Parametric PDE discovery using UBIC

Using the uncertainty-penalized Bayesian information criterion (UBIC) originally proposed in Adaptive Uncertainty-Penalized Model Selection for Data-Driven PDE Discovery to discover parametric PDEs automatically.

• Please first install our modified pysindy package archived at this OneDrive link (Password: UBIC). The more updated version is avaiable at this repository.
• To use the L0BnB best-subset solver, please install the package.

The three major files for reproducing the results in arXiv:2408.08106 (accepted as a workshop paper in the Machine Learning and the Physical Sciences workshop, NeurIPS 2024) are in the following.

• Burgers' PDE: Parametric_Burgers-DEV3.ipynb
• Advection-diffusion PDE: Spatial_Advection_Diffusion_WeakLib_KRR-DEV3.ipynb
• Kuramoto-Sivashinsky PDE: Spatial_KS_Equation_Chaotic-DEV2.ipynb

Citing UBIC

@article{thanasutives2023adaptive,
  author={Thanasutives, Pongpisit and Morita, Takashi and Numao, Masayuki and Fukui, Ken-ichi},
  journal={IEEE Access},
  title={Adaptive Uncertainty-Penalized Model Selection for Data-Driven PDE Discovery},
  year={2024},
  volume={12},
  pages={13165-13182},
  doi={10.1109/ACCESS.2024.3354819}
}

@misc{thanasutives2024adaptation,
  title={Adaptation of uncertainty-penalized Bayesian information criterion for parametric partial differential equation discovery}, 
  author={Thanasutives, Pongpisit and Fukui, Ken-ichi},
  year={2024},
  eprint={2408.08106},
  archivePrefix={arXiv},
  primaryClass={cs.LG},
  url={https://arxiv.org/abs/2408.08106}, 
}

@inproceedings{thanasutives2024uncertainty,
  title={Uncertainty-Penalized Bayesian Information Criterion for Parametric Partial Differential Equation Discovery},
  author={Thanasutives, Pongpisit and Fukui, Ken-ichi},
  booktitle={Machine Learning and the Physical Sciences Workshop @ NeurIPS 2024},
  year={2024},
  url={https://ml4physicalsciences.github.io/2024/files/NeurIPS_ML4PS_2024_5.pdf}
}