lmns3d / truncationerror

Sparse Identification of Truncation Errors (SITE) for Data-Driven Discovery of Modified Differential Equations

Sparse Identification of Truncation Errors (SITE)

This project contains the implementation of SITE, an approach to identify modified differential equations from simulation data as shown in 'Sparse Identification of Truncation Errors'. All codes used to generate the data and the plots of the paper are given here. A detailed explanation of the approach can be found in the preprint.

Built With

• SymPy - For the symbolic computations in the method of manufactured solutions and analytic derivations of modified differential equations (version 1.3)
• geomdl - For computations with NURBS (version 4.4.1)
• PySwarms - For the particle swarm optimization (version 0.3.1)
• findiff - For finite difference approximations (version 0.6.2)
• scikit-learn - For the implementation of Lasso (version 0.20.2)

We also used numpy (version 1.15.4), scipy (version 1.1.0) and matplotlib (version 3.0.2).

To run the SR3 sparse regression algorithm, the MATLAB-Python interface is used. If you want to run SR3, you have to set up the MATLAB Engine API.

Example

The functionality of the SITE approach can be controlled from within the 'main_file'. All controllable parameters are explained in this file as well.

Updates

Feel free to submit bug-fix requests through the issues tab on GitHub.

Code Author

Stephan Thaler

Co-authors of the paper: Ludger Paehler and Nikolaus A. Adams

License

This project is licensed under the MIT License - see the LICENSE file for details

Acknowledgments

• Samuel Rudy for parts of the PDE-FIND implementation and the consent to publish these parts here
• Travis Askham and Peng Zheng for the implementation of SR3

Citation

@article{thaler2019site,
  title={Sparse Identification of Truncation Errors},
  author={Thaler, Stephan and Paehler, Ludger and Adams, Nikolaus A.},
  journal={arXiv preprint arXiv:1904.03669},
  year={2019}
}