mlsanityData to 14 Oct 2026

A Bregman Proximal Viewpoint on Neural Operators

arXiv 2610.20120 ↗First posted 14 Oct 2026cs.LGcited by 0

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Abstract (arXiv)

We present several advances on neural operators by viewing the action of operator layers as the minimizers of Bregman regularized optimization problems over Banach function spaces. The proposed framework allows interpreting the activation operators as Bregman proximity operators from dual to primal space. This novel viewpoint is general enough to recover classical neural operators as well as a new variant, coined Bregman neural operators, which includes the inverse activation operator and features the same expressivity of standard neural operators. Numerical experiments support the added benefits of the Bregman variant of Fourier neural operators for training deeper and more accurate models.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 20 of its 34 references that are in the map. First posted on arXiv 14 Oct 2026.

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References · 20

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  3. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  4. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
  5. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
  6. 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 413
  7. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 349
  8. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 336
  9. 2021Factorized Fourier Neural Operatorscited by 249
  10. 2023Convolutional Neural Operators for robust and accurate learning of PDEscited by 214
  11. 2022Learning Operators with Coupled Attentioncited by 90
  12. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 89
8 more
  1. 2021Improved architectures and training algorithms for deep operator networkscited by 86
  2. 2023Operator Learning with Neural Fields: Tackling PDEs on General Geometriescited by 84
  3. 2023Neural Inverse Operators for Solving PDE Inverse Problemscited by 65
  4. 2019Lipschitz Certificates for Layered Network Structures Driven by Averaged Activation Operatorscited by 55
  5. 2023Group Equivariant Fourier Neural Operators for Partial Differential Equationscited by 45
  6. 2018Deep Neural Network Structures Solving Variational Inequalitiescited by 26
  7. 2015Forward-Backward Splitting with Bregman Distancescited by 8
  8. 2021Residual fourier neural operator for thermochemical curing of compositescited by 5

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