Description
We demonstrate Bayesian optimization (BO) of the maximum energy of laser-driven protons in the Target Normal Sheath Acceleration regime by adaptively controlling the actuators of a deformable mirror (DM) to shape the Advanced Laser Light Source (ALLS) 150 TW laser wavefront. After initialization of DM actuators without correction (zeroed actuators), a multi-step BO approach identified an optimal configuration with 20 out of 48 actuators to achieve a 70% (see Figure) maximum proton energy increase using less than 150 experimental data samples (laser shots). BO, used together with a Random Forest (RF) model, surpassed conventional wavefront correction by 24%, which typically minimizes aberrations to converge towards a flat wavefront by leveraging real-time feedback from a wavefront analyzer. Firstly, a dataset of 360 DM actuator configurations was generated, revealing defocus as the primary influence. Then, a RF model, trained on this data, provided noise-reduced predictions and reduced experimental cost and time. Finally, BO efficiently navigated the search space identifying an optimal DM configuration using the RF model as the objective function. This approach remained effective despite system misalignments, demonstrating its robustness for optimizing complex, high-dimensional laser-plasma interactions. This data-driven method integrating advanced wavefront control challenges the preference for a flatter wavefront in laser-driven ion acceleration.