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

Purpose: 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. Materials and Methods: 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. Results: 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. Conclusion: 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.