Weighted Levenberg-Marquardt methods for fitting multichannel nuclear cross section data

M. Imbrisak, A. Lovell, M. Mumpower

Submitted submitted (2025)

We present an extension of the Levenberg-Marquardt algorithm for fitting multichannel nuclear cross section data. Our approach offers a practical and robust alternative to conventional trust-region methods for analyzing experimental data. The CoH3 code, based on the Hauser-Feshbach statistical model, involves a large number of interdependent parameters, making optimization challenging due to the presence of "sloppy" directions in parameter space. To address the uneven distribution of experimental data across reaction channels, we construct a weighted Fisher Information Metric by integrating prior distributions over dataset weights. This framework enables a more balanced treatment of heterogeneous data, improving both parameter estimation and convergence robustness. We show that the resulting weighted Levenberg-Marquardt method yields more physically consistent fits for both raw and smoothed datasets, using experimental data for 148Sm as a representative example. Additionally, we introduce a geometric scaling strategy to accelerate convergence -- a method based on the local geometry of the manifold.