Robust Subgroup Method Using DE Algorithm for Resonance Self-Shielding Calculation

TL;DR

The paper tackles a systematic absorption bias in resonance self-shielding subgroup fits caused by model misspecification and data contamination, especially in benchmarks sensitive to $^{238}$U resonances. It proposes a robust subgroup method that embeds an M-estimator with scale pre-estimation (MAD) and Tukey's bisquare loss within a Differential Evolution optimizer, enforcing physical feasibility via an $\epsilon$-constrained scheme. TheRE-DE framework reduces leverage and multicollinearity effects in the strong self-shielding regime, yielding more faithful subgroup parameters and improved transport predictions, particularly for $^{238}$U-sensitive cases, while also revealing fidelity-dependent instability as a key consideration. The work highlights practical pathways for extending robustness to higher-dimensional subgroup kernels and broader robust-statistics methods, with implications for improving accuracy in high-fidelity lattice transport simulations.

Abstract

This paper presents an enhanced version of the subgroup method for resonance self-shielding treatment, termed the robust subgroup method, which integrates Robust Estimation (RE) with a Differential Evolution (DE) algorithm. The RE approach is employed to handle model misspecification and data contamination, while the DE algorithm serves as an optimization tool within the RE framework to obtain constrained solutions. Numerical validation against experimental benchmarks shows that the proposed method removes a systematic absorption bias in conventional subgroup fits that would otherwise depress reactivity. This bias appears only in benchmarks sensitive to U-238. Mechanistically, it reflects a threshold-like conditioning failure: strong self-shielding leverage dominates the loss and is magnified by dilution-induced multicollinearity. This adverse conditioning appears to be seeded by a narrow, sparse resonance structure at low energies in fertile even-even nuclides, thereby causing rapid self-shielding response saturation and a weak Doppler broadening. By bounding influence and enforcing feasibility within an RE-DE framework, the inferred subgroup parameters track the underlying physics more faithfully, improving the predictive fidelity of subsequent transport simulations.

Figures (2)

• Figure 1: Causal chain of threshold-like artifacts
• Figure 2: Magnitude of the relative error of $k_{calc}$ with respect to experimental data in cases sensitive to $^{238}$U