mlsanityData to 7 Oct 2026

NUNO: A General Framework for Learning Parametric PDEs with Non-Uniform Data

arXiv 2305.18694 ↗First posted 30 May 2023cs.LG cs.AIcited by 15

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Abstract (arXiv)

The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use mesh-based techniques such as the FFT. To address this, we introduce the Non-Uniform Neural Operator (NUNO), a comprehensive framework designed for efficient operator learning with non-uniform data. Leveraging a K-D tree-based domain decomposition, we transform non-uniform data into uniform grids while effectively controlling interpolation error, thereby paralleling the speed and accuracy of learning from non-uniform data. We conduct extensive experiments on 2D elasticity, (2+1)D channel flow, and a 3D multi-physics heatsink, which, to our knowledge, marks a novel exploration into 3D PDE problems with complex geometries. Our framework has reduced error rates by up to 60% and enhanced training speeds by 2x to 30x. The code is now available at https://github.com/thu-ml/NUNO.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 20 of its 39 references that are in the map. First posted on arXiv 30 May 2023.

Builds on

20 of 39 references.

References · 20

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8 more
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 3; 2025: 5; 2026: 6.

15 papers.

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  1. 2024DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Trainingcited by 137
  2. 2025Machine learning for modelling unstructured grid data in computational physics: a reviewcited by 12
  3. 2025Mixture-of-Experts Operator Transformer for Large-Scale PDE Pre-Trainingcited by 10
  4. 2024Towards General Neural Surrogate Solvers with Specialized Neural Acceleratorscited by 8
  5. 2025Operator Learning with Domain Decomposition for Geometry Generalization in PDE Solvingcited by 6
  6. 2024Reference Neural Operators: Learning the Smooth Dependence of Solutions of PDEs on Geometric Deformationscited by 5
  7. 2025Physics-informed Temporal Alignment for Auto-regressive PDE Foundation Modelscited by 5
  8. 2025GFocal: A Global-Focal Neural Operator for Solving PDEs on Arbitrary Geometriescited by 2
  9. 2023Enhancing Solutions for Complex PDEs: Introducing Complementary Convolution and Equivariant Attention in Fourier Neural Operatorscited by 1
  10. 2026Benchmarking Long Roll-outs of Auto-regressive Neural Operators for the Compressible Navier-Stokes Equations with Conserved Quantity Correctioncited by 1
  11. 2026Stabilizing autoregressive forecasts in chaotic systems via multi-rate latent recurrencecited by 0
  12. 2026UniFluids: Unified Neural Operator Learning with Conditional Flow-matchingcited by 0
3 more
  1. 2026Linear-Nonlinear Fusion Neural Operator for Partial Differential Equationscited by 0
  2. 2026Geometry-aware Latent Autoregressive Generative Model for PDEs in Complex Domainscited by 0
  3. 2026Beyond Arbitrary Geometry: Topology Generalization In neural PDE Operatorscited by 0