Phonon-informed Neural Thermal Scattering (NeTS) Optimization for Crystalline Graphite and Beryllium Metal

Abstract

Fast neutrons born from fission lose energy through scattering interactions in the process of slowing-down. As neutrons thermalize to the order of $k$ $b$ $T$ (where $k$ $b$ is the Boltzmann constant, and $T$ is the temperature of the medium), their de Broglie wavelength and energy approaches the order of inter-atomic spacing and quantized lattice vibrations, i.e., phonons. At thermal energies, the thermal scattering law (TSL), i.e., $S$($α, β$), captures crystal binding contributions to the total reaction rate, or cross section. This dimensionless material property describes the energy ($β$) and momentum ($α$) exchanges available in a medium. Currently, $S$($α, β$) is evaluated in the Full Law Analysis Scattering System Hub (FLASSH) code for discrete inputs and stored as ENDF/B File 7 for 0-phonon elastic (MT 2) and n-phonon inelastic (MT 4) processes. Further processing recasts $S$($α, β$) into cumulative distribution functions for sampling post-collision scattering kinematics. In practice, interpolation schemes are employed to access data between tabulated values. An improvement to this juncture of the nuclear data pipeline is supplying cross sections on-the-fly (OTF), as has been developed for the un-resolved resonance region to minimize non-physical interpolation errors. This capability may improve simulation accuracy for accident and transient analyses, where rapidly varying changes in temperature and pressure are difficult to predict beforehand. To do so, deep artificial neural networks (ANNs) can be employed which collapse non-linear, complex data into a lightweight dictionary of neural weights and biases. This has been successfully demonstrated for the hydrogen in light water $S$($α, β$) dataset in the form of a Neural Thermal Scattering (NeTS) module. In this work, the NeTS framework is extended to consider the impact of material-dependent dynamical features on optimal neural pre-processing and architecture design decisions, such as number of neurons per hidden layer, residual skip connections and neural depth. New NeTS modules for crystalline graphite and beryllium metal illuminate a novel correlation between dynamical nonlinearity and optimal neural parametrization when deploying $S$($α, β$) on-the-fly.