mlsanityData to 14 Oct 2026

Multiscale Neural Operator: Learning Fast and Grid-independent PDE Solvers

arXiv 2207.11417 ↗First posted 23 Jul 2022cs.LG cs.AI cs.CEcited by 12

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Abstract (arXiv)

Numerical simulations in climate, chemistry, or astrophysics are computationally too expensive for uncertainty quantification or parameter-exploration at high-resolution. Reduced-order or surrogate models are multiple orders of magnitude faster, but traditional surrogates are inflexible or inaccurate and pure machine learning (ML)-based surrogates too data-hungry. We propose a hybrid, flexible surrogate model that exploits known physics for simulating large-scale dynamics and limits learning to the hard-to-model term, which is called parametrization or closure and captures the effect of fine- onto large-scale dynamics. Leveraging neural operators, we are the first to learn grid-independent, non-local, and flexible parametrizations. Our textitmultiscale neural operator is motivated by a rich literature in multiscale modeling, has quasilinear runtime complexity, is more accurate or flexible than state-of-the-art parametrizations and demonstrated on the chaotic equation multiscale Lorenz96.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 59 of its 144 references that are in the map. First posted on arXiv 23 Jul 2022.

Builds on

59 of 144 references.

References · 59

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38 more
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50 most cited of 59 All 59 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 3; 2023: 2; 2024: 3; 2025: 2; 2026: 2.

12 papers.

  1. 2022Transformer Meets Boundary Value Inverse Problemscited by 22
  2. 2023AI Foundation Models for Weather and Climate: Applications, Design, and Implementationcited by 21
  3. 2024Knowledge-guided Machine Learning: Current Trends and Future Prospectscited by 14
  4. 2022Adaptive physics-informed neural operator for coarse-grained non-equilibrium flowscited by 7
  5. 2025Generalized Spherical Neural Operators: Green's Function Formulationcited by 3
  6. 2024Physics-constrained coupled neural differential equations for one dimensional blood flow modelingcited by 2
  7. 2022NLP Inspired Training Mechanics For Modeling Transient Dynamicscited by 1
  8. 2023An enrichment approach for enhancing the expressivity of neural operators with applications to seismologycited by 0
  9. 2024How to Re-enable PDE Loss for Physical Systems Modeling Under Partial Observationcited by 0
  10. 2025SA-EMO: Structure-Aligned Encoder Mixture of Operators for Generalizable Full-waveform Inversioncited by 0
  11. 2026SPAMoE: Spectrum-Aware Hybrid Operator Framework for Full-Waveform Inversioncited by 0
  12. 2026Factorized Neural Operators Decompose Dynamic and Persistent Responsescited by 0