NeuralOperator: Learning in Infinite Dimensions

neuraloperator is a comprehensive library for learning neural operators in PyTorch. It is the official implementation for Fourier Neural Operators and Tensorized Neural Operators.

Unlike regular neural networks, neural operators enable learning mapping between function spaces, and this library provides all of the tools to do so on your own data.

Neural operators are also resolution invariant, so your trained operator can be applied on data of any resolution.

Checkout the documentation for more!

Installation

Just clone the repository and install locally (in editable mode so changes in the code are immediately reflected without having to reinstall):

git clone https://github.com/NeuralOperator/neuraloperator
cd neuraloperator
pip install -e .
pip install -r requirements.txt

You can also just pip install the most recent stable release of the library on PyPI:

pip install neuraloperator

Quickstart

After you've installed the library, you can start training operators seamlessly:

from neuralop.models import FNO

operator = FNO(n_modes=(32, 32),
               hidden_channels=64,
               in_channels=2,
               out_channels=1)

Tensorization is also provided out of the box: you can improve the previous models by simply using a Tucker Tensorized FNO with just a few parameters:

from neuralop.models import TFNO

operator = TFNO(n_modes=(32, 32),
                hidden_channels=64,
                in_channels=2,
                out_channels=1,
                factorization='tucker',
                implementation='factorized',
                rank=0.05)

This will use a Tucker factorization of the weights. The forward pass will be efficient by contracting directly the inputs with the factors of the decomposition. The Fourier layers will have 5% of the parameters of an equivalent, dense Fourier Neural Operator!

Checkout the documentation for more!

Using with Weights and Biases

Our Trainer natively supports logging to W&B. To use these features, create a file in neuraloperator/config called wandb_api_key.txt and paste your W&B API key there. You can configure the project you want to use and your username in the main yaml configuration files.

Contributing

NeuralOperator is 100% open-source, and we welcome contributions from the community!

Our mission for NeuralOperator is to provide access to well-documented, robust implementations of neural operator methods from foundations to the cutting edge. The library is primarily intended for methods that directly relate to operator learning: new architectures, meta-algorithms, training methods and benchmark datasets. We are also interested in integrating interactive examples that showcase operator learning in action on small sample problems.

If your work provides one of the above, we would be thrilled to integrate it into the library. Otherwise, if your work simply relies on a version of the NeuralOperator codebase, we recommend publishing your code separately using a procedure outlined in our developer's guide, under the section "Publishing code built on the library".

If you spot a bug or a typo in the documentation, or have an idea for a feature you'd like to see, please report it on our issue tracker, or even better, open a Pull Request.

For detailed development setup, testing, and contribution guidelines, please refer to our Contributing Guide.

Code of Conduct

All participants are expected to uphold the Code of Conduct to ensure a friendly and welcoming environment for everyone.

Citing NeuralOperator

If you use NeuralOperator in an academic paper, please cite [1]

@article{kossaifi2025librarylearningneuraloperators,
   author    = {Jean Kossaifi and
                  Nikola Kovachki and
                  Zongyi Li and
                  David Pitt and
                  Miguel Liu-Schiaffini and
                  Valentin Duruisseaux and
                  Robert Joseph George and
                  Boris Bonev and
                  Kamyar Azizzadenesheli and
                  Julius Berner and
                  Anima Anandkumar},
   title     = {A Library for Learning Neural Operators},
   journal   = {arXiv preprint arXiv:2412.10354},
   year      = {2025},
}

and consider citing [2], [3]:

@article{kovachki2021neural,
   author    = {Nikola B. Kovachki and
                  Zongyi Li and
                  Burigede Liu and
                  Kamyar Azizzadenesheli and
                  Kaushik Bhattacharya and
                  Andrew M. Stuart and
                  Anima Anandkumar},
   title     = {Neural Operator: Learning Maps Between Function Spaces},
   journal   = {CoRR},
   volume    = {abs/2108.08481},
   year      = {2021},
}

@article{berner2025principled,
   author    = {Julius Berner and
                  Miguel Liu-Schiaffini and
                  Jean Kossaifi and
                  Valentin Duruisseaux and
                  Boris Bonev and
                  Kamyar Azizzadenesheli and
                  Anima Anandkumar},
   title     = {Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning},
   journal   = {arXiv preprint arXiv:2506.10973},
   year      = {2025},
}

[1]	Kossaifi, J., Kovachki, N., Li, Z., Pitt, D., Liu-Schiaffini, M., Duruisseaux, V., George, R., Bonev, B., Azizzadenesheli, K., Berner, J., and Anandkumar, A., "A Library for Learning Neural Operators", ArXiV, 2025. doi:10.48550/arXiv.2412.10354.

[2]	Kovachki, N., Li, Z., Liu, B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A., and Anandkumar A., "Neural Operator: Learning Maps Between Function Spaces", JMLR, 2021. doi:10.48550/arXiv.2108.08481.

[3]	Berner, J., Liu-Schiaffini, M., Kossaifi, J., Duruisseaux, V., Bonev, B., Azizzadenesheli, K., and Anandkumar, A., "Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning", arXiv preprint arXiv:2506.10973, 2025. https://arxiv.org/abs/2506.10973.