Compact and Efficient Linear Accelerator Phase Space Modeling via Implicit Neural Representation Learning

Phase Space Files (PSF) are commonly used to restart Monte Carlo simulations from pre-calculated conditions, but are large and unwieldy. This study introduces and evaluates a compact representation of PSF using Sinusoidal Implicit Representation Networks (SIREN) that enables limitless sampling while preserving dosimetric accuracy. Approach: Three models were developed to account for the different types of particles found in photon phase spaces: primary photons, secondary photons, electrons. For each particle type, a sequence of 2 or 3 SIRENs were trained to learn the implicit neural representation of the probabilistic distribution of particle position, direction and energy. Once trained, PSFs of any desired size can be generated by sampling the probability density functions (PDF) implicitly represented by the model. We applied this approach to vendor-provided 6 and 10 MV photon phase spaces. Model accuracy was validated by using the network-sampled particles as input to an EGSnrc Monte Carlo dose calculation in a water phantom. Scalability is further investigated by training the model on 20% of the original PSF particles. Main results: SIREN reproduced marginal probability distributions and depth dose curves with excellent agreement. Lateral profiles showed small discrepancies in penumbra shoulders. 2%/0 mm Gamma pass rates were 97.2%, 98.1%, 96.9% and 99.2% for 6X, 6FFF, 10X and 10FFF, respectively. Mean voxel-wise dose difference was 0.44%(6X), 0.36%(6FFF), 0.51%(10X) and 0.25%(10FFF) versus vendor PSFs. Training on 20% of particles slightly reduced the 6X gamma pass rate from 97.2% to 96.3% while maintaining dose profile agreement. The approach achieved ~30 000-fold compression (1.6MB vs 50GB) with an average sampling time of ~0.8 s per 10^6 particles on an NVIDIA RTX6000Ada. Significance: The SIREN-based approach allows for a compact representation of Monte Carlo PSF with high dosimetric fidelity. It remains robust with reduced training data and would enable on-the-fly sampling of particles without recycling.