Dynamic Mode Decomposition for Subcritical Metal Systems

Survey of Dynamic Mode Decomposition Methods

“…In the nuclear engineering community, this comprises of the time dependent neutron diffusion or transport equations and the nuclide production-destruction equations characteristic of burnup calculations. These applications have been explored in [6], [8], and [1]. This section will explore the efficacy of standard DMD when various different time scales exist.…”

“…In some instances, there may be many different signals, but only a few may be relevant. This is the precise type of problem investigated in [6]. This section uses the same setup as the previous example, but the time scales are shuffled and the first three signals are promoted in amplitude three to four orders of magnitude far above the remainder.…”

“…In recent years, various other fields, such as nuclear engineering, have begun to adopt this method. For example, DMD has been used for estimating α-eigenvalues [8], as an ROM for pulsed neutron problems [6], for predicting isotopic composition in burnup calculations [1], as acceleration techniques for iterative methods [9] [10], and in capturing dynamic behaviors in molten salt reactor transients [3]. This report seeks to demonstrate the capabilities and limits of the standard DMD algorithm, and identify problem spaces where variants may be better suited.…”

Reduced order models for nonlinear radiative transfer based on moment equations and POD/DMD of Eddington tensor

“…These techniques have seen extensive use in the fluid dynamics community for the modeling of general nonlinear flows [19,20], linearized flows [21], compressible flows [22], turbulence [23,11] and other applications [24,25]. Naturally the same techniques also have a wide range of applicability in the development of ROMs for particle transport, and have been used to model linear particle transport problems [26,27,28,29,30,31], neutron transport in reactor-physics problems [32,33,34], and nonlinear radiative transfer [35,36,37,38,39].…”

Data-Driven Acceleration of Thermal Radiation Transfer Calculations with the Dynamic Mode Decomposition and a Sequential Singular Value Decomposition

“…It has enjoyed considerable acceptance in the computational fluid dynamics community for understanding the properties of flows [3] and for comparing simulation and experiment [1]. For neutron transport problems it was introduced as a technique to estimate time-eigenvalues [4], for creating reduced order models [5], to understand stability [6], and for accelerating power iterations for k-eigenvalue problems [7]. In this work we turn to the problem of accelerating discrete ordinates solutions to radiative transfer problems (primarily x-ray radiative transfer for time-dependent high-energy density physics applications).…”