Smooth Piecewise Cutting for Neural Operator to Handle Discontinuities and Sharp Transitions

This repository is the official implementation of Smooth Piecewise Cutting for Neural Operator to Handle Discontinuities and Sharp Transitions by Ha Dang, Sebastian Schmidt and Jürgen Hesser.

Directory Structure

Each folder represents a problem demonstrated in the paper, with the following structure:

inviscid_burgers/
├── checkpoints/
├── data/
├── 1_Evaluation_with_TestSet.ipynb
├── DeepONet.ipynb
├── flexDeepONet.ipynb
├── HyperDeepONet.ipynb
├── FNO.ipynb
├── Cut_DeepONet.ipynb
└── CuttingNet.ipynb

Note: The inviscid_burgers, linear_advection, and parsimonious_model folders contain experiments comparing the performance of Cut-DeepONet to other methods. They have the same structure.

Installation & Use Guide

Setting up

• Install the requirements, run: pip install -r requirements.txt
• Create checkpoints folder

Dataset & Pre-trained models

• You can create your own dataset using the files in the data folder, or you can download the dataset from the link below and copy it into the data folder.
• To save training time, you can download the pretrained models here. These models were trained using the included dataset; copy them into your checkpoints folder.

Note: Dataset and Pretrained Models is the link to download the dataset and pretrained models.

Training

To retrain the models presented in the paper, run all cells in the corresponding training notebooks for each model: DeepONet.ipynb, flexDeepONet.ipynb, HyperDeepONet.ipynb, FNO.ipynb, and Cut_DeepONet.ipynb (Cut_DeepONet.ipynb requires training CuttingNet.ipynb first).

Evaluation

If you already have the checkpoints, or if you download the pretrained models from the link below, you can run 1_Evaluation_with_TestSet.ipynb. You can replace the test dataset at the beginning of the notebook. At the end of the evaluation, a plot comparing all methods will be generated

Cite this work

If you use this code for academic research, you are encouraged to cite the following paper:

@misc{dang2026smoothpiecewisecuttingneural,
      title={Smooth Piecewise Cutting for Neural Operator to Handle Discontinuities and Sharp Transitions}, 
      author={Ha Dang and Sebastian Schmidt and Juergen Hesser},
      year={2026},
      eprint={2605.19823},
      archivePrefix={arXiv}, 
}

Questions

To get help on how to use the data or code, simply open an issue in the GitHub "Issues" section.

License