Neural Representation Learning for Compact and Efficient Modeling of Monte Carlo Phase Space Data

Monte Carlo (MC) simulations provide gold standard dose calculations in radiation therapy but generate large phase space (PHSP) files that limit clinical implementation. We developed NeRP-MC, the first neural representation learning approach for PHSP data modeling, and evaluated its ability to model particle distributions from minimal training data.

We investigated proton PHSP modeling at 242 and 140 MeV. For both energies, a reference proton pencil beam PHSP containing 25 million particles was generated using TOPAS. A multi-layer perceptron with Fourier feature encoding was trained to predict particle energies from spatial and momentum inputs. We evaluated NeRP-MC in 3 scenarios: 1) compact energy modeling given full spatial and momentum information, 2) energy modeling from sparse PHSP data (1.25 million particles, 20-fold reduction), and 3) replacing the PHSP with parametric Gaussian spatial/momentum distributions and network-predicted energies conditioned on the Gaussian-sampled inputs. Validation used in-water dose distributions compared via gamma index analysis.

The trained network requires only 600 KB for storage versus 3 GB for the original PHSP and predicts 25 million particle energies in under 0.5 seconds on an NVIDIA A100 GPU. NeRP-MC generated energies showed close agreement with reference data across all 3 scenarios. Depth-dose profiles, lateral profiles, and penumbra regions were accurately reproduced. Gamma pass rates exceeded 99% at 3%/2 mm and 90% at the strictest 1%/1 mm criterion.

NeRP-MC offers compact modeling and fast prediction of particle energies from particle spatial and momentum information and promises to replace the large-scale PHSP with a parametric Gaussian model of spatial and angular variables and the NeRP model of particle energy variables. NeRP-MC has the potential to advance MC simulation efficiency for radiation therapy through a substantial reduction in computational and storage requirements while maintaining dosimetric accuracy.