In this work, Fourier Neural Operators are employed to improve control and optimizationof an experimental module of the IFMIF-DONES linear accelerator,otherwise hindered by its simulations high complexity. The models are trainedto predict beam envelopes along the lattice’s longitudinal axis, considering variationsin quadrupole strengths and particle injections. They serve three purposes:enabling fast inference of beam envelopes, creating an environment for training aDeep Reinforcement Learning agent responsible for shaping the beam, and developingan optimizer for identifying optimal accelerator parameters. The resultingmodels offer significantly faster predictions (up to 3 orders of magnitude) comparedto traditional simulators, with maximum percentage errors below 2 %. Thisaccelerated simulation capability makes it feasible to train control agents, sincethe time per step taken is reduced from 3s to 4 × 10e−3s. Additionally, StochasticGradient Descent was applied to optimize one of the models itself, determining thebest parameters for a given target and thus solving the inverse problem within seconds.These results demonstrate the synergy and potential of these Deep Learningmodels, offering promising pathways to advance control and optimization strategiesin the IFMIF-DONES accelerator and in other complex scientific facilities.