Global Optimal estimation of fission model parameters without gradient-based methods
A Kalman Filter approach is currently used to optimally fit parameters of a fission model (such as the models in GNASH/TALYS etc.) to experimental (n,f) cross sections and uncertainties. The high dimensionality of the parameter space can often result in gradient-based optimization methods becoming fixated on local minima in their search for optimal parameters. This can result in different optimal parameter sets being returned by such techniques at different incident neutron energies -- a situation that one would obviously wish to avoid for nuclear data applications. In a quest for robust estimation methods, we explore optima in n-dimensional polyhedra. In particular, I will show application to the evaluated Pu239(n,f) data in the ENDF/B-VII database over the incient neutron energy range 0.1-8.5 MeV. Conditions under which the geometric methods are guaranteed to find global optima will be discussed with a specific implementation using Chebyshev polynomials, and an extension to evaluated data with uncertainties will be formulated to understand how covariance matrices enter into this optimal estimation method.