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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U-HNO: A U-shaped Hybrid Neural Operator with Sparse-Point Adaptive Routing for Non-stationary PDE Dynamics
May 13, 2026Yingzhe Ma, Xiao Yang, Yuxin Xie +2Fourier Neural Operator PDE Surrogate Modeling
University of Electronic Science and Technology of China · Peking University
Don't Fix the Basis -- Learn It: Spectral Representation with Adaptive Basis Learning for PDEs
May 11, 2026Xuxiang Zhao, Angelica I. Aviles-RiveroFourier Neural Operator Representation Learning
Qiuzhen College, Tsinghua University · YMSC, Tsinghua University
HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations
May 10, 2026Lennon J. ShikhmanFourier Neural Operator PDE Solving
College of Computing, Georgia Institute of Technology Atlanta, GA, United States
Can We Formally Verify Neural PDE Surrogates? SMT Compilation of Small Fourier Neural Operators
May 9, 2026Ali Baheri, Ignacio Laguna PeraltaNeural Network Verification Fourier Neural Operator
Rochester Institute of Technology, Rochester, NY, USA · Lawrence Livermore National Laboratory, Livermore, CA, USA
Neural Operators as Efficient Function Interpolators
May 8, 2026Vasilis Niarchos, Angelos Sirbu, Sokratis TrifinopoulosNeural Surrogate Modeling Fourier Neural Operator
Department of Physics, CCTP and ITCP, University of Crete, 71303, Greece · Theoretical Physics Department, CERN, Geneva, Switzerland · Physik-Institut, Universität Zürich, 8057 Zürich, Switzerland
Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation
May 4, 2026Nicole HaoFourier Neural Operator PDE Solving
Department of Mathematics, Cornell University
Isotropic Fourier Neural Operators
May 4, 2026Michael F. StaddonFourier Neural Operator Neural PDE Solvers
Independent Researcher
Learning Neural Operator Surrogates for the Black Hole Accretion Code
Apr 28, 2026Matthias Nägele, Cedric Bös, Chester Tan +3Fourier Neural Operator PDE Surrogate Modeling
Institute for Theoretical Physics and Astrophysics, Julius-Maximilians-Universität Würzburg, Würzburg, Germany · Chair for Machine Learning for Complex Networks, Julius-Maximilians-Universität Würzburg, Würzburg, Germany
Multi-scale Dynamic Wake Modeling and Prediction of Floating Offshore Wind Turbines via Physics-Informed Neural Networks and Fourier Neural Operators
Apr 27, 2026Guodan Dong, Jianhua Qin, Chang XuFourier Neural Operator PDE Surrogate Modeling
College of Renewable Energy Hohai University Changzhou 213200 China · College of Water Conservancy and Hydropower Engineering Nanjing 210098 China · National Technology Innovation Center for Wind Power Hohai University Changzhou 213200 China
Neural Adjoint Method for Meta-optics: Accelerating Volumetric Inverse Design via Fourier Neural Operators
Apr 19, 2026Chanik Kang, Hyewon Suk, Haejun ChungNeural Surrogate Modeling Fourier Neural Operator
Hanyang University, Department of Artificial Intelligence Semiconductor Engineering Seoul, Korea · Hanyang University, Department of Electronic Engineering Seoul, Korea
Translation Invariance of Neural Operators for the FitzHugh-Nagumo Model
Mar 18, 2026Luca PellegriniFourier Neural Operator PDE Operator Learning
Department of Mathematics, University of Pavia, Pavia, Italy · Euler Institute, Faculty of Informatics, Universit`a della Svizzera italiana, Lugano, Switzerland
From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing
Mar 7, 2025Prashant K. JhaNeural Surrogate Modeling Fourier Neural Operator
Department of Mechanical Engineering, South Dakota School of Mines and Technology, Rapid City, SD 57701, USA.

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U-HNO: A U-shaped Hybrid Neural Operator with Sparse-Point Adaptive Routing for Non-stationary PDE Dynamics

Yingzhe Ma, Xiao Yang, Yuxin Xie, Zihan Xiong+1

University of Electronic Science and Technology of China · Peking University

Fourier Neural Operator PDE Surrogate Modeling Neural Operators

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Solutions to many partial differential equations (PDEs) display coexisting smooth global transport and localized sharp features within a single trajectory: shock fronts, thin interfaces, and concentrated high-frequency content sit on top of slowly varying backgrounds. This poses a challenge for neural operators: Fourier-based architectures mix nonlocal interactions efficiently but tend to under-resolve localized non-smooth features, whereas spatially local architectures recover fine detail at the cost of long-range propagation and rollout stability. Existing hybrid operators paper over this tension with a fixed, spatially uniform fusion that forces the same trade-off everywhere. We propose U-HNO, a U-shaped hybrid neural operator whose central design is Sparse-Point Adaptive Routing (SPAR): at every spatial location, a per-pixel hard mask selects whether the global Fourier branch or the local multi-scale Gaussian branch should dominate, and the sparsity ratio is a function of the local contrast of the routing signal, so smooth and shock-aligned regions receive different mixtures of global and local computation. SPAR is embedded in a hierarchical encoder-bottleneck-decoder backbone with skip connections so that the dual branches and the gate operate at every resolution. Training combines pointwise supervision with a finite-difference H^1 gradient term and a band-wise spectral consistency regularizer. Across benchmarks spanning 1D Burgers, Kuramoto-Sivashinsky, KdV, 2D advection, Allen-Cahn, Navier-Stokes, Darcy flow, and 3D transonic compressible Navier-Stokes from PDEBench, U-HNO achieves state-of-the-art rollout accuracy on the majority of tasks in both relative L^2 and H^1 metrics, with the largest gains on problems dominated by sharp localized features. Ablations show that removing any single component substantially degrades rollout error.

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