DATA Repository - robust sPOD

This repository contains the data for the paper:

Title: A robust shifted proper orthogonal decomposition: Proximal methods for decomposing flows with multiple transports.
Authors: Philipp Krah, Arthur Marmin, Beata Zorawski, Julius Reiss, Kai Schneider
Abstract:
We present a new methodology for decomposing flows with multiple transports that further extends the shifted proper orthogonal decomposition (sPOD). The sPOD tries to approximate transport-dominated flows by a sum of co-moving data fields. The proposed methods stem from sPOD but optimize the co-moving fields directly and penalize their nuclear norm to promote low rank of the individual data in the decomposition. Furthermore, we add a robustness term to the decomposition that can deal with interpolation error and data noises. Leveraging tools from convex optimization, we derive three proximal algorithms to solve the decomposition problem. We report a numerical comparison with existing methods against synthetic data benchmarks and then show the separation ability of our methods on 1D and 2D incompressible and reactive flows. The resulting methodology is the basis of a new analysis paradigm that results in the same interpretability as the POD for the individual co-moving fields.      
URL: https://doi.org/10.48550/arXiv.2403.04313

For the numerical examples flow data is generated, which is decomposed by the algorithm.
The data contains:

• two-cylinder vortex shedding example at Reynolds number 200
• Wildland fire 1D without wind
• Wildland fire 2D with wind

Please cite our paper if you make use of the data. 

The sPOD source code can be found here: https://github.com/MOR-transport/sPOD