The so-called “smooth orthogonal decomposition” technique, developed in the nonlinear vibrations and fatigue community, is applied to an oceanographic data set. This decomposition technique overcomes some limitations of the proper orthogonal decomposition technique by identifying modes which behave smoothly in time and thus being sensitive to both variance amplitude as well as frequency. This i...

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...

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...

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...

Mathematical models for human tissue and blood flow both represent time dependent nonlinear partial differential equations in three space dimensions. Their numerical solution based on appropriate space/time discretizations requires computational times that even when using state-of-the-art algorithmic solvers are far from being acceptable for real time OR scenarios. A way to overcome this diffic...

Proper Orthogonal Decomposition (POD), alternatively known as Principal Component Analysis or the Karhunen-Loève decomposition, is a model-reduction technique which generates the optimal linear subspace of dimension D for a given set of higher-dimensional data. That is, if the data are contained within an attractor, the POD process can produce the affine linear space that best approximates the ...

Future Work Conclusions The aim of the following research is to therefore remove this obstacle to the application of kriging whilst developing a strategy for use at higher dimensions. The goal of an initial investigation was therefore to determine if these hyperparameters should be tuned after every update, and to what degree they should be tuned, in order for the model to remain effective. Thi...