Front Transport Reduction for Complex Moving Fronts

This is the repository to the publication:

@article{KrahBuechholzHaeringerReiss2022,
title={Front Transport Reduction for Complex Moving Fronts}, 
author = {Krah, Philipp and B{\"u}chholz, Steffen and H{\"a}ringer, Matthias and Reiss, Julius},
year = {2023},
month = {06},
volume = {96},
journal = {Journal of Scientific Computing},
doi = {10.1007/s10915-023-02210-9}
}

Please cite our work if you use the code. You can read the publication here.

All Matlab and Python sources are contained in the lib/ folder.

The examples/ folder, contains the following examples of the paper:

• 01_moving_disk.py: Implements the results of the 2D disk that moves in a circle. It includes:
  • training of autoencoder networks and FTR-thresholding algorithm, POD
  • online predictions using Fourier-Koopman forecasting
• 02_topo_change.py: Same as first example but with topology changing fronts
• 03_bunsen_flame.py: Imports the multi-slit bunsen flame data and computes a low rank description from it
• 04_advection_FTR_galerkin.m: basic FTR example in 1D advection example including:
  • generation of data from a PDE
  • dim. reduction using FTR, POD
  • galerkin projections
• 05_reaction_diffusion_FTR_galerkin.m: basic FTR example for 1D reaction-diffusion equation
• 06_reaction_diffusion_hyper-FTR_galerkin.py: hyper-FTR example for 1D reaction-diffusion equation
• 07_ARD_2d_hyper-FTR.py: hyper-FTR example for advection-reaction-diffusion equation in 2D