Guide to Spectral Proper Orthogonal Decomposition

An introduction to the proper orthogonal decomposition

A tutorial is presented on the Proper Orthogonal Decomposition (POD), which finds applications in computationally processing large amounts of high-dimensional data with the aim of obtaining low-dimensional descriptions that capture much of the phenomena of interest. The discrete version of the POD, which is the singular value decomposition (SVD) of matrices, is described in some detail. The con...

Artificial viscosity proper orthogonal decomposition

We introduce improved reduced-order models for turbulent flows. These models are inspired from successful methodologies used in large eddy simulation, such as artificial viscosity, applied to standardmodels created by proper orthogonal decomposition of flows coupled with Galerkin projection. As a first step in the analysis and testing of our new methodology, we use the Burgers equation with a s...

A New Look at Proper Orthogonal Decomposition

We investigate some basic properties of the proper orthogonal decomposition (POD) method as it is applied to data compression and model reduction of finite dimensional nonlinear systems. First we provide an analysis of the errors involved in solving a nonlinear ODE initial value problem using a POD reduced order model. Then we study the effects of small perturbations in the ensemble of data fro...

Proper orthogonal decomposition of solar photospheric motions.

The spatiotemporal dynamics of the solar photosphere is studied by performing a proper orthogonal decomposition (POD) of line of sight velocity fields computed from high resolution data coming from the MDI/SOHO instrument. Using this technique, we are able to identify and characterize the different dynamical regimes acting in the system. Low-frequency oscillations, with frequencies in the range...

Model Reduction via Proper Orthogonal Decomposition