Fourier Neural Operator

Also known as FNO

Fourier Neural Operators (FNOs) learn mappings from input functions, such as coefficients or initial conditions, to PDE solution fields, using Fourier transforms to mix information across space. Common extensions add physics-informed losses, multiscale or local components, geometry and symmetry handling, and temporal memory. They are used as fast surrogates for problems including fluid flow, wave propagation, porous media, and inverse design, and are evaluated on prediction accuracy, rollouts, and generalization across resolutions or parameter settings. A central challenge is that strong accuracy on familiar data does not ensure reliable behavior under high-frequency, boundary, geometry, or resolution shifts, while added physical structure and efficiency can trade off against one another.

Latest papers

71 papers14 papers in the last four weeks, up 180% on the four weeks before. 0.1% of all new papers.

Performance of Neural Operator Baselines on 'The Well' Dataset
Oct 25, 2026Yash Pincha, Andy Dimnaku, Andrew Chiang +3Neural Operators Neural Surrogate Modeling
An actively trained neural operator for near-explicit atmospheric chemistry
Oct 24, 2026Zhi-Song Liu, Wenqing Peng, Ammar Kheder +2Neural Surrogate Modeling Fourier Neural Operator
Department of Computational Engineering, LUT University, Finland. · Atmospheric Modelling Center, Lahti (AMC-Lahti), Finland. · Institute for Atmospheric and Earth System Research (INAR), University of Helsinki, Finland. +1
Neural Operator Splitting for Fluid Dynamics in Complex Geometry
Oct 20, 2026Jianxiang Li, Xi Deng, Hong Chul Nam +1PDE Operator Learning Neural Operators
New York University
Learnable Splines for Unstructured Neural Operators
Oct 15, 2026Vignesh Gopakumar, Zhuoyuan Wang, Ander Gray +12PDE Operator Learning Neural Operators
Centre for Artificial Intelligence, University College London · Computing + Mathematical Sciences, Caltech · LIX, École Polytechnique, CNRS, Institut Polytechnique de Paris +2
A Bregman Proximal Viewpoint on Neural Operators
Oct 14, 2026Abdel-Rahim Mezidi, Jordan Patracone, Saverio Salzo +4Neural Operators Fourier Neural Operator
Université Jean Monnet Saint-Etienne, CNRS, Institut d’Optique Graduate School, Inria, Laboratoire Hubert Curien UMR 5516, F-42023, SAINT-ETIENNE, France · DIAG, Sapienza University of Rome, 00185 Rome, Italy · Computational Statistics and Machine Learning, IIT, Genova, Italy +1
Global-in-time Spectral Duhamel-Picard Method for Post-Exposure Bake Simulation and Physics-Informed Neural Operators for EUV Lithography
Oct 13, 2026Doyun Kim, Mircea Dusa, Werner Gilijns +1Reaction-Diffusion Systems Semiconductor Manufacturing
IMEC, Kapeldreef 75, 3001 Leuven, Belgium
Wong--Zakai Convergence and FNO Learning for Stochastic Volterra Equations
Oct 13, 2026Wonjae Lee, Jiuk Jang, Hyungbin ParkNeural Operators Fourier Neural Operator
InnoCore AI Meta-Scientist Research Group, KAIST, Daejeon 34141, South Korea. · Department of Mathematical Sciences, Seoul National University, Seoul 08826, South Korea. · Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, 1, Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea.
Full Waveform Inversion with a Learned Preconditioner
Oct 11, 2026Jeongjin ParkSeismic Imaging Inverse Problems
Neural Surrogate Modeling of Ultrasonic Wave Propagation in Heterogeneous Media
Oct 9, 2026Burla Nur Korkmaz, Petro Moilanen, Ari Salmi +2Neural Surrogate Modeling PDE Surrogate Modeling
Department of Computer Science, University of Helsinki, Finland
CAFE+FNO: Fourier Kernel Generation via Multiplicative Feature Composition
Oct 7, 2026Hyungjoon Juen, Minwoo ShinFourier Neural Operator PDE Operator Learning
Department of Software, Yonsei University (Mirae Campus), Wonju 26493, Republic of Korea
Targeted search shows that random-device testing underestimates worst-case error in a simulated wave-based neural operator
Oct 5, 2026Samrendra Roy, Jason Yoo, Souvik Chakraborty +1Fourier Neural Operator Uncertainty Quantification
Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA · Department of Applied Mechanics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India · Yardi School of Artificial Intelligence (ScAI), Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India +1
Localized Operator Learning with Adaptive Partition-of-Unity Mixture-of-Expert Networks
Oct 3, 2026Madison Cooley, Ramansh Sharma, Shandian Zhe +2PDE Operator Learning Operator Learning
Scientific Computing Institute, University of Utah, Salt Lake City, UT · Kahlert School of Computing, University of Utah, Salt Lake City, UT
BAT-NO: A Boundary-Condition-Aware Transformer Neural Operator for Crashworthiness Prediction of Vehicle Components
Oct 2, 2026Haoran Li, Yingxue Zhao, Haosu Zhou +4Neural Surrogate Modeling Neural Operators
Dyson School of Design Engineering, Imperial College London, London, UK · Keysight Technologies, Bagneux, France · Prometheus, UK
Transolver- $σ$ : Joint Spectral-Physical Subspace Modeling for Neural PDE Solving
Sep 29, 2026Haonan Shangguan, Hang Zhou, Haixu Wu +3Fourier Neural Operator Neural PDE Solvers
School of Software, BNRist, Tsinghua University · MIT CSAIL
KATOsuper: Surrogate-accelerated neural topology optimization with sensitivity-consistent Fourier neural operators
Sep 23, 2026Shengyu Yan, Jasmin JelovicaNeural Surrogate Modeling Topology Optimization
Department of Mechanical Engineering, The University of British Columbia, 6250 Applied Science Ln, Vancouver, V6T 1Z4, Canada · Department of Civil Engineering, The University of British Columbia, 6250 Applied Science Ln, Vancouver, V6T 1Z4, Canada
A Data-Free Physics-Informed Neural Operator for Level-Set Interface Advection
Sep 18, 2026Muhammad Akbar KhanPDE Operator Learning Physics-Informed Neural Operators
Department of Mathematics, NED University of Engineering and Technology, Karachi 75270, Pakistan
Physics-Informed Conformal Prediction: Embedding PDE Consistency into Distribution-Free Uncertainty Quantification for Neural Operators
Sep 14, 2026Michael ChinFourier Neural Operator Uncertainty Quantification
Independent Researcher
Learning Metamaterial Eigenmodes with Wavelet-Encoded Fourier Neural Operators
Sep 8, 2026Han Zhang, Alexander Ogren, Cynthia Rudin +2Fourier Neural Operator PDE Surrogate Modeling
Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC, USA · Department of Mechanical Engineering, California Institute of Technology, Pasadena, CA, USA · Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA
Fast Surrogate Modeling of Excitable and Oscillatory FitzHugh-Nagumo Dynamics with Parametric Neural Operators
Sep 3, 2026Andrew Franck, Justin LiNeural Surrogate Modeling Dynamical Systems
Occidental College, Los Angeles, CA 90041, USA
Selection, Representation, and Execution in Sparse Fourier Neural Operators
Aug 30, 2026Abdul Qadir Ibrahim, Martin BurgerEfficient Neural Network Inference Fourier Neural Operator
Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany
Euclidean Fourier Neural Operators
Aug 28, 2026Nathanael Bosch, Niklas Frederik Schmitz, Michael F. HerbstFourier Neural Operator Neural Operators
Mathematics for Materials Modelling (MatMat), Institute of Mathematics & Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
Helix-FNO: Spectral-Domain Operator Learning Coupled with a High-Fidelity Mechanistic Model for Fast Surrogate Simulation
Aug 23, 2026Jiabao Zhao, Chuwei Wang, Jinxi YangNeural Surrogate Modeling PDE Operator Learning
University of Science and Technology Liaoning Anshan, Liaoning, China · Wuhan University Wuhan, Hubei, China
MoFE: A Novel Mixture-of-Experts Framework with Fourier Neural Operators for Cryptocurrency Forecasting
Aug 18, 2026Bowen Liu, Mingming SunFinancial Forecasting Financial Time Series
School of Art and Science University of Rochester Rochester, USA · AGI Lab Beijing Institute of Mathematical Sciences and Applications Beijing, China
Lesion-Aware Adaptive Fourier Neural Operator for CT-to-PSMA PET Synthesis in Prostate Cancer
Aug 11, 2026Rashmi Bhaskara, Waleed M. Almutairi, Matthew Gopaulchan +5Fourier Neural Operator PET/CT Imaging
aSchool of Health Sciences, Purdue University, West Lafayette, 47907, IN, USA · bDepartment of Radiology, Indiana University School of Medicine, Indianapolis, 46202, IN, USA · cDepartment of Urology, Indiana University School of Medicine, Indianapolis, 46202, IN, USA +1
Flux-form spatiotemporal neural operators for coarse-grained dynamics of multiscale PDEs
Aug 11, 2026Junfeng ChenPDE Surrogate Modeling PDE Operator Learning
Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, China
ADEx-FNO: A Unified Ambient-Domain Framework for Fourier Neural Operators on Varying Geometries
Aug 9, 2026Roberto Nuca, Giovanni Testa, Luca Galimberti +1Fourier Neural Operator PDE Surrogate Modeling
Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia · Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, Milan, Italy · Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
Physics-Informed Neural Operator for Warm-Starting Background-Decomposed and Preconditioned PSFD: Enabling Scalable 3-D EUV Mask Simulation
Jul 28, 2026Doyun Kim, Werner GillijnsFourier Neural Operator Semiconductor Manufacturing
IMEC, Kapeldreef 75, 3001 Leuven, Belgium
Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs
Jul 26, 2026Cheng Jing, Uvini Balasuriya Mudiyanselage, Abhishek Verma +3Fourier Neural Operator PDE Solving
Arizona State University · Applied Materials Inc.
Fourier Neural Operators for Rayleigh-Bénard Convection
Jul 2, 2026Chelsea Maria John, Thibaut Lunet, Sebastian Götschel +3Fourier Neural Operator PDE Surrogate Modeling
Jülich Supercomputing Centre, Jülich, Germany · Hamburg University of Technology, Hamburg, Germany
From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators
Jul 1, 2026Nisha Chandramoorthy, Daniel Sanz-Alonso, Nathan WaniorekDynamical Systems Fourier Neural Operator
University of Chicago

Oct 25, 2026J/K move · Enter open · S save

Performance of Neural Operator Baselines on 'The Well' Dataset

Yash Pincha, Andy Dimnaku, Andrew Chiang, Adarsh Ganeshram+2

Neural Operators Neural Surrogate Modeling Fourier Neural Operator Benchmark Design Hyperparameter Optimization

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The Well, a 15-terabyte dataset spanning 16 physical simulation domains, provides an extensive benchmark for developing and evaluating machine learning surrogate models for complex physical systems. The baselines released with the benchmark were presented by their authors as illustrative examples obtained at small computational cost, trained with zero to very limited hyperparameter tuning and under a highly constraining 12-hour per-run wall-clock limit. These results have subsequently been treated as fully tuned benchmarks, and in some cases effectively interpreted as unconstrained performance baselines. We perform a short non-exhaustive hyperparameter search for the Tucker-factorized Fourier Neural Operator (TFNO) under the same 12-hour per-run wall-clock limit, while using only a single input timestep rather than the history of up to four used by the published baselines. Despite this more restrictive setup, tuning alone reduces VRMSE below both published FNO and TFNO baselines on 15 of 17 tasks, sometimes by several orders of magnitude. This sensitivity to a modest tuning effort underscores that the released neural operator baselines should not be treated as architectural benchmarks.