mlsanityData to 7 Oct 2026

MENO: Memory-Efficient Neural Operator

arXiv 2609.27739 ↗First posted 23 Sep 2026cs.LGcited by 0

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Abstract (arXiv)

We propose the Memory-Efficient Neural Operator (MENO) as a high-performance PDE neural solver based on the Manifold Function Encoder (MFE). MENO features three primary advantages: (1) MENO has a significantly smaller memory footprint and much faster training speed than other popular architectures, with the memory footprint being independent of the data resolution, and therefore holds the potential for scaling up to large-scale models. (2) MENO can accept PDE inputs of arbitrary form, including arbitrary geometric domains and arbitrary discretizations. In particular, it is capable of handling cross-geometry scenarios, i.e., where the input functions and the output solutions are defined on different manifolds. (3) MENO exhibits strong generalization capability, and achieves the best accuracy on most of the benchmarks we tested, compared with the results reported in the literature. The code is available on GitHub at https://github.com/jpzxshi/MENO, and all numerical examples in this paper can be run with a single command to reproduce the reported results.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 26 of its 34 references that are in the map. First posted on arXiv 23 Sep 2026.

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References · 26

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  12. 2021Multiwavelet-based Operator Learning for Differential Equationscited by 229
14 more
  1. 2022U-NO: U-shaped Neural Operatorscited by 219
  2. 2023Convolutional Neural Operators for robust and accurate learning of PDEscited by 207
  3. 2022MIONet: Learning multiple-input operators via tensor productcited by 180
  4. 2025Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometriescited by 89
  5. 2022Deep transfer operator learning for partial differential equations under conditional shiftcited by 83
  6. 2025Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domainscited by 56
  7. 2025AB-UPT: Scaling Neural CFD Surrogates for High-Fidelity Automotive Aerodynamics Simulations via Anchored-Branched Universal Physics Transformerscited by 49
  8. 2023MgNO: Efficient Parameterization of Linear Operators via Multigridcited by 40
  9. 2023Domain Agnostic Fourier Neural Operatorscited by 36
  10. 2026Transolver-3: Scaling Up Transformer Solvers to Industrial-Scale Geometriescited by 20
  11. 2024DIMON: Learning Solution Operators of Partial Differential Equations on a Diffeomorphic Family of Domainscited by 14
  12. 2024A hybrid iterative method based on MIONet for PDEs: Theory and numerical examplescited by 13
  13. 2024AhmedML: High-Fidelity Computational Fluid Dynamics Dataset for Incompressible, Low-Speed Bluff Body Aerodynamicscited by 13
  14. 2024A deformation-based framework for learning solution mappings of PDEs defined on varying domainscited by 2

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