Nuclear Computations under Uncertainty New methods to infer and propagate nuclear data uncertainty across Monte Carlo simulations

Abstract

This thesis introduces new methods to efficiently infer and propagate nuclear data uncertainty across Monte Carlo simulations of nuclear technologies. The main contributions come in two areas: 1. novel statistical methods and machine learning algorithms (Embedded Monte Carlo); 2. new mathematical parametrizations of the quantum physics models of nuclear interactions and their uncertainties (Stochastic Windowed Multipole Cross Sections).

1. Embedded Monte Carlo infers the uncertainty in nuclear codes inputs (reactor geometry, nuclear data, etc.) from samples of noisy outputs (e.g. experimental observations), and in turn propagates this uncertainty back to the simulation outputs(reactor power, reaction rates, flux, multiplication factor, etc.), without ever converging any single Monte Carlo reactor simulation. Such embedding of the uncertainty within the Nested Monte Carlo computations vastly outperforms previous methods(10–100 times less runs), and is achieved by approximating the input parametersBayesian posterior via variational inference, and reconstructing the outputs distribution via moments estimators. We validate the Embedded Monte Carlo method on anew analytic benchmark for neutron slowdown we derived.

2. Stochastic Windowed Multipole Cross Sections is an alternative way to parametrize nuclear interactions and their uncertainties (equivalent to R-matrix theory), whereby one can sample on-the-fly uncertain nuclear cross sections and analytically compute their thermal Doppler broadening. This drastically reduces the memory footprint of nuclear data (at least 1,000-fold), without incurring additional computational costs.

These contributions are documented in nine peer-reviewed journal articles (eight published and one under review) and seven conference articles (six published and one under review), constituting the core of this thesis.