Simulating particle beam interactions includes identifying a set of n functions F1, F2, . . . , Fn corresponding to a plurality of different physical aspects of a particle beam, performing simulations of each Fi using a full physics model, selecting for each Fi a distribution function fi that models relevant behavior and reducing computation of the full physics model for each Fi by replacing Fi with a distribution function fi. The computation reduction includes comparing a set of simulations wherein each fi replaces its respective Fi to determine if relevant behavior is accurately modeled and selecting one of fi or Fi for each n, for a Monte Carlo simulation based on a runtime and accuracy criteria.