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. tFUSOperator: Operator Learning for Transcranial Focused Ultrasound Digital Twins

    Aug 3, 2026Minjee Seo, Haris Ghafoor, Minju Seol +2PDE Operator LearningDigital Twins

    School of Mathematics and Computing (Computational Science and Engineering), Yonsei University, Seoul, Republic of Korea · Innovative & Intelligent Computational Science Institute (IN2CSI), Seoul, Republic of Korea

  2. Amortizing the Calibration Triple: A Projection-Consistent Neural Operator for Local-Stochastic Volatility

    Aug 2, 2026Xiaozhen Wang, Anaïs Després, Martin Dureau +1Quantitative FinanceModel Calibration

    1CEREMADE, Université Paris Dauphine-PSL · 2LaMME, Université Évry Paris-Saclay · 3AIML Global Markets, Barclays

  3. CoSynFlow: Conformal Symplectic Neural Flows for Cross-System Prediction of Dissipative Hamiltonian Dynamics

    Aug 1, 2026Baige Xu, Takaharu YaguchiNeural Operators

    RIKEN AIP · Motooka Nishi-ku, Fukuoka, Japan · IMI, Kyushu University

  4. Neural Operator Learning for Collision-Aware Trajectory Planning of Spacecraft Swarms

    Jul 31, 2026Sidhdharth D. Sikka, Suyi Gao, Zehui Lu +2Collision AvoidanceTrajectory Optimization

    Manifold Research Group and the School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907 USA · Department of Mathematics, Purdue University, West Lafayette, IN 47907 USA · Independent Researcher, Fremont, CA USA

  5. HERO: History-Enriched Rollout Training for Long-Horizon Autoregressive Neural Operators

    Jul 31, 2026Jiaquan Zhang, Shuxu Chen, Haifan Meng +6Neural Surrogate ModelingPDE Operator Learning

    School of Computer Science and Engineering, UESTC · Electronics and Information Convergence Engineering, KHU · Department of Mathematical Sciences, UOL +3

  6. Geometry-aware Incremental Neural Operator for Long-Horizon PDE prediction

    Jul 31, 2026Jiaquan Zhang, Shuxu Chen, Haifan Meng +6PDE Surrogate ModelingPDE Operator Learning

    School of Information and Software Engineering, UESTC · Electronics and Information Convergence Engineering, KHU · School of Computer Science and Engineering, UESTC +4

  7. Orca: Neural Operators for Causal Reasoning in Continuous Time

    Jul 30, 2026Gerrit Großmann, David A. Selby, Sebastian J. VollmerStructural Causal ModelsCausal Counterfactual Generation

    German Research Center for Artificial Intelligence (DFKI), Kaiserslautern, Germany

  8. Inverse Learning of Latent Risk-Neutral Densities from Irregular Option Quotes

    Jul 29, 2026Lennon J. Shikhman, Michael Galarnyk, Aadi Dash +1Quantitative FinanceDeep Operator Networks

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

  9. No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study

    Jul 26, 2026Georg Winkler, Martin StollNeural Surrogate ModelingPDE Surrogate Modeling

    Department of Mathematics, Chemnitz University of Technology, 09111, Chemnitz, Germany

  10. Neural operator discovery from heterogeneous trajectories

    Jul 25, 2026Zituo Chen, Qiaofeng Li, Jiaxin Hu +1Latent Dynamics ModelingNonlinear System Identification

    Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, 02139, MA, USA. · State Key Laboratory of Fluid Power & Mechatronic Systems, Zhejiang University, 866 Yuhangtang Road, Hangzhou, 310058, Zhejiang Province, China.

  11. Generalized Neural Operator for Parametric and Boundary-Value Problems

    Jul 24, 2026Ruoyan Li, Yizhou Sun, Wei WangEfficient Neural Network InferencePDE Solving

    University of California, Los Angeles

  12. Countercurrent Multiplier Networks: A Renal-Inspired Iterative Operator with Provably Bounded Fixed-Point Dynamics

    Jul 21, 2026Snigdha Chandan KhilarDynamical SystemsIterative Refinement

    Independent Researcher

  13. Adaptive Mamba Neural Operators

    Jul 20, 2026Zeyuan Song, Zheyu JiangPDE SolvingPDE Operator Learning

    School of Chemical Engineering Oklahoma State University Stillwater, OK 74078, USA

  14. NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes

    Jul 15, 2026Anastasis Kratsios, Giulia Livieri, Philipp SchmockerNeural Network Approximation TheoryNeural Operators

  15. Deep Learning-based Surrogate Modelling of the LOD Method for Multiscale Problems

    Jul 14, 2026Marc Haltmayer, Jaemin Seo, Yuseung Lee +3PDE SolvingPDE Surrogate Modeling

    Department of Artificial Intelligence, Chung-Ang University, 84 Heukseok-ro, Dongjak-gu, Seoul, 06974, Republic of Korea · Computational Science and Engineering Team, Samsung Electronics, 41 Samsung-ro, Giheung-gu, Yongin-si, 17113, Republic of Korea

  16. An Agentic AI Scientific Community for Automated Neural Operator Discovery

    Jul 13, 2026Luis Loo, Ulisses Braga-NetoAI Agents for Scientific DiscoveryLLM Agent Orchestration

    Department of Electrical & Computer Engineering Texas A&M University, College Station, TX

  17. PGD-NO: A Neural Operator with Precomputed Geometry Decomposition for 3D Million-scale Physics Simulations

    Jul 9, 2026Weiheng Zhong, Jing Bi, Victor Oancea +1PDE Surrogate ModelingPDE Operator Learning

    Department of Civil and Environmental Engineering, Grainger College of Engineering, University of Illinois Urbana-Champaign, Urbana, IL, US · Dassault Systemes Americas, Johnston, RI, US · Siebel School of Computing and Data Science, Grainger College of Engineering, University of Illinois Urbana-Champaign, Urbana, IL, US

  18. Hybrid Least Squares/Gradient Descent Methods for MIONets

    Jul 8, 2026Jun Choi, Chang-Ock Lee, Minam MoonGradient DescentNeural Network Optimization

    Department of Mathematical Sciences, KAIST, Daejeon 34141, KOREA · Department of Mathematics, Korea Military Academy, Seoul 01805, KOREA

  19. Knowledge-Constrained Shape Optimization with a Mixture-of-Experts Neural Operator for High-Confidence Design

    Jul 7, 2026Wenhao Fan, Yuanwei Bin, Jianghan Gu +4Neural Surrogate ModelingAutomotive Aerodynamics

    School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China · 2Eastern Institute of Technology, Ningbo, Ningbo 315200, Zhejiang, China · 3TenFong Technology Co., Ltd., Shenzhen 518000, Guangdong, China +1

  20. Quadrature-Aware Complex-Linear Neural Operator for Boundary-to-Field Prediction in Resonant Acoustics

    Jul 5, 2026Muhammad Idrees Khan, Hua-Dong YaoComplex-Valued Neural NetworksOperator Learning

    Department of Mechanical Engineering, Chalmers University of Technology Gothenburg 41296, Sweden

  21. LLT: Local Linear Transformer for PDE Operator Learning

    Jul 4, 2026Oded Ovadia, Eli TurkelPDE Surrogate ModelingTransformer Attention

    School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

  22. LiNO: Lifting based multiresolution neural operator

    Jul 2, 2026Himanshu Pandey, Subham Patel, Ratikanta BeheraWavelet MethodsPDE Operator Learning

    Department of Computational and Data Sciences, Indian Institute of Science, Bangalore 560012, India · IISc Mathematics Initiative, Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India

  23. Self-explainable Operator Learning for Discovering Spatial Patterns in Functional Data

    Jul 2, 2026Mojgan Alishiri, Amirhossein ArzaniNeural Network InterpretabilityOperator Learning

    1Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT, 84112, United States · 2Mechanical Engineering Department, University of Utah, Salt Lake City, UT, 84112, United States

  24. GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems

    Jul 1, 2026Meenakshi Krishnan, Pranav Pulijala, Ke Chen +2PDE SolvingImage Reconstruction

    University of Maryland, College Park · University of Delaware, Newark

  25. From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators

    Jul 1, 2026Nisha Chandramoorthy, Daniel Sanz-Alonso, Nathan WaniorekDynamical SystemsFourier Neural Operator

    University of Chicago

  26. Randomized neural operator for parametric PDEs with fast training and conformal uncertainty quantification

    Jun 28, 2026Zirui Deng, Jingbo Sun, Deyu Meng +1Uncertainty QuantificationPDE Surrogate Modeling

    School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

  27. OperatorSHAP: Fast and Accurate Shapley Value Estimation for Neural Operators

    Jun 26, 2026Joshua Stiller, Santo M. A. R. Thies, Felix Czaja +1Shapley Value AttributionNeural Operators

    LMU Munich, MCML · LMU Munich · LMU Munich, MCML, DFKI

  28. Real vs. Complex Spectral Bases for Neural Operators: The Role of Green's Function Alignment

    Jun 23, 2026Jason Sulskis, Sathya RaviFourier Neural OperatorPDE Operator Learning

    Department of Computer Science, University of Illinois at Chicago · Applied Systems Laboratory, Systems Integration Division, Georgia Tech Research Institute

  29. The Fractal Neural Operator: Overcoming Spectral Bias in Chaotic Attractors via Prime-Harmonic Weierstrass Encodings

    Jun 22, 2026Kanishk AwadhiyaSpectral BiasChaotic Dynamical Systems

    Independent Researcher

  30. Neural Operator Processes for Probabilistic Operator Learning under Partial Observations

    Jun 22, 2026Jose Miguel Lara-Rangel, Serge GuillasNeural ProcessesPDE Operator Learning

    University College London London, United Kingdom