mlsanityData to 14 Oct 2026

On the locality of local neural operator in learning fluid dynamics

arXiv 2312.09820 ↗First posted 15 Dec 2023physics.flu-dyn cs.LGcited by 6

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Abstract (arXiv)

This paper launches a thorough discussion on the locality of local neural operator (LNO), which is the core that enables LNO great flexibility on varied computational domains in solving transient partial differential equations (PDEs). We investigate the locality of LNO by looking into its receptive field and receptive range, carrying a main concern about how the locality acts in LNO training and applications. In a large group of LNO training experiments for learning fluid dynamics, it is found that an initial receptive range compatible with the learning task is crucial for LNO to perform well. On the one hand, an over-small receptive range is fatal and usually leads LNO to numerical oscillation; on the other hand, an over-large receptive range hinders LNO from achieving the best accuracy. We deem rules found in this paper general when applying LNO to learn and solve transient PDEs in diverse fields. Practical examples of applying the pre-trained LNOs in flow prediction are presented to confirm the findings further. Overall, with the architecture properly designed with a compatible receptive range, the pre-trained LNO shows commendable accuracy and efficiency in solving practical cases.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 22 of its 47 references that are in the map. First posted on arXiv 15 Dec 2023.

Builds on

22 of 47 references.

References · 22

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10 more
  1. 2020Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Predictioncited by 138
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Cited by year

Citing papers per year: 2024: 2; 2025: 4.

6 papers.

  1. 2024Neural Operators with Localized Integral and Differential Kernelscited by 62
  2. 2024Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modelingcited by 36
  3. 2025Generalized Spherical Neural Operators: Green's Function Formulationcited by 3
  4. 2025GALDS: A Graph-Autoencoder-based Latent Dynamics Surrogate model to predict neurite material transportcited by 2
  5. 2025PDE Solvers Should Be Local: Fast, Stable Rollouts with Learned Local Stencilscited by 2
  6. 2025Virtual domain extension for imposing boundary conditions in flow simulation using pre-trained local neural operatorcited by 0