Controlling PINN Optimization Dynamics with Reinforcement Learning

Training a physics-informed neural network (PINN) requires decisions about loss weights, optimizer settings, and the allocation of updates as the solution evolves. We study reinforcement learning (RL) as a controller for these decisions in a holographic inverse problem: reconstructing a scalar potential jointly with bulk fields constrained by gravitational equations and reference data. We formulate the control loop and analyze eight experience-collection schedules for a localized model-based controller, using $20$ completed replicates and a non-localized reference. The three strongest individual final-controller evaluations have potential root mean square errors of $0.761$, $0.770$, and $1.14$. Schedule means and medians reveal substantial variation, while saved cycle evaluations show that additional training can reverse earlier gains. Examining the recovered wells and their rising branches further distinguishes a low scalar loss from accurate potential reconstruction. These results identify promising individual trajectories and motivate controller evaluation that accounts for physical geometry, replicate stability, and the distribution of experience across training stages.