Admissible Reconstruction of Reaction-Channel Levels on Fixed Subgroup Support for Cross-Section-Space Probability Table Constructions

TL;DR

This paper introduces a convex optimization approach for reconstructing reaction-channel levels in cross-section-space probability tables, ensuring nonnegativity and physical interpretability while maintaining key information.

Contribution

It formulates an admissible constrained reconstruction problem that preserves low-order channel data and guarantees nonnegativity through convex optimization with linear constraints.

Findings

Nonnegativity violations are limited to few energy groups.

Admissible reconstruction restores nonnegativity where needed.

Single-retention formulation exhibits more stable behavior.

Abstract

In cross-section-space probability table constructions, reaction-channel levels are reconstructed on fixed total-subgroup nodes and probabilities. Although the standard full-matching reconstruction is uniquely determined, it does not in general preserve componentwise nonnegativity of the channel levels. We impose nonnegativity both for physical interpretability and because, on fixed positive total-subgroup nodes and probabilities, it provides a sufficient structural condition for nonnegativity of the folded effective cross section over all dilutions. We therefore formulate an admissible constrained reconstruction problem on the fixed subgroup support, in which selected low-order channel information is retained exactly and the remaining matching conditions are fitted in a weighted least-squares sense. After null-space reduction, the problem becomes a convex optimization problem with linear inequality constraints. For the single-retention formulation, nonnegative feasibility is automatic when the retained \(0\)-order aggregate is nonnegative, whereas for a two-retention variant it additionally requires a compatibility condition with the fixed total-subgroup nodes. Numerical results for a representative U-238 capture benchmark show that nonnegativity violations are confined to a small subset of energy groups. On these groups, the admissible reconstruction restores nonnegativity, but at the cost of some response-level deterioration relative to full matching. In the comparison, the single-retention formulation shows the more stable overall behavior.