Fast proton transport and neutron production in proton therapy using Fourier neural operators

Objective. Real-time adaptive proton range verification systems based on produced neutrons require accurate information on their non-isotropic momentum distributions within seconds, for which general-purpose Monte Carlo (MC) methods are too computationally expensive. We therefore present a first study for a surrogate model based on Fourier neural operators (FNO) for fast prediction of angle- and energy-resolved proton transport and neutron production within proton therapy.Approach. We treat the phantom and the proton beam's state as depth-evolving series, respectively of different materials, and of spatial, angular, and energy phase space density distributions. FNO models were trained to compute changes in proton distributions along with those of produced neutrons per unit of depth, and they were used auto-regressively to simulate the entire phantom. For training and evaluation, two datasets of 47 MC simulations featuring different primary intensities were produced. Simulated geometries were extracted from a thoracic CT scan as series of laterally homogeneous materials.Main Results. An average relativeL2-norm error of0.067and0.137was achieved by the predicted proton and neutron distributions, respectively. This corresponded to an average spatial gamma passing rate (2 %, 2 mm) of99.95%and99.40%, and an average error in the mean of the longitudinal intensity distribution of 0.238 mm and 0.871 mm. Training with higher primary intensities improved neutron density metrics by up to30%. Inference over depths of 40 cm at a resolution of 0.5 mm required on average 23.17 s per beam.Significance. Our proton beam surrogate generates accurate phase space distributions of neutrons at MC-level accuracy within seconds, while demonstrating robust generalization with respect to irradiated geometry and beam characteristics. This first study is relevant for prototyping and operation of range verification systems and for other tasks such as neutron dose estimation, with methods being extendable to other kinds of secondary particles.