KPCA-DeepONet

kpca_deeponet is a library that utilizes nonlinear model reduction for operator learning.

Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on the combination of model reduction and neural networks, POD-DeepONet, has been able to outperform other architectures in terms of accuracy for several benchmark tests. In this contribution, we extend this idea towards nonlinear model order reduction by proposing an efficient framework that combines neural networks with kernel principal component analysis (KPCA) for operator learning. Our results demonstrate the superior performance of KPCA-DeepONet over POD-DeepONet.

Comparison of the KPCA-DeepONet (orange) and POD-DeepONet (blue)

More details about the implementation and results are available in our paper.

Installation

Clone the repository and locally install it in editable mode:

git clone https://github.com/HamidrezaEiv/KPCA-DeepONet.git
cd KPCA-DeepONet
pip install -e .
pip install -r requirements.txt

You can also just pip install the library:

pip install kpca-deeponet

Citation

If you use kpca_deeponet in an academic paper, please cite:

@inproceedings{eivazi2024nonlinear,
               title={Nonlinear model reduction for operator learning},
               author={Hamidreza Eivazi and Stefan Wittek and Andreas Rausch},
               booktitle={The Second Tiny Papers Track at ICLR 2024},
               year={2024},
               url={https://openreview.net/forum?id=Jw6TUpB7Rw},
               doi={10.5281/zenodo.13754046}
               }