Neural Operator-Enabled Gain Scheduling for a Transport PDE with Nonlinear Recirculation

The source code for the paper titled Neural Operator-Enabled Gain Scheduling for a Transport PDE with Nonlinear Recirculation.

Sysetm Requirements

All of the code is written in Python 3 and relies on standard packages such as numpy, Pytorch, Scipy, and the deep learning package DeepXDE. Additionally, all code in this work is nicely formatted in a jupyter-notebook. A basic installation will require the installation of Python, jupyter along with DeepXDE and PyTorch. Please see the import statements in the Jupyter-notebooks to make sure all files are included. Versions for each package is given at the first block of the jupyter-notebook and is included in the requirements.txt file.

Demos

Dataset and Models

All precomputed datasets and models are available here Google Drive

Gain Scheduling with Neural Operator Approximated Kernels

• Please see the jupyter-notebook gainScheduling.ipynb. All the datasets are available in the drive, but if one ones to make their own data, the generation code is commented out in the notebook. Likewise to compute one's own models, please comment out the load_dict in the notebook. The figures in the paper are computed with a high resolution $dt=0.00001$, but this may take some time on others comptuers. As such, the author recommends to use $dt=0.0001$ for exploring the algorithms and playing around and then uses a finer resolution when developing figures.

Cite this work

@misc{lamarque2024gain,
      title={Gain Scheduling with a Neural Operator for a Transport PDE with Nonlinear Recirculation}, 
      author={Maxence Lamarque and Luke Bhan and Rafael Vazquez and Miroslav Krstic},
      year={2024},
      eprint={2401.02511},
      archivePrefix={arXiv},
      primaryClass={eess.SY}
}

Questions

Feel free to leave any questions in the issues of Github or email the author Luke at lbhan@ucsd.edu

License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.