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

TL;DR

This paper extends the Levenberg-Marquardt algorithm with weighting and geometric scaling to improve fitting of multichannel nuclear cross section data, addressing challenges of data heterogeneity and parameter sloppiness.

Contribution

It introduces a weighted Fisher Information Metric and a geometric scaling strategy, providing a more robust and physically consistent fitting method for complex nuclear data analysis.

Findings

Weighted Levenberg-Marquardt improves fit quality for experimental nuclear data.

The method enhances convergence robustness and physical consistency.

Application to ${}^{148}$Sm data demonstrates effectiveness.

Abstract

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 CoH$_3$ 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 ${}^{148}$Sm as a representative example. Additionally, we introduce a geometric scaling strategy to accelerate convergence -- a method based on the local geometry of the manifold.