All Times ET
Keywords: functional variance propagation, dimension reduction, sliced inverse regression, regularization
Neutronics simulations are computationally intense and depend on many correlated functional inputs, presenting interesting challenges for uncertainty quantification. This talk surveys several emergent data science problems and solutions: (i) effective display of functional co-variation modes that drive output uncertainties; (ii) functional input dimension reduction with regularized sliced inverse regression; (iii) computer experiment design over multiple input functions; and (iv) scalar-on-function surrogate modeling.
A physical simulation of neutronically active materials can compute, for example, the criticality level of a given geometric configuration. Results are used to design power reactors and establish safety protocols for nuclear material handling. Inputs to a simulation include cross-sections that quantify how neutrons interact with atomic nuclei. Cross-sections depend upon incident neutron energy and possibly angle. Nuclear data libraries publish cross-section means and functional covariances.
Understanding how input uncertainties from many cross-section functions compound and compensate when propagated through a simulation across-a large set of uncertain inputs is useful, for example, when designing a new set of experiments to best reduce output uncertainties over a variety of future neutronics applications. We derive and illustrate the primary driving mode of correlated input uncertainty to demystify how errors propagate.
As the driving mode depends on input to output gradient functions which are typically not provided by the simulation, a second piece of our work generalizes the old sliced inverse regression technique to estimate high-dimensional functional gradients. We also discuss using estimated gradients for design of new experiments over a dimension-reduced functional input space.