Neural Operators

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Overview

Neural operators learn maps from input fields, parameters, or geometries to output fields, often approximating the solution map of a partial differential equation. DeepONet uses branch and trunk networks, Fourier Neural Operators learn interactions in spectral space, and graph and transformer operators handle irregular meshes and complex geometries; physics-informed losses and structure-preserving designs add physical constraints. These models can make repeated simulation, forecasting, and inverse design much faster than running a numerical solver for every case. A central challenge is making predictions reliable across new resolutions, geometries, and physical regimes while preserving stability over long rollouts and matching classical solvers when high accuracy is required.

Latest papers

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313 papers52 papers in the last four weeks, up 24% on the four weeks before. 0.3% of all new papers.

  1. Physics-Informed Neural Systems for the Simulation of EUV Electromagnetic Wave Diffraction from a Lithography Mask

    Mar 16, 2026Vasiliy A. Es'kin, Egor V. IvanovNeural PDE SolversNeural Operators

    Department of Radiophysics, University of Nizhny Novgorod 23 Gagarin Ave., Nizhny Novgorod 603022, Russia

  2. Gauge-Equivariant Intrinsic Neural Operators for Geometry-Consistent Learning of Elliptic PDE Maps

    Mar 16, 2026Pengcheng ChengPDE Operator LearningNeural Operators

    School of Mathematics, Jilin University, Changchun, 130012, China

  3. Windowed Fourier Propagator: A Frequency-Local Neural Operator for Wave Equations in Inhomogeneous Media

    Mar 15, 2026Yiyang Cai, Zixuan Qiu, Yunlu Shu +4PDE Operator LearningNeural Operators

    School of Mathematical Sciences, Fudan University, Shanghai, 200433, China · Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, 200438, China · Center for Applied Mathematics, Fudan University, Shanghai, 200438, China

  4. NOIR: Neural Operator mapping for Implicit Representations

    Mar 13, 2026Sidaty El Hadramy, Nazim Haouchine, Michael Wehrli +1Neural OperatorsMedical Image Synthesis

    Department of Biomedical Engineering, University of Basel, Allschwil, Switzerland · Harvard Medical School, Brigham and Women’s Hospital, Boston, United States

  5. Topological DeepONets and a generalization of the Chen-Chen operator approximation theorem

    Mar 12, 2026Vugar IsmailovNeural Network Approximation TheoryDeep Operator Networks

  6. Inverse Neural Operator for ODE Parameter Optimization

    Mar 12, 2026Zhi-Song Liu, Wenqing Peng, Helmi Toropainen +5Parameter EstimationOrdinary Differential Equations

    Department of Computational Engineering, Lappeenranta-Lahti University of Technology, Lahti, Finland · Atmospheric Modelling Center Lahti (AMC-Lahti), Finland · University of Helsinki, Helsinki, Finland +3

  7. A neural operator for predicting vibration frequency response curves from limited data

    Mar 10, 2026D. Bluedorn, A. Badawy, B. E. Saunders +2Neural Surrogate ModelingNeural Operators

    Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM 88003, USA. · Knight Foundation School of Computing and Information Science, Florida International University, Miami, FL 33199, USA. · Sandia National Laboratories, Albuquerque, NM 87123, USA.

  8. Wiener Chaos Expansion based Neural Operator for Singular Stochastic Partial Differential Equations

    Mar 9, 2026Dai Shi, Luke Thompson, Andi Han +3Stochastic PDEsPDE Surrogate Modeling

    University of Cambridge · University of Sydney · Chinese Academy of Science

  9. Tau-BNO: Brain Neural Operator for Tau Transport Model

    Mar 9, 2026Nuutti Barron, Heng Rao, Urmi Saha +6Neural Surrogate ModelingPDE Surrogate Modeling

    Department of Radiology and Biomedical Imaging, University of California San Francisco, USA · College of Computer Science and Engineering, Northeastern University, China · Department of Computer Science, Wake Forest University, USA +1

  10. Extending Neural Operators: Robust Handling of Functions Beyond the Training Set

    Mar 4, 2026Blaine Quackenbush, Paul J. AtzbergerNeural OperatorsOOD Generalization

    Department of Mathematics, University of California Santa Barbara (UCSB). · Department of Mathematics, Department of Mechanical Engineering, University of California Santa Barbara (UCSB)

  11. Shape Derivative-Informed Neural Operators with Application to Risk-Averse Shape Optimization

    Mar 3, 2026Xindi Gong, Dingcheng Luo, Thomas O'Leary-Roseberry +2PDE Operator LearningNeural Operators

    Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, USA · School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia · Centre for Data Science, Queensland University of Technology, Brisbane, Australia +3

  12. From Complex Dynamics to DynFormer: Rethinking Transformers for PDEs

    Mar 3, 2026Pengyu Lai, Yixiao Chen, Dewu Yang +3PDE Surrogate ModelingNeural Operators

    School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, China

  13. Neural Operator-Grounded Continuous Tensor Function Representation and Its Applications

    Mar 2, 2026Ruoyang Su, Xi-Le Zhao, Sheng Liu +3Neural OperatorsTensor Completion

    School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China · School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China · Department of Mathematics, Hong Kong Baptist University, Hong Kong, China

  14. One Operator to Rule Them All? On Boundary-Indexed Operator Families in Neural PDE Solvers

    Mar 2, 2026Lennon J. ShikhmanPDE Operator LearningNeural Operators

    College of Computing, Georgia Institute of Technology · Department of Mathematics and Systems Engineering, Florida Institute of Technology

  15. Operator Learning Using Weak Supervision from Walk-on-Spheres

    Mar 1, 2026Hrishikesh Viswanath, Hong Chul Nam, Xi Deng +3PDE Operator LearningPhysics-Informed ML

    Purdue University, USA · ETH Zurich, Switzerland · California Institute of Technology, USA +1

  16. A level-wise training scheme for learning neural multigrid smoothers with application to integral equations

    Mar 1, 2026Lingfeng Li, Yin King Chu, Raymond Chan +1Neural OperatorsNeural PDE Solvers

    Hetao Institute of Mathematics and Interdisciplinary Sciences, Shenzhen, Guangdong, China. · Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China. · Department of Data Science, Department of Operations and Risk Management,Lingnan University, Tuen Mun, Hong Kong, China. +1

  17. Random Features for Operator-Valued Kernels: Bridging Kernel Methods and Neural Operators

    Mar 1, 2026Mike Nguyen, Nicole MückeRandom Feature MethodsKernel Methods

    Technical University of Braunschweig

  18. A Boundary Integral-based Neural Operator for Mesh Deformation

    Feb 27, 2026Zhengyu Wu, Jun Liu, Wei WangNeural OperatorsPDE Operator Learning

    School of Electronics and Information Engineering, Hangzhou Dianzi University, Hangzhou, China

  19. Neural Operators Can Discover Functional Clusters

    Feb 26, 2026Yicen Li, Jose Antonio Lara Benitez, Ruiyang Hong +3ClusteringUnsupervised Clustering

    McMaster University and the Vector Institute, Main St., Hamilton, L8S 4L8, Ontario, Canada · Rice University, Main St., Houston, 77005, Texas, United States

  20. NESTOR: A Nested MOE-based Neural Operator for Large-Scale PDE Pre-Training

    Feb 25, 2026Dengdi Sun, Xiaoya Zhou, Xiao Wang +4Neural OperatorsPDE Surrogate Modeling

    School of Artificial Intelligence, Anhui University, Hefei, China · School of Computer Science and Technology, Anhui University, Hefei, China

  21. The Error of Deep Operator Networks Is the Sum of Its Parts: Branch-Trunk and Mode Error Decompositions

    Feb 25, 2026Alexander Heinlein, Johannes TarazDeep Operator NetworksNeural Operators

    Delft Institute of Applied Mathematics, Delft University of Technology, Delft, 2628CD, The Netherlands

  22. From Basis to Basis: Gaussian Particle Representation for Interpretable PDE Operators

    Feb 25, 2026Zhihao Li, Yu Feng, Zhilu Lai +1PDE Operator LearningNeural Operators

    The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China · The Hong Kong University of Science and Technology, Hong Kong SAR, China

  23. Structure-Aware Epistemic Uncertainty Quantification for Neural Operator PDE Surrogates

    Feb 24, 2026Haoze Song, Zhihao Li, Mengyi Deng +4Uncertainty QuantificationEpistemic Uncertainty

    The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China · The Hong Kong University of Science and Technology, Hong Kong SAR, China

  24. SGNO: Spectral Generator Neural Operators for Stable Long Horizon PDE Rollouts

    Feb 21, 2026Jiayi Li, Penghao Jiang, Hira Saleem +3PDE Surrogate ModelingNeural Operators

  25. Geometric Neural Operators via Lie Group-Constrained Latent Dynamics

    Feb 18, 2026Jiaquan Zhang, Fachrina Dewi Puspitasari, Songbo Zhang +7Neural PDE SolversPDE Operator Learning

    School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, China · Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China · Institute of Software Chinese Academy of Sciences, Beijing, China +2

  26. Flowers: A Warp Drive for Neural PDE Solvers

    Feb 17, 2026Till Muser, Alexandra Spitzer, Matti Lassas +2Neural PDE SolversPDE Surrogate Modeling

    Department of Mathematics and Computer Science, University of Basel, Basel, Switzerland · Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland · Simons Chair in Computational and Applied Mathematics and Earth Science, Rice University, Houston, TX, USA

  27. Neural-POD: A Plug-and-Play Neural Operator Framework for Infinite-Dimensional Functional Nonlinear Proper Orthogonal Decomposition

    Feb 17, 2026Changhong Mou, Binghang Lu, Guang LinProper Orthogonal DecompositionOrthogonal Representation Learning

    Department of Mathematics and Statistics, Utah State University, 3900 Old Main Hill, Logan, UT, 84322, USA. · School of Electrical and Computer Engineering, Purdue University, 610 Purdue Mall, West Lafayette, IN, 47907, USA. · Department of Mathematics, Purdue University, 610 Purdue Mall, West Lafayette, IN, 47907, USA. +1

  28. Learning Data-Efficient and Generalizable Neural Operators via Fundamental Physics Knowledge

    Feb 16, 2026Siying Ma, Mehrdad M. Zadeh, Mauricio Soroco +3PDE Surrogate ModelingNeural Operators

    Simon Fraser University · Georgia Institute of Technology

  29. Transolver-3: Scaling Up Transformer Solvers to Industrial-Scale Geometries

    Feb 4, 2026Hang Zhou, Haixu Wu, Haonan Shangguan +4Efficient Neural Network InferenceNeural PDE Solvers

    School of Software, BNRist, Tsinghua University, China.

  30. SFO: Learning PDE Operators via Spectral Filtering

    Jan 23, 2026Noam Koren, Rafael Moschopoulos, Kira Radinsky +1PDE Surrogate ModelingPDE Operator Learning

    Department of Computer Science Technion - Israel Institute of Technology · Department of Computer Science Princeton University