On High-Performance Computing (HPC) systems, several hyperparameter configurations can be evaluated in parallel to speed up the Hyperparameter Optimization (HPO) process. State-of-the-art HPO methods follow a bandit-based approach and build on top of successive halving, where the final performance of a combination is estimated based on a lower than fully trained fidelity performance metric and more promising combinations are assigned more resources over time. Frequently, the number of epochs is treated as a resource, letting more promising combinations train longer. Another option is to use the number of workers as a resource and directly allocate more workers to more promising configurations via data-parallel training. This article proposes a novel Resource-Adaptive Successive Doubling Algorithm (RASDA), which combines a resource-adaptive successive doubling scheme with the plain Asynchronous Successive Halving Algorithm (ASHA). Scalability of this approach is shown on up to 1,024 Graphics Processing Units (GPUs) on modern HPC systems. It is applied to different types of Neural Networks (NNs) and trained on large datasets from the Computer Vision (CV), Computational Fluid Dynamics (CFD), and Additive Manufacturing (AM) domains, where performing more than one full training run is usually infeasible. Empirical results show that RASDA outperforms ASHA by a factor of up to 1.9 with respect to the runtime. At the same time, the solution quality of final ASHA models is maintained or even surpassed by the implicit batch size scheduling of RASDA. With RASDA, systematic HPO is applied to a terabyte-scale scientific dataset for the first time in the literature, enabling efficient optimization of complex models on massive scientific data. The implementation of RASDA is available on https://github.com/olympiquemarcel/rasda