLECS simulation environment. The simulation results verify the effectiveness of the proposed control approach and efficiency optimization scheme. Throughout the simulation period, the PEM electrolyzer sustains an optimal efficiency of 69.9% under maximum PV power output. A limitation of this study is that the efficiency model is derived from the literature and does not yet consider all operational factors, indicating the need for refinement in future work.