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. Learning and extrapolating scale-invariant processes

    Jan 21, 2026Anaclara Alvez-Canepa, Cyril Furtlehner, François P. LandesInvariant Representation LearningNeural Operators

    Laboratoire Interdisciplinaire des Sciences du Numérique (LISN) · Université Paris-Saclay and · INRIA-Saclay

  2. PGOT: A Physics-Geometry Operator Transformer for Complex PDEs

    Dec 29, 2025Zhuo Zhang, Xi Yang, Ying Miao +5Neural PDE SolversPDE Surrogate Modeling

    National University of Defense Technology · Peking University · National University of Singapore +2

  3. GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformer

    Dec 23, 2025Corey Adams, Rishikesh Ranade, Ram Cherukuri +1Neural Surrogate ModelingStructural Mechanics

    NVIDIA Corporation, Santa Clara, US

  4. Efficient Generative Transformer Operators For Million-Point PDEs

    Dec 4, 2025Armand Kassaï Koupaï, Lise Le Boudec, Patrick GallinariPDE Surrogate ModelingTransformer Neural Operator

    Sorbonne Université, CNRS, ISIR, 75005 Paris, France · Criteo AI Lab, Paris, France

  5. CarBench: A Comprehensive Benchmark for Neural Surrogates on High-Fidelity 3D Car Aerodynamics

    Nov 25, 2025Mohamed Elrefaie, Dule Shu, Matt Klenk +1Automotive AerodynamicsNeural Surrogate Modeling

    Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA · Schwarzman College of Computing, Massachusetts Institute of Technology, Cambridge, MA, USA · Future Product Innovation, Toyota Research Institute, Los Altos, CA, USA

  6. Solver-Integrated Adversarial Attacking and Training of Neural Operators

    Oct 21, 2025Yifei SunAdversarial TrainingAdversarial Attacks

  7. Neural Operators Which Certifiably Simultaneously Solve Infinitely Many Convex Programs using Logarithmic Rank and Linear Complexity

    Aug 20, 2025Anastasis Kratsios, Ariel Neufeld, Philipp SchmockerNeural OperatorsOperator Learning

    Department of Mathematics, McMaster University and the Vector Institute, Canada · Division of Mathematical Sciences, Nanyang Technological University, Singapore

  8. PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems

    Jul 29, 2025Tiantian Sun, Jian ZuNeural OperatorsDeep Operator Networks

    School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, P.R. China

  9. Discretization-independent operator learning for partial differential equations

    Jul 9, 2025Jacob Hauck, Yanzhi ZhangPDE Operator LearningNeural Network Approximation Theory

    Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409

  10. Spatiotemporal Reconstruction of Global Radiation from Sparse Sensor Sequences

    May 24, 2025Kazuma Kobayashi, Tapas Tripura, Jay Phil Yoo +5Neural OperatorsInverse Problems

    Nuclear, Plasma and Radiological Engineering, The Grainger College of Engineering, University of Illinois Urbana-Champaign, IL, USA. · Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi, India. · Civil and Urban Engineering Department, New York University Abu Dhabi, Abu Dhabi, UAE. +3

  11. From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing

    Mar 7, 2025Prashant K. JhaNeural Surrogate ModelingFourier Neural Operator

    Department of Mechanical Engineering, South Dakota School of Mines and Technology, Rapid City, SD 57701, USA.

  12. Active Learning with Bayesian Multi-Fidelity Laplace Neural Operators for Oscillatory Parametric PDEs

    Feb 1, 2025Bongseok Kim, Haoyang Zheng, Michael Penwarden +1Dynamical SystemsSurrogate Modeling

    School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, 47907, IN, USA. · Department of Mathematics, Purdue University, 150 North University Street, West Lafayette, 47907, IN, USA.

  13. Polynomial Scaling is Possible For Neural Operator Approximations of Structured Families of BSDEs

    Oct 18, 2024Takashi Furuya, Anastasis KratsiosStochastic Differential EquationsPDE Solving

    Doshisha University, Japan · Department of Mathematics McMaster University and Vector Institute, Canada