Variable Dynamic Mode Decomposition for Estimating Time Eigenvalues in Nuclear Systems

TL;DR

This paper introduces Variable Dynamic Mode Decomposition (VDMD), a novel method for accurately estimating neutron transport eigenvalues in complex nuclear systems with multiple time scales, extending the capabilities of traditional DMD.

Contribution

The paper develops VDMD, an extension of DMD that handles non-uniform time steps, enabling eigenvalue estimation in systems with large time scale separations.

Findings

VDMD accurately computes eigenvalues in delayed supercritical systems.

VDMD performs comparably to DMD in systems with uniform time steps.

The method effectively captures multiple, very different relevant time scales.

Abstract

We present a new approach to calculating time eigenvalues of the neutron transport operator (also known as $\alpha$ eigenvalues) by extending the dynamic mode decomposition (DMD) to allow for non-uniform time steps. The new method, called variable dynamic mode decomposition (VDMD), is shown to be accurate when computing eigenvalues for systems that were infeasible with DMD due to a large separation in time scales (such as those that occur in delayed supercritical systems). The $\alpha$ eigenvalues of an infinite medium neutron transport problem with delayed neutrons and consequently having multiple, very different relevant time scales are computed. Furthermore, VDMD is shown to be of similar accuracy to the original DMD approach when computing eigenvalues in other systems where the previously studied DMD approach can be used.