# HyperNOs: Automated and Parallel Library for Neural Operators Research

arXiv: https://arxiv.org/abs/2503.18087 · HTML: https://mlsanity.com/paper/2503.18087/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 39 references that are in the map.
- First posted on arXiv 23 Mar 2025.

## Builds on (most cited first, 23 of 23)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Ray: A Distributed Framework for Emerging AI Applications](https://mlsanity.com/paper/1712.05889/) (2017)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [A System for Massively Parallel Hyperparameter Tuning](https://mlsanity.com/paper/1810.05934/) (2018)
- [Poseidon: Efficient Foundation Models for PDEs](https://mlsanity.com/paper/2405.19101/) (2024)
- [NOMAD: Nonlinear Manifold Decoders for Operator Learning](https://mlsanity.com/paper/2206.03551/) (2022)
- [Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learning](https://mlsanity.com/paper/2305.19913/) (2023)
- [Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations](https://mlsanity.com/paper/2112.08125/) (2021)
- [Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning](https://mlsanity.com/paper/2402.10926/) (2024)
- [Solving Seismic Wave Equations on Variable Velocity Models with Fourier Neural Operator](https://mlsanity.com/paper/2209.12340/) (2022)
- [Solving Electromagnetic Scattering Problems by Isogeometric Analysis with Deep Operator Learning](https://mlsanity.com/paper/2409.20280/) (2024)

## Built on by (most cited first, 2 of 2)

- [Learning High-dimensional Ionic Model Dynamics Using Fourier Neural Operators](https://mlsanity.com/paper/2505.14039/) (2025)
- [Translation Invariance of Neural Operators for the FitzHugh-Nagumo Model](https://mlsanity.com/paper/2603.17523/) (2026)

## Abstract (arXiv)

This paper introduces HyperNOs, a PyTorch library designed to streamline and automate the process of exploring neural operators, with a special focus on hyperparameter optimization for comprehensive and exhaustive exploration. Indeed, HyperNOs takes advantage of state-of-the-art optimization algorithms and parallel computing implemented in the Ray-tune library to efficiently explore the hyperparameter space of neural operators. We also implement many useful functionalities for studying neural operators with a user-friendly interface, such as the possibility to train the model with a fixed number of parameters or to train the model with multiple datasets and different resolutions. We integrate Fourier neural operators and convolutional neural operators in our library, achieving state of the art results on many representative benchmarks, demonstrating the capabilities of HyperNOs to handle real datasets and modern architectures. The library is designed to be easy to use with the provided model and datasets, but also to be easily extended to use new datasets and custom neural operator architectures.