Normalizing flows for thermal scattering sampling

Abstract

This paper presents the use of normalizing flows for sampling thermal inelastic scattering kinematics for use in high-fidelity Monte Carlo simulations of neutrons. This approach maps a complex distribution relating the incoming energy of neutrons to its outgoing distributions (angle and dimensionless outgoing energy), to a simpler prior distribution that can be easily sampled. This mapping is performed by connecting cubic splines through a series of neural networks that are trained on samples representative of the target distribution. The process is demonstrated for neutron collisions with hydrogen nucleus in water over the thermal energy range. Performance is also assessed demonstrating that sampling a single parameter set, as needed in history-based Monte Carlo, is quite costly. However, this paper also demonstrate that potential benefits could be observed in a vectorized approach to neutron transport such as event-based Monte Carlo where neutrons are grouped by event type thus allowing to query the neural network for multiple samples at once.