The field of laser-ion acceleration faces significant challenges in handling high-dimensional, computationally intensive problems, often constrained by budgets and available computational power. Reliably achieving high ion energies with current laser technologies through ultra-high intensity pulses in near-critical to overdense plasmas remains difficult, necessitating detailed, costly simulations to explore various acceleration mechanisms and optimize outcomes. Due to the high computational cost of these simulations, there is a need for precise, scalable, and efficient adaptive sampling methods that balance exploring new mechanisms while exploiting known parameter dependencies and that can operate in high-performance computing environments. In this work, we propose and investigate a scalable adaptive sampling approach that intrinsically supports parallel processing. We apply this method to data obtained from particle-in-cell simulations using multilayer perceptrons (MLPs), chosen for their flexibility in modeling complex dependencies. We benchmark our results against Bayesian optimization, and we highlight the limitations of MLPs when accounting for the intrinsic uncertainty present in the acceleration process.