Instant Artificial Intelligence Velocimetry-Thermometry (AIVT)

This repository serves as a collection of code implementations for published and upcoming papers on Artificial Intelligence Velocimetry-Thermometry (AIVT). It will be continuously updated with new research developments and additional resources.

Papers

Currently, this repository contains the code for the following paper:

1. Toscano, J. D., Käufer, T., Wang, Z., Maxey, M., Cierpka, C., & Karniadakis, G. E. (2025). AIVT: Inference of turbulent thermal convection from measured 3D velocity data by physics-informed Kolmogorov-Arnold networks. Science Advances, 11(19). DOI: 10.1126/sciadv.ads5236 Link: Science Advances DOI: 10.1126/sciadv.ads5236

If you find this content useful please consider citing our work as follows:

@article{toscano2025aivt,
  title={AIVT: Inference of turbulent thermal convection from measured 3D velocity data by physics-informed Kolmogorov-Arnold networks},
  author={Toscano, Juan Diego and K{\"a}ufer, Theo and Wang, Zhibo and Maxey, Martin and Cierpka, Christian and Karniadakis, George Em},
  journal={Science Advances},
  volume={11},
  number={19},
  year={2025},
  month={May},
  day={7},
  doi={10.1126/sciadv.ads5236},
  URL={https://www.science.org/doi/10.1126/sciadv.ads5236}
}

Instructions

1. Clone the repository:

   git clone https://github.com/jdtoscano94/Instant-AIVT.git
   cd YOUR_REPO_FOLDER

2. Download the dataset:
   The dataset is available here.

3. Move the data to the correct directory:

   mv path_to_downloaded_data ../Data/Rayleigh-Benard-Convection/

4. Run our models using the provided Jupyter notebooks.
   The repository includes results for the following models:

   • cKAN with 149k parameters
   • MLP with 151k parameters
   • MLP with 282k parameters

   Each notebook contains all the necessary code to replicate the results presented in the paper. The results were generated using JAX, ensuring efficient computation with accelerated hardware support.

Note: To run these notebooks, you need the source files located in ../Instant_AIVT. These files should be automatically downloaded when the project is cloned. Ensure that all dependencies are installed before executing the notebooks.

References

If you use this repository in your research, please cite our related work:

@article{toscano2025pinns,
  title={From pinns to pikans: Recent advances in physics-informed machine learning},
  author={Toscano, Juan Diego and Oommen, Vivek and Varghese, Alan John and Zou, Zongren and Ahmadi Daryakenari, Nazanin and Wu, Chenxi and Karniadakis, George Em},
  journal={Machine Learning for Computational Science and Engineering},
  volume={1},
  number={1},
  pages={1--43},
  year={2025},
  publisher={Springer}
}

@article{anagnostopoulos2024residual,
  title={Residual-based attention in physics-informed neural networks},
  author={Anagnostopoulos, Sokratis J and Toscano, Juan Diego and Stergiopulos, Nikolaos and Karniadakis, George Em},
  journal={Computer Methods in Applied Mechanics and Engineering},
  volume={421},
  pages={116805},
  year={2024},
  publisher={Elsevier}
}

@article{anagnostopoulos2024learning,
  title={Learning in PINNs: Phase transition, total diffusion, and generalization},
  author={Anagnostopoulos, Sokratis J and Toscano, Juan Diego and Stergiopulos, Nikolaos and Karniadakis, George Em},
  journal={arXiv preprint arXiv:2403.18494},
  year={2024}
}

@article{shukla2024comprehensive,
  title={A comprehensive and fair comparison between mlp and kan representations for differential equations and operator networks},
  author={Shukla, Khemraj and Toscano, Juan Diego and Wang, Zhicheng and Zou, Zongren and Karniadakis, George Em},
  journal={Computer Methods in Applied Mechanics and Engineering},
  volume={431},
  pages={117290},
  year={2024},
  publisher={Elsevier}
}


@article{toscano2024inferring,
  title={Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks},
  author={Toscano, Juan Diego and K{"a}ufer, Theo and Wang, Zhibo and Maxey, Martin and Cierpka, Christian and Karniadakis, George Em},
  journal={arXiv preprint arXiv:2407.15727},
  year={2024}
}

@article{toscano2024kkans,
  title={KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics},
  author={Toscano, Juan Diego and Wang, Li-Lian and Karniadakis, George Em},
  journal={arXiv preprint arXiv:2412.16738},
  year={2024}
}