Mathematical Considerations on Randomized Orthgonal Decomposition Method for Developing Twin Data Models

TL;DR

This paper presents a novel Randomized Orthogonal Decomposition method for creating twin data models, offering orthonormal modes that improve data projection, demonstrated through viscous Burgers equation simulations.

Contribution

The paper introduces ROD, a new orthogonal decomposition technique that enhances twin data modeling by maximizing data projection and overcoming limitations of existing methods.

Findings

ROD produces orthonormal shape modes with improved data projection.

The method demonstrates high numerical accuracy in viscous Burgers simulations.

ROD offers better computational performance compared to traditional techniques.

Abstract

This paper introduces the approach of Randomized Orthogonal Decomposition (ROD) for producing twin data models in order to overcome the drawbacks of existing reduced order modelling techniques. When compared to Fourier empirical decomposition, ROD provides orthonormal shape modes that maximize their projection on the data space, which is a significant benefit. A shock wave event described by the viscous Burgers equation model is used to illustrate and evaluate the novel method. The new twin data model is thoroughly evaluated using certain criteria of numerical accuracy and computational performance.