To optimize proton maximum energy, we adjusted the deformable mirror’s actuators, which directly influence the laser spot size and shape (measured by a wavefront analyzer). Starting with all voltages set to 0V, we aimed to find the optimal configuration to maximize proton energy. Utilizing the ALLS 150 TW laser’s high-repetition rate and a multi-target holder, we collected a dataset of approximately 200 samples. Bayesian Optimization (BO) was then employed to guide the process by creating a surrogate model of the objective function, enabling efficient parameter space exploration.

By controlling 20 out of 48 actuators, we identified configurations that significantly improved proton energy (70 %) while minimizing experimental iterations (200 data points). This adaptive approach integrates data-driven optimization with precise wavefront control, achieving enhanced ion acceleration. Our method challenges the notion that Gaussian beams are optimal for Target Normal Sheath Acceleration and provides a robust strategy for facilities lacking terawatt/petawatt attenuators to visualize the full-power laser spot. This demonstrates the potential of combining advanced optical control with optimization algorithms to enhance high-intensity laser-driven ion acceleration systems. Furthermore, our method offers a robust strategy for facilities that lack terawatt/petawatt attenuators to visualize the full-power laser spot, demonstrating how machine learning-driven optical optimization can significantly enhance high-intensity laser-based ion acceleration.