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Presented is an algorithm based on dynamic mode decomposition (DMD) for acceleration of the power method (PM). The power method is a simple technique for determining the dominant eigenmode of an operator A, and variants of the power method are widely used in reactor analysis. Dynamic mode decomposition is an algorithm for decomposing a time-series of spatially-dependent data and producing an explicit-in-time reconstruction for that data. By viewing successive power-method iterates as snapshots of a time-varying system tending toward a steady state, DMD can be used to predict that steady state using (a sometime surprisingly small) n iterates. The process of generating snapshots with the power method and extrapolating forward with DMD can be repeated. The resulting restarted, DMD-accelerated power method (or DMD-PM(n)) was applied to the two-dimensional IAEA diffusion benchmark and compared to the unaccelerated power method and Arnoldi's method. Results indicate that DMD-PM(n) can reduce the number of power iterations required by approximately a factor of 5. However, Arnoldi's method always outperformed DMD-PM(n) for an equivalent number of matrix-vector products Av. In other words, DMD-PM(n) cannot compete with leading eigensolvers if one is not limited to snapshots produced by the power method. Contrarily, DMD-PM(n) can be readily applied as a post process to existing power-method applications for which Arnoldi and similar methods are not directly applicable. A slight variation of the method was also found to produce reasonable approximations to the first and second harmonics without substantially affecting convergence of the dominant mode.

There is growing interest in the development of transient, multiphysics models for nuclear reactors and analysis of uncertainties in those models. Reduced-order models (ROMs) provide a computationally cheaper alternative to compute uncertainties. However, the application of ROMs to transient systems remains a challenging task. Here, a 1-D, twogroup, time-dependent, diffusion model was used to explore the potential of three different ROMs: the intrusive POD-Galerkin and DMD-Galerkin methods and the purely datadriven DMD. For the problem studied, POD-Galerkin exhibited by far the best accuracy and was selected for further application to uncertainty propagation. Perturbations were introduced to the initial condition and to the cross-section data. A greedy-POD sampling procedure was used to construct a reduced space that captured much of the variation in the uncertain these parameters. Results indicate that relatively few samples of the uncertain parameters are needed to produce a basis for POD-Galerkin that leads to distributions of the quantities of interest that match well with those obtained from the full-order model using brute-force, forward sampling.