mlsanityData to 14 Oct 2026

A Library for Learning Neural Operators

arXiv 2412.10354 ↗First posted 13 Dec 2024cs.LG cs.AIcited by 38

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Abstract (arXiv)

We present NeuralOperator, an open-source Python library for operator learning. Neural operators generalize neural networks to maps between function spaces instead of finite-dimensional Euclidean spaces. They can be trained and inferenced on input and output functions given at various discretizations, satisfying a discretization convergence properties. Part of the official PyTorch Ecosystem, NeuralOperator provides all the tools for training and deploying neural operator models, as well as developing new ones, in a high-quality, tested, open-source package. It combines cutting-edge models and customizability with a gentle learning curve and simple user interface for newcomers.

Key facts. Cited by 38 papers in the map (data through 14 Oct 2026). Builds on 18 of its 27 references that are in the map. First posted on arXiv 13 Dec 2024.

Builds on

18 of 27 references.

References · 18

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  4. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
  5. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 303
  6. 2023Spherical Fourier Neural Operators: Learning Stable Dynamics on the Spherecited by 233
  7. 2023Neural Operators for Accelerating Scientific Simulations and Designcited by 221
  8. 2019Towards Physics-informed Deep Learning for Turbulent Flow Predictioncited by 204
  9. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 197
  10. 2019Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networkscited by 145
  11. 2016TensorLy: Tensor Learning in Pythoncited by 104
  12. 2024Operator Learning: Algorithms and Analysiscited by 85
6 more
  1. 2023Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEscited by 68
  2. 2024Neural Operators with Localized Integral and Differential Kernelscited by 62
  3. 2024Calibrated Uncertainty Quantification for Operator Learning via Conformal Predictioncited by 26
  4. 2022Incremental Spatial and Spectral Learning of Neural Operators for Solving Large-Scale PDEscited by 25
  5. 2023Guaranteed Approximation Bounds for Mixed-Precision Neural Operatorscited by 9
  6. 2023Tipping Point Forecasting in Non-Stationary Dynamics on Function Spacescited by 8

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 11; 2026: 27.

38 papers.

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  1. 2025Operator Learning: A Statistical Perspectivecited by 17
  2. 2025Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learningcited by 12
  3. 2025Towards a Physics Foundation Modelcited by 8
  4. 2025Flow Straight and Fast in Hilbert Space: Functional Rectified Flowcited by 6
  5. 2026SMART: Scalable Mesh-free Aerodynamic Simulations from Raw Geometries using a Transformer-based Surrogate Modelcited by 4
  6. 2026One Operator for Many Densities: Amortized Approximation of Conditioning by Neural Operatorscited by 4
  7. 2025Toward Data-Driven Surrogates of the Solar Wind with Spherical Fourier Neural Operatorcited by 3
  8. 2025Provable Mixed-Noise Learning with Flow-Matchingcited by 2
  9. 2025Efficient Generative Transformer Operators For Million-Point PDEscited by 2
  10. 2025Residual-augmented flow matching operators for probabilistic partial differential equationscited by 2
  11. 2026Hypothesis-driven construction of mesoscopic dynamicscited by 2
  12. 2026Iterative Refinement Neural Operators are Learned Fixed-Point Solvers: A Principled Approach to Spectral Bias Mitigationcited by 2
26 more
  1. 2025Thompson Sampling in Function Spaces via Neural Operatorscited by 1
  2. 2025Physics-Informed Neural Operators for Cardiac Electrophysiologycited by 1
  3. 2025Autoregressive Surrogate Modeling of the Solar Wind with Spherical Fourier Neural Operatorcited by 1
  4. 2026Hybrid operator learning of wave scattering maps in high-contrast mediacited by 1
  5. 2026Equation Recast for Canonical Operator Learning Across Parametric PDEscited by 1
  6. 2026Preconditioned Physics-Informed Neural Operator Trainingcited by 1
  7. 2026Translation Invariance of Neural Operators for the FitzHugh-Nagumo Modelcited by 0
  8. 2026Do Neural Operators Forget Geometry? The Forgetting Hypothesis in Deep Operator Learningcited by 0
  9. 2026QuadNorm: Resolution-Robust Normalization for Neural Operatorscited by 0
  10. 2026Neural Operators as Efficient Function Interpolatorscited by 0
  11. 2026Fourier Neural Operators with rank-1 lattice points and hyperbolic crosscited by 0
  12. 2026OperatorSHAP: Fast and Accurate Shapley Value Estimation for Neural Operatorscited by 0
  13. 2026Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEscited by 0
  14. 2026Self-explainable Operator Learning for Discovering Spatial Patterns in Functional Datacited by 0
  15. 2026Neural Operator Surrogates for Two-Dimensional Neutron Flux Estimationcited by 0
  16. 2026DFSC: Error-Controlled Differentiable Mittag-Leffler Propagation for Fractional Scientific Machine Learningcited by 0
  17. 2026ADEx-FNO: A Unified Ambient-Domain Framework for Fourier Neural Operators on Varying Geometriescited by 0
  18. 2026Distillation of Foundation Models for Time-dependent PDEscited by 0
  19. 2026Conformal Uncertainty Quantification Guarantees for Neural Operatorscited by 0
  20. 2026Cost-Accuracy Trade-offs: Neural Operator vs Classical Numerical Solvercited by 0
  21. 2026NeuIDO: Neural Intrinsic Dynamics Operator for Physics-Informed 4D World Modelscited by 0
  22. 2026Counterfactual Predictions in Scientific Emulators Without Controlled Experimentscited by 0
  23. 2026FTD-GNO: Memory-Efficient Graph Neural Operators through Functional Tensor Decomposition of the Kernelcited by 0
  24. 2026Stochastic Adaptive Fourier Decomposition for Operator Learningcited by 0
  25. 2026Neural Surrogate Modeling of Ultrasonic Wave Propagation in Heterogeneous Mediacited by 0
  26. 2026Mesh-Free Convolution: Learned Spectral Attenuation and Transportcited by 0