Flux distribution tallies using proper orthogonal decomposition in Monte Carlo calculations

ABSTRACT

In this paper, a new tallying method for a neutron flux distribution using the proper orthogonal decomposition is proposed for dimensionality reduction. The target spatial flux distribution is expanded by orthogonal basis vectors. Expansion coefficients are tallied during the random walk of the Monte Carlo calculation. The orthogonal basis vectors are extracted from the pre-calculated snapshots by the singular value decomposition. The proposed method is verified in the multi-group Monte Carlo calculation with the one-dimensional heterogeneous whole core geometry as a feasibility study. The flux distribution for each of the assemblies and energy groups is expanded by the basis vectors. The fewer basis vectors obtained from snapshots can reconstruct the target distribution well compared with the conventional Legendre polynomials used in the functional expansion tallies. The dimension of the solution in the proposed method is reduced by a factor of twenty compared with the conventional cell tally. In addition, the statistical error is reduced through dimensionality reduction thanks to the methodological feature of the proposed method. The results indicate that the proposed method has the capability of dimensionality reduction to tally the finely discretized flux distribution.

KEYWORDS:

• Proper orthogonal decomposition
• dimensionality reduction
• tally method
• Monte Carlo calculation
• multi-group calculation
• numerical simulation
• verification

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/00223131.2024.2365445.

Additional information

Funding

The author(s) reported that there is no funding associated with the work featured in this article.