Data Assimilation and Parameter Estimation for the Kuramoto-Sivashinsky Equation

This repository is the source code for the paper Concurrent MultiParameter Learning Demonstrated on the Kuramoto-Sivashinsky Equation by Pachev, Whitehead, and McQuarrie.

Contents

• KS_order.py: Main source file for current simulations.
• batch_simulations.py: Run several simulation and save output data in .npz files.
• paper_simulations.py: Simulations chosen for the paper.
• finite_difference.py: Defines a function stable_fdcoeffs() for computing the finite difference coefficients to estimate a function derivative at a point given function values on a nonuniform grid. Used by KS_order.KSAssim.
• simulation_results.py: Defines a convenience class for reading / visualizing data saved by batch_simulations.py.

Citation

If you find this repository useful, please consider citing our paper:

Pachev, B., Whitehead, J., and McQuarrie, S. A., Concurrent multiparameter learning demonstrated on the Kuramoto-Sivashinsky equation. SIAM Journal on Scientific Computing, 44(5):A2974–A2990, 2022.

@article{pachev2022multiparameter,
  author = {Pachev, Benjamin and Whitehead, Jared P. and McQuarrie, Shane A.},
  title = {Concurrent MultiParameter Learning Demonstrated on the {K}uramoto--{S}ivashinsky Equation},
  journal = {SIAM Journal on Scientific Computing},
  volume = {44},
  number = {5},
  pages = {A2974-A2990},
  year = {2022},
  doi = {10.1137/21M1426109},
}