NOTICE: This package is being maintained and bug-fixed. New features will be added, but with no planned timeline. Contributions from external developers via pull requests are welcome though.

An extensible Python package with data-driven pipelines for physics-informed machine learning.

Call for contributions: If you have developed and/or published new architectures using PyTorch and intend to make them opensource, consider include them as part of SimulAI, which works as an unified repository for scientific machine learning models, continuously tested and maintained. SimulAI was already packaged under a friendly license (Apache) and it can be used to more easily share state of the art models whithin the scientific community.

The SimulAI toolkit provides easy access to state-of-the-art models and algorithms for physics-informed machine learning. Currently, it includes the following methods described in the literature:

• Physics-Informed Neural Networks (PINNs)
• Deep Operator Networks (DeepONets)
• Variational Encoder-Decoders (VED)
• Operator Inference (OpInf)
• Koopman Autoencoders (experimental)
• Echo State Networks (experimental GPU support)
• Transformers
• U-Nets

In addition to the methods above, many more techniques for model reduction and regularization are included in SimulAI. See documentation.

Python version requirements: 3.9 <= python <= 3.12

For installing the most recent stable version from PyPI:

pip install simulai-toolkit

For installing from the latest commit sent to GitHub (just for testing and developing purposes):

pip uninstall simulai-toolkit
pip install -U git+https://github.com/IBM/simulai#egg=simulai-toolkit

If you are interested in directly contributing to this project, please see CONTRIBUTING.

Some methods implemented on SimulAI support multiprocessing with MPI.

In order to use it, you will need a valid MPI distribution, e.g. MPICH, OpenMPI. As an example, you can use conda to install MPICH as follows:

conda install -c conda-forge mpich gcc

If you have problems installing gcc using the command above, we recommend you to install it using Homebrew.

Tensorboard is supported for monitoring neural network training tasks. For a tutorial about how to set it see this example.

Please, refer to the SimulAI API documentation before using the toolkit.

Additionally, you can refer to examples in the respective folder.

This software is licensed under Apache license 2.0. See LICENSE.

If you are interested in directly contributing to this project, please see CONTRIBUTING.

If you find SimulAI to be useful, please consider citing it in your published work:

@misc{simulai,
  author = {IBM},
  title = {SimulAI Toolkit},
  subtitle = {A Python package with data-driven pipelines for physics-informed machine learning},
  note = "https://github.com/IBM/simulai",
  doi = {10.5281/zenodo.7351516},
  year = {2022},
}

or, via Zenodo:

@software{joao_lucas_de_sousa_almeida_2023_7566603,
      author       = {João Lucas de Sousa Almeida and
                      Leonardo Martins and
                      Tarık Kaan Koç},
      title        = {IBM/simulai: 0.99.13},
      month        = jan,
      year         = 2023,
      publisher    = {Zenodo},
      version      = {0.99.25},
      doi          = {10.5281/zenodo.7566603},
      url          = {https://doi.org/10.5281/zenodo.7566603}
    }

João Lucas de Sousa Almeida, Pedro Roberto Barbosa Rocha, Allan Moreira de Carvalho and Alberto Costa Nogueira Jr. A coupled Variational Encoder-Decoder - DeepONet surrogate model for the Rayleigh-Bénard convection problem. In When Machine Learning meets Dynamical Systems: Theory and Applications, AAAI, 2023.

João Lucas S. Almeida, Arthur C. Pires, Klaus F. V. Cid, and Alberto C. Nogueira Jr. Non-intrusive operator inference for chaotic systems. IEEE Transactions on Artificial Intelligence, pages 1–14, 2022.

Pedro Roberto Barbosa Rocha, Marcos Sebastião de Paula Gomes, Allan Moreira de Carvalho, João Lucas de Sousa Almeida and Alberto Costa Nogueira Jr. Data-driven reduced-order model for atmospheric CO2 dispersion. In AAAI 2022 Fall Symposium: The Role of AI in Responding to Climate Challenges, 2022.

Pedro Roberto Barbosa Rocha, João Lucas de Sousa Almeida, Marcos Sebastião de Paula Gomes, Alberto Costa Nogueira, Reduced-order modeling of the two-dimensional Rayleigh–Bénard convection flow through a non-intrusive operator inference, Engineering Applications of Artificial Intelligence, Volume 126, Part B, 2023, 106923, ISSN 0952-1976, https://doi.org/10.1016/j.engappai.2023.106923. (https://www.sciencedirect.com/science/article/pii/S0952197623011077)

Jaeger, H., Haas, H. (2004). "Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication," Science, 304 (5667): 78–80. DOI:10.1126/science.1091277.

Lu, L., Jin, P., Pang, G., Zhang, Z., Karniadakis, G. E. (2021). "Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators," Nature Machine Intelligence, 3 (1): 218–229. ISSN: 2522-5839. DOI:10.1038/s42256-021-00302-5.

Eivazi, H., Le Clainche, S., Hoyas, S., Vinuesa, R. (2022) "Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows" Expert Systems with Applications, 202. ISSN: 0957-4174. DOI:10.1016/j.eswa.2022.117038.

Raissi, M., Perdikaris, P., Karniadakis, G. E. (2019). "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations," Journal of Computational Physics, 378 (1): 686-707. ISSN: 0021-9991. DOI:10.1016/j.jcp.2018.10.045.

Lusch, B., Kutz, J. N., Brunton, S.L. (2018). "Deep learning for universal linear embeddings of nonlinear dynamics," Nature Communications, 9: 4950. ISSN: 2041-1723. DOI:10.1038/s41467-018-07210-0.

McQuarrie, S., Huang, C. and Willcox, K. (2021). "Data-driven reduced-order models via regularized operator inference for a single-injector combustion process," Journal of the Royal Society of New Zealand, **51**(2): 194-211. ISSN: 0303-6758. DOI:10.1080/03036758.2020.1863237.