Fourier Neural Operator

Also known as FNO

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4 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

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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
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
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
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
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
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
Fourier Neural Operators with Least-Squares Readout Refit for Learning Random Obstacle-to-Solution Maps
Jun 28, 2026Chenhui Zhu, Fei WangFourier Neural Operator PDE Solving
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, P. R. China. · School of Mathematics and Statistics & State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China.
BREIT: A Framework for Brain Stroke Reconstruction using Multi-Frequency 3D EIT
Jun 27, 2026Djahid Abdelmoumene, Ishak Ayad, Maï K. Nguyen +1Medical Imaging Fourier Neural Operator
ETIS (UMR 8051), CY Cergy Paris University, ENSEA, CNRS, Cergy France · AGM (UMR 8088), CY Cergy Paris University, CNRS, Cergy, France · Paris-Saclay University, CentraleSupélec, Inria, CVN, Gif-sur-Yvette, France
Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs
Jun 26, 2026Alex Colagrande, Paul Caillon, Eva Feillet +1Fourier Neural Operator Neural PDE Solvers
Miles Team, LAMSADE, Université Paris Dauphine-PSL, Paris, France · Université Paris-Saclay, CNRS, LISN, 91400, Orsay, France · ESPCI PSL, Paris, France
Operator Learning for Cubic Nonlinear Schrödinger Equation on Periodic Domains
Jun 25, 2026Emmanuel E. Oguadimma, Victory C. Obieke, Xueying YuFourier Neural Operator PDE Solving
Real vs. Complex Spectral Bases for Neural Operators: The Role of Green's Function Alignment
Jun 23, 2026Jason Sulskis, Sathya RaviFourier Neural Operator PDE Operator Learning
Electronic Systems Laboratory, Applied Embedded Systems Division Georgia Tech Research Institute · Department of Computer Science University of Illinois at Chicago
How Much Memory Do We Need? Adaptive Memory Gate for Neural Operators
Jun 11, 2026Jihyeon Hur, Yongseok Kwon, Min-Gi Jo +2Memory-Augmented Neural Networks Fourier Neural Operator
1KAIST, Republic of Korea.
SirenFNO: Efficient and Full Frequency Learning of Fourier Neural Operators
Jun 9, 2026Pengqing Shi, Jie Yin, Stephen Tierney +1Fourier Neural Operator Spectral Bias
The University of Sydney, Australia
Fourier Neural Operators with rank-1 lattice points and hyperbolic cross
Jun 7, 2026Jakob Dilen, Alexander Keller, Frances Y. Kuo +1Neural Network Generalization Fourier Neural Operator
GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operators
Jun 6, 2026Jason Sulskis, Sathya RaviFourier Neural Operator Physics-Informed Neural Operators
Department of Computer Science University of Illinois at Chicago · Electronic Systems Laboratory, Applied Embedded Systems Division Georgia Tech Research Institute
EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs
Jun 2, 2026Sungwon Kim, Juho Song, Seungmin Shin +3Fourier Neural Operator PDE Surrogate Modeling
Graduate School of Data Science, KAIST, Daejeon, Republic of Korea · Mathematical Sciences, KAIST, Daejeon, Republic of Korea · LG Electronics, Pyeong-taek, Republic of Korea +1
Limits of Resolution Equivariance in Fourier Neural Operators
May 30, 2026Alex Colagrande, Paul Caillon, Eva Feillet +1Fourier Neural Operator Equivariant Neural Networks
Miles Team, LAMSADE, Universit´e Paris Dauphine-PSL, Paris, France · Universit´e Paris-Saclay, CNRS, LISN, France · ESPCI PSL, Paris, France
Sequential Physics-Constrained Neural Operator Forward Modeling for the $\textit{Norne}$ Reservoir System
May 27, 2026Clement Etienam, Juntao Yang, Oleg Ovcharenko +4Fourier Neural Operator PDE Surrogate Modeling
NVIDIA Corporation
MTL-FNO: A Lightweight Multi-Task Fourier Neural Operator for Sparse Field Reconstruction
May 26, 2026Siyu Ye, Shihang Li, Zhiqiang Gong +4Fourier Neural Operator Multi-Task Learning
Defense Innovation Institute, Academy of Military Science, Beijing, 100071, China · Intelligent Game and Decision Laboratory, Beijing, 100071, China
Neural Operators for Design-Space Surrogate Modeling of Tendon-Actuated Continuum Robots
May 18, 2026Branden Frieden, James M. Ferguson, Alan Kuntz +1Neural Surrogate Modeling Fourier Neural Operator
The Robotics Center and the Kahlert School of Computing at the University of Utah, Salt Lake City, UT 84112, USA. · The Departments of Computer Science and Electrical and Computer Engineering at Vanderbilt University, Nashville, TN, 37203, USA.
PACE-FNO: Physics-Aligned Canonical Equivariance for Fourier Neural Operators
May 18, 2026Jiaxiao Xu, Changhong Mou, Yeyu Zhang +1Fourier Neural Operator OOD Generalization
Shanghai University of Finance and Economics · Utah State University · University of Edinburgh
Stability and Discretization Error of State Space Model Neural Operators
May 17, 2026Abderrahim Bendahi, Adrien Fradin, Johan Peralez +2Fourier Neural Operator Convergence Analysis
École polytechnique Paris, France · Université Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007 Villeurbanne, France · CNRS, UniversitéJulieLyonDigne1, INSA Lyon, LIRIS Lyon, France +1
Frequency Bias and OOD Generalization in Neural Operators under a Variable-Coefficient Wave Equation
May 13, 2026Runlong Xie, An LuoFourier Neural Operator PDE Solving
Independent Researcher · School of Statistics, University of Minnesota, MN, USA.

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CAFE+FNO: Fourier Kernel Generation via Multiplicative Feature Composition

Hyungjoon Juen, Minwoo Shin

Department of Software, Yonsei University (Mirae Campus), Wonju 26493, Republic of Korea

Fourier Neural Operator PDE Operator Learning Fourier Feature Embeddings Compositional Representation Learning

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The Fourier Neural Operator (FNO) learns solution operators of partial differential equations (PDEs) through Fourier-space kernel parameterization, but frequency truncation can limit the learning of high-frequency variations. AM-FNO and SirenFNO generate kernels for all grid modes from spectral coordinates using shared networks, making coordinate encoding and generator design important. Recent work on implicit neural representations (INRs) has proposed constructing frequency interactions through explicit feature composition rather than relying on subsequent MLPs to form them implicitly. Building on this approach, we propose CAFE+FNO, which incorporates Content-Aware Frequency Encoding+ (CAFE+) into Fourier kernel generation. CAFE+ combines Fourier--Chebyshev features through parallel affine branches and a Hadamard product, forming interactions within and across the two feature families. A kernel MLP maps the resulting representation of each normalized spectral coordinate to a complex channel-mixing matrix. Each layer shares its generator across all stored modes, making the number of trainable parameters independent of the number of modes for a fixed architecture. We compare CAFE+FNO with existing FNO variants on five PDE benchmarks and conduct ablation studies on basis configuration, multiplicative composition, and bandwidth learnability. Code and experimental configurations are available at https://github.com/fabsk101/CAFEPlusFNO.git.

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