Complex Neural Operator for Learning the Dynamics of Continuous Physical Systems

Figure 1. Overview of CoNO.

Codebase for Reproducibility

1. Install Python 3.8. For convenience, please go ahead and execute the following command.

pip install -r requirements.txt

2. Prepare Data. You can obtain experimental datasets from the following links (Download).

Datasets	Tasks	Geometry	Download Link
Elasticity-P	Estimate material inner stress	Point Cloud	[Google Cloud]
Elasticity-G	Estimate material inner stress	Regular Grid	[Google Cloud]
Plasticity	Estimate material deformation over time	Structured Mesh	[Google Cloud]
Navier-Stokes	Predict future fluid velocity	Regular Grid	[Google Cloud]
Darcy	Estimate fluid pressure through medium	Regular Grid	[Google Cloud]
AirFoil	Estimate airflow velocity around airfoil	Structured Mesh	[Google Cloud]
Pipe	Estimate fluid velocity in a pipe	Structured Mesh	[Google Cloud]

3. Train and evaluate model. We provide the experiment scripts of all benchmarks under the folder ./scripts/. You can reproduce the experiment results as the following examples:

bash scripts/elas_cono.sh # for Elasticity-P
bash scripts/elsa_interp_cono.sh # for Elasticity-G
bash scripts/plas_cono.sh # for Plasticity
bash scripts/ns_cono.sh # for Navier-Stokes
bash scripts/darcy_cono.sh # for Darcy
bash scripts/airfoil_cono.sh # for Airfoil
bash scripts/pipe_cono.sh # for Pipe

Note: You must change the argument --data-path in the above script files to your dataset path.

Main Results

Figure 2. Main Results.

Showcases

Figure 3. Showcases.

Citation

If you found the GitHub codebase useful, please cit following work:

@article{tiwari2024cono,
  title={CoNO: Complex Neural Operator for Continous Dynamical Physical Systems},
  author={Tiwari, Karn and Krishnan, NM and Prathosh, AP},
  journal={arXiv preprint arXiv:2406.02597},
  year={2024}
}

@article{bedi2025neural,
  title={A Neural Operator for Forecasting Carbon Monoxide Evolution in Cities},
  author={Bedi, Sanchit and Tiwari, Karn and Kota, Sri Harsha and Krishnan, NM and others},
  journal={arXiv preprint arXiv:2501.06007},
  year={2025}
}

Acknowledgement

We appreciate the following GitHub repos a lot for their valuable code base or datasets on which we have built our code:

1. https://github.com/neuraloperator/neuraloperator

2. https://github.com/neuraloperator/Geo-FNO

3. https://github.com/tunakasif/torch-frft

4. https://github.com/soumickmj/pytorch-complex

5. https://github.com/thuml/Latent-Spectral-Models