Neural-Operator

This is a collection of research papers on neural operators.

Update Log

• [2024.05.18] We update the ICML 2023 and ICLR 2023 paper list of neural operator.
• [2024.05.15] We update the NeurIPS 2023 paper list of neural operator.
• [2024.05.10] We release the awesome neural operator.

Table of Contents

• Classification of neural operator networks
• Papers
  • Sub-journal of nature
  • ICLR 2024
  • ICML 2024
  • JMLR 2024
  • NeurIPS 2023
  • ICML 2023
  • ICLR 2023
  • NeurIPS 2022
  • ICML 2022
  • ICLR 2022
  • NeurIPS 2021
  • ICLR 2021
  • ICML 2021
  • JMLR 2021
  • Other
• Tutorial
• Codebase
• Contributing

Classification of neural operator networks

We’ll start this section with a disclaimer:

Papers

Sub-journal of nature

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• Neural operators for accelerating scientific simulations and design

  • Kamyar Azizzadenesheli, Nikola Kovachki, Zongyi Li, Miguel Liu-Schiaffini, Jean Kossaifi & Anima Anandkumar
  • Key: dyna architecture
  • ExpEnv: None

• Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows

  • Ivan Zanardi, SimoneVenturi  & Marco Panesi
  • Key: The framework combines dimensionality reduction and neural operators; hierarchical and adaptive deep learning strategy
  • ExpEnv: Te code used in the current study is available from the corresponding author upon reasonable request.

ICLR 2024

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• Title

  • Key:
  • ExpEnv:

ICML 2024

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• Transolver: A Fast Transformer Solver for PDEs on General Geometries
  • Haixu Wu, Huakun Luo, Haowen Wang, Jianmin Wang, Mingsheng Long
  • Key: Physics-Attention; Transformer
  • ExpEnv: Codes

JMLR 2024

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• Text

  • Key:
  • ExpEnv: None

NeurIPS 2023

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• Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learning
  • Francesca Bartolucci, Emmanuel de Bézenac, Bogdan Raonic, Roberto Molinaro, Siddhartha Mishra, Rima Alaifari
  • Key: operator learning; Representation equivalent Neural Operators (ReNO); the concept of operator aliasing
  • ExpEnv: Supplemental
• Geometry-Informed Neural Operator for Large-Scale 3D PDEs
  • Zongyi Li, Nikola Kovachki, Chris Choy, Boyi Li, Jean Kossaifi, Shourya Otta, Mohammad Amin Nabian, Maximilian Stadler, Christian Hundt, Kamyar Azizzadenesheli, Animashree Anandkumar
  • Key: geometry-informed neural operator (GINO)
  • ExpEnv: Codes
• Convolutional Neural Operators for robust and accurate learning of PDEs
  • Bogdan Raonic, Roberto Molinaro, Tim De Ryck, Tobias Rohner, Francesca Bartolucci, Rima Alaifari, Siddhartha Mishra, Emmanuel de Bézenac
  • Key: convolutional neural operators (CNOs)
  • ExpEnv: Supplemental
• Domain Agnostic Fourier Neural Operators
  • Ning Liu, Siavash Jafarzadeh, Yue Yu
  • Key: convolutional neural operators (CNOs)
  • ExpEnv: Codes;Supplemental
• ASPEN: Breaking Operator Barriers for Efficient Parallelization of Deep Neural Networks
  • Jongseok Park, Kyungmin Bin, Gibum Park, Sangtae Ha, Kyunghan Lee
  • Key:
  • ExpEnv: Codes
  • Globally injective and bijective neural operators
    • Takashi Furuya, Michael Puthawala, Matti Lassas, Maarten V. de Hoop
    • Key: Fredholm theory and Leray-Schauder degree theory
    • ExpEnv: None
  • Deep Equilibrium Based Neural Operators for Steady-State PDEs
    • Tanya Marwah, Ashwini Pokle, J. Zico Kolter, Zachary Lipton, Jianfeng Lu, Andrej Risteski
    • Key:
    • ExpEnv: Codes; Supplemental
  • Equivariant Neural Operator Learning with Graphon Convolution
    • Chaoran Cheng, Jian Peng
    • Key:
    • ExpEnv: Codes; Supplemental
  • Training neural operators to preserve invariant measures of chaotic attractors
    • Ruoxi Jiang, Peter Y. Lu, Elena Orlova, Rebecca Willett
    • Key:
    • ExpEnv: href="https://github.com/roxie62/neural_operators_for_chaos">Codes
  • DeepPCR: Parallelizing Sequential Operations in Neural Networks
    • Federico Danieli, Miguel Sarabia, Xavier Suau Cuadros, Pau Rodriguez, Luca Zappella
    • Key:
    • ExpEnv: None
  • Operator Learning with Neural Fields: Tackling PDEs on General Geometries
    • Louis Serrano, Lise Le Boudec, Armand Kassaï Koupaï, Thomas X Wang, Yuan Yin, Jean-Noël Vittaut, Patrick Gallinari
    • Key:
    • ExpEnv: Supplemental

  • text

    • Key:
    • ExpEnv:

ICML 2023

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• Variational Autoencoding Neural Operators

  • Jacob H. Seidman · Georgios Kissas · George J. Pappas · Paris Perdikaris
  • Key: Variational Autoencoding Neural Operators (VANO)
  • ExpEnv: Poster

• Group Equivariant Fourier Neural Operators for Partial Differential Equations

  • Jacob Helwig · Xuan Zhang · Cong Fu · Jerry Kurtin · Stephan Wojtowytsch · Shuiwang Ji
  • Key: Fourier neural operators (FNOs) in the frequency domain
  • ExpEnv: Poster; Codes

• GNOT: A General Neural Operator Transformer for Operator Learning

  • Zhongkai Hao · Zhengyi Wang · Hang Su · Chengyang Ying · Yinpeng Dong · LIU SONGMING · Ze Cheng · Jian Song · Jun Zhu
  • Key: general neural operator transformer (GNOT)
  • ExpEnv: Poster; Codes

• Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere

  • Zhongkai Hao · Zhengyi Wang · Hang Su · Chengyang Ying · Yinpeng Dong · LIU SONGMING · Ze Cheng · Jian Song · Jun Zhu
  • Key: Spherical FNOs (SFNOs)
  • ExpEnv: Poster;

ICLR 2023

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• Factorized Fourier Neural Operators

  • Alasdair Tran, Alexander Mathews, Lexing Xie, Cheng Soon Ong
  • Key: fourier transform, fourier operators, pde, navier stokes
  • ExpEnv: Poster; Codes

• Equivariant Hypergraph Diffusion Neural Operators

  • Peihao Wang, Shenghao Yang, Yunyu Liu, Zhangyang Wang, Pan Li
  • Key: Hypergraph Neural Network, Hypergraph Diffusion, Equivariant Network
  • ExpEnv: Poster; Codes

• Koopman Neural Operator Forecaster for Time-series with Temporal Distributional Shifts

  • Rui Wang, Yihe Dong, Sercan O Arik, Rose Yu
  • Key: Time series forecasting, Temporal distributional shifts, Koopman Theory
  • ExpEnv: Poster;

NeurIPS 2022

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• NeurOLight: A Physics-Agnostic Neural Operator Enabling Parametric Photonic Device Simulation
  • Jiaqi Gu, Zhengqi Gao, Chenghao Feng, Hanqing Zhu, Ray Chen, Duane Boning, David Pan
  • Key:
  • ExpEnv: none
• Operative dimensions in unconstrained connectivity of recurrent neural networks
  • Jiaqi Gu, Zhengqi Gao, Chenghao Feng, Hanqing Zhu, Ray Chen, Duane Boning, David Pan
  • Key:
  • ExpEnv: operativeDimensions

ICML 2022

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• • Key:
  • ExpEnv:

ICLR 2022

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• Efficient Token Mixing for Transformers via Adaptive Fourier Neural Operators
  • John Guibas, Morteza Mardani, Zongyi Li, Andrew Tao, Anima Anandkumar, Bryan Catanzaro
  • Key: self attention, linear complexity, high-resolution inputs, operator learning, Fourier transform
  • ExpEnv: None

NeurIPS 2021

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• Faster Neural Network Training with Approximate Tensor Operations
  • Menachem Adelman, Kfir Levy, Ido Hakimi, Mark Silberstein
  • Key:
  • ExpEnv: Reviews And Public Comment
• Rethinking Neural Operations for Diverse Tasks
  • Nicholas Roberts, Mikhail Khodak, Tri Dao, Liam Li, Christopher Ré, Ameet Talwalkar
  • Key:
  • ExpEnv: Reviews And Public Comment

ICLR 2021

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• Fourier Neural Operator for Parametric Partial Differential Equations
  • Zongyi Li, Nikola Borislavov Kovachki, Kamyar Azizzadenesheli, Burigede liu, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar
  • Key: Partial differential equation, Fourier transform, Neural operators
  • ExpEnv: Codes

ICML 2021

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• Paper Title
• Author1, Author2, and Author3
• Key: Key insights
• ExpEnv: Experiment environment

JMLR 2021

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• Neural Operator: Learning Maps Between Function Spaces
  • Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar
  • Key: Deep Learning, Operator Learning, Discretization-Invariance, Partial Differential Equations, Navier-Stokes Equation
  • ExpEnv: Codes

Other

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• Paper Title
• Author1, Author2, and Author3
• Key: Key insights
• ExpEnv: Experiment environment

Tutorial

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• Details about the tutorial.

Codebase

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• Details about the codebase.

Contributing

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• Details about contributing.