mlsanityData to 14 Oct 2026

ReBaNO: Reduced Basis Neural Operator Mitigating Generalization Gaps and Achieving Discretization Invariance

arXiv 2509.09611 ↗First posted 11 Sep 2025cs.LG cs.NA math.NAcited by 2

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Abstract (arXiv)

We propose a novel data-lean operator learning algorithm, the Reduced Basis Neural Operator (ReBaNO), to solve a group of PDEs with multiple distinct inputs. Inspired by the Reduced Basis Method and the recently introduced Generative Pre-Trained Physics-Informed Neural Networks, ReBaNO relies on a mathematically rigorous greedy algorithm to build its network structure offline adaptively from the ground up. Knowledge distillation via task-specific activation function allows ReBaNO to have a compact architecture requiring minimal computational cost online while embedding physics. In comparison to state-of-the-art operator learning algorithms such as PCA-Net, DeepONet, FNO, and CNO, numerical results demonstrate that ReBaNO significantly outperforms them in terms of eliminating/shrinking the generalization gap for both in- and out-of-distribution tests and being the only operator learning algorithm achieving strict discretization invariance.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 37 of its 70 references that are in the map. First posted on arXiv 11 Sep 2025.

Builds on

37 of 70 references.

References · 37

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  4. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  5. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 634
  6. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
  7. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
  8. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 473
  9. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 349
  10. 2021Choose a Transformer: Fourier or Galerkincited by 343
  11. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 326
  12. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 297
25 more
  1. 2020Model Reduction and Neural Networks for Parametric PDEscited by 258
  2. 2021Factorized Fourier Neural Operatorscited by 249
  3. 2021Multiwavelet-based Operator Learning for Differential Equationscited by 234
  4. 2017Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanicscited by 214
  5. 2023Convolutional Neural Operators for robust and accurate learning of PDEscited by 214
  6. 2019Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networkscited by 200
  7. 2019Transfer learning enhanced physics informed neural network for phase-field modeling of fracturecited by 116
  8. 2022Physics-Informed Deep Neural Operator Networkscited by 113
  9. 2025Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometriescited by 97
  10. 2024Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equationscited by 91
  11. 2022Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modelingcited by 65
  12. 2023Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learningcited by 57
  13. 2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
  14. 2022Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarioscited by 46
  15. 2022Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Networkcited by 45
  16. 2023Operator learning with PCA-Net: upper and lower complexity boundscited by 44
  17. 2023Domain Agnostic Fourier Neural Operatorscited by 38
  18. 2023GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEscited by 20
  19. 2024Peridynamic Neural Operators: A Data-Driven Nonlocal Constitutive Model for Complex Material Responsescited by 18
  20. 2023Data-Driven Design for Metamaterials and Multiscale Systems: A Reviewcited by 17
  21. 2024Deep Neural Operator Enabled Digital Twin Modeling for Additive Manufacturingcited by 14
  22. 2022Loss Landscape Engineering via Data Regulation on PINNscited by 11
  23. 2023MetaNO: How to Transfer Your Knowledge on Learning Hidden Physicscited by 10
  24. 2024TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNscited by 5
  25. 2024Meta-learning Loss Functions of Parametric Partial Differential Equations Using Physics-Informed Neural Networkscited by 2

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Cited by year

Citing papers per year: 2025: 2.

2 papers.

  1. 2025Variationally correct operator learning: Reduced basis neural operator with a posteriori error estimationcited by 7
  2. 2025Reduced-Basis Deep Operator Learning for Parametric PDEs with Independently Varying Boundary and Source Datacited by 1

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