Uncertainty Quantification for the Fission Matrix Method: A Rigorous Mathematical Framework and Computationally Efficient Alternatives

Valerio Mascolino

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arXiv · 2609.33161

Uncertainty Quantification for the Fission Matrix Method: A Rigorous Mathematical Framework and Computationally Efficient Alternatives

Valerio Mascolino

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Abstract

The fission matrix (FM) method recasts neutron transport in matrix form, enabling fast, interpolation-based reactor calculations from a pre-computed database of Monte Carlo-derived coefficients. Propagation of the underlying Monte Carlo statistical uncertainty to the FM eigenvalue and eigenvector is rarely rigorous: prior approaches assume independent coefficients without testing this against their actual covariance. This work derives a full-covariance Delta-method framework for propagating uncertainty to keff and the fission source, and evaluates it with two cheaper alternatives, a diagonal-covariance approximation and direct resampling of the FM coefficients, using an OpenMC model of the JSI TRIGA Mark-II reactor. For the all-rods-out case, these three estimators and an empirical benchmark of 100 independent Monte Carlo runs agree within 5.7% for keff and 1% for the fission source. The sign of the diagonal approximation's bias flips between the two statistics levels, so it must be checked case by case. With a global fixed-source FM generation strategy, the diagonal, resampling, and independent-run estimators agree within about 2% and lie roughly 10% below the full-covariance estimate, a gap attributed to covariance sampling noise. The large off-diagonal covariance is nearly symmetric and mostly cancels when propagated, rather than being small or negative as previously assumed. For the FM control-rod interpolation and combination strategy (FM-CRd), keff matches an exact perturbed reference within 60 pcm (about two standard deviations) and the fission source within 0.7%, while the diagonal and resampling estimators agree closely and are conservative by about a factor of two. Given this and the prohibitive memory cost of the full covariance, the diagonal Delta method is recommended as the practical default, with the full covariance reserved for one-time characterization of a system.

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Valerio Mascolino. 2026-09-27. Uncertainty Quantification for the Fission Matrix Method: A Rigorous Mathematical Framework and Computationally Efficient Alternatives. https://arxiv.org/abs/2609.33161

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