A data-efficient surrogate modeling method for a cyclotron-based proton therapy beamline based on active learning

High-fidelity beamline models typically involve particle-tracking and particle–matter interaction, which are intensive computationally demanding and time-consuming. This has led researchers to adopt data-driven surrogate models as an alternative to complex physics simulations. Training a data-driven model requires many labeled data, prompting researchers to simulate diverse beamline settings and obtain corresponding labels. However, the required dataset grows increasingly large as the number of adjustable parameters increases. Therefore, this study proposes a data-efficient surrogate modeling method that employs a student–teacher framework combined with active learning (AL) query strategies to minimize labeled samples while ensuring model accuracy. The proposed method is evaluated on the energy selection system (ESS) design of the Huazhong University of Science and Technology proton therapy facility (HUST-PTF). The results show that: (i) Training the surrogate model using 684 labeled samples selected via query strategy achieves a relative error below 5% for 90% of the samples in the test set. (ii) Compared to the beamline model built by Beam Delivery Simulation (BDSIM), the computational efficiency of the surrogate model is enhanced by a factor of [Formula: see text].