Neojax

neojax (Neural Operators in JAX) is an implementation of Neural Operators built on top of JAX and Equinox. It provides a clean, modular API inspired by the original neuraloperator library.

Currently, neojax is in its early stages. Expect possible breaking changes.

The following models and features are available:

Full feature list

• Fourier Neural Operator (FNO).
• Symmetrical domain padding (DomainPadding).
• Pointwise MLP (Channel-MLP) expansions for improved expressivity.
• Various skip connections (Linear, Soft-Gating, Identity).
• Normalization in FNO blocks.
• U-Net Fourier Neural Operator (UNO).
• Geometry-aware Fourier Neural Operator (GeoFNO) for irregular geometries and mesh domains.
• Tucker-factorized FNO.
• Recurrent Neural Operator (RNO).
• Deep Operator Network (DeepONet).
• Multigrid Neural Operator (MgNO).
• Geometry Informed Neural Operator (GiNO).
• Transolver Neural Operator.
• Convolutional Neural Operator (CNO).
• Training Orchestration Utilities (Trainer and TrainState).
• Positional embeddings (GridEmbeddingNd, SinusoidalEmbedding, ReferenceGridEmbeddingNd).
• (Relative) \(L^{p}\)-loss.
• General \(W^{k,p}\) Sobolev loss.
• Loss Compositions.
• Data Normalization and Scaling.
• Various Normalizer classes.
• Physical scales to non-dimensionalize inputs.
• Dataset utilities (Data-agnostic, downloading utilities, etc.).
• Data Pipelines (Schemas, Processors, DataBundle).
• Benchmark Module (Model-/Data-agnostic even for non-neojax models).

It is designed to be fully compatible with all JAX features such as vmap, jit, and grad.

Installation

Install the python package via pypi

pip3 install neojax-operators

The core library is designed to have as few dependencies as possible. Some submodules therefore rely on additional dependencies. Install them as needed:

• Running the examples: neojax-operators[ex]
• Using the PDE data generation: neojax-operators[gen]
• Using data downloading and some other data features: neojax-operators[data]
• Using the benchmark module: neojax-operators[benchmark]

Quickstart

Neojax exposes a similar API to Neuraloperators and Equinox and should therefore be familiar to use:

import jax.numpy as jnp
import jax.random as jr
from neojax.models import FNO

key = jr.key(0)

fno = FNO(
      key=key,
      modes=(12, 12),
      hidden_channels=64,
      in_channels=2,
      out_channels=1,
      n_layers=2
)

x = jnp.ones((2, 64, 64))

pred = fno(x)

For a more detailed introduction refer to the Examples.

Neojax vs Neuraloperator Benchmarks

Please refer to the Benchmarks.

Motivation

JAX is widely used in Scientific Machine Learning (SciML) for its functional transformations (jit, vmap, grad) and NumPy-like API. Neural Operators are a common approach for solving PDEs in this space, but a native JAX implementation was missing. neojax fills that gap.

Design Choices

neojax started as a port of the PyTorch neuraloperator library, but was rewritten from the ground up as a JAX-native implementation instead. Porting PyTorch idioms directly into a functional framework added unnecessary complexity; building on equinox gives neojax a class-based API while staying consistent with JAX's pure-functional design.

Roadplan

In upcoming releases more models and components will be added in roughly the following order:

1. LocalNO, SFNO, RNO, and others
2. Graph Neural Operators
3. Debugging utilities

And much more to come!

Contributions

If you'd like to contribute any features, models, or fix implementation errors, please do so. Any contributions are appreciated. Have a look at the CONTRIBUTING.md guide for details on how to do so. I am also open to advice on restructuring and any other design choices that could be improved.

Citation

If you use neojax in your research, please cite it using the following BibTeX entry:

@software{neojax,
  author = {Paul Gekeler},
  title = {neojax: Neural Operators in Jax},
  year = {2026},
  url = {https://github.com/paulgekeler/neojax}
}