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U-NO: U-shaped Neural Operators

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arxiv 2204.11127 v3 pith:A4T5ZDIX submitted 2022-04-23 cs.LG

Md Ashiqur Rahman , Zachary E. Ross , Kamyar Azizzadenesheli This is my paper · ORCID
classification cs.LG
keywords neuraloperatorsu-noequationslearningnavier-stokesu-shapeddarcy
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Neural operators generalize classical neural networks to maps between infinite-dimensional spaces, e.g., function spaces. Prior works on neural operators proposed a series of novel methods to learn such maps and demonstrated unprecedented success in learning solution operators of partial differential equations. Due to their close proximity to fully connected architectures, these models mainly suffer from high memory usage and are generally limited to shallow deep learning models. In this paper, we propose U-shaped Neural Operator (U-NO), a U-shaped memory enhanced architecture that allows for deeper neural operators. U-NOs exploit the problem structures in function predictions and demonstrate fast training, data efficiency, and robustness with respect to hyperparameters choices. We study the performance of U-NO on PDE benchmarks, namely, Darcy's flow law and the Navier-Stokes equations. We show that U-NO results in an average of 26% and 44% prediction improvement on Darcy's flow and turbulent Navier-Stokes equations, respectively, over the state of the art. On Navier-Stokes 3D spatiotemporal operator learning task, we show U-NO provides 37% improvement over the state of art methods.

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Cited by 14 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. SPAMoE: Spectrum-Aware Hybrid Operator Framework for Full-Waveform Inversion

    cs.LG 2026-04 unverdicted novelty 7.0 of 10

    SPAMoE reduces average MAE by 44.4% on ten OpenFWI sub-datasets via a spectral-preserving DINO encoder plus frequency-routed MoE of FNO, MNO and LNO experts.

  2. No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study

    math.NA 2026-07 conditional novelty 6.0 of 10

    No single flow-surrogate architecture transfers from a boundary-driven Stokes film to a self-sustained Kármán wake; time treatment decides the winner and pointwise RMSE ranks the wrong models.

  3. Identifiability-Aware Source Apportionment in City-Scale Advection-Diffusion Systems

    eess.SP 2026-07 conditional novelty 6.0 of 10

    IASA makes source apportionment report what a sensor network can actually tell apart: the rank and singular values of the projected response matrix set the finest defensible attribution resolution.

  4. Adaptive Mamba Neural Operators

    cs.LG 2026-07 reject novelty 6.0 of 10

    AMO builds adaptive Takenaka-Malmquist bases inside a Mamba state-space model for PDE operator learning, but the claimed equivalence to adaptive Fourier decomposition is not supported by the implemented recurrence.

  5. Autoregressive One-Step Generative Modeling for Dynamical System Forecasting

    cs.LG 2026-05 unverdicted novelty 6.0 of 10

    MeLISA extends pixel-space MeanFlow to one-step window-conditioned autoregressive forecasting, improving long-horizon turbulence statistics over neural-operator baselines.

  6. Modeling turbulent and self-gravitating fluids with Fourier neural operators

    astro-ph.GA 2025-07 conditional novelty 6.0 of 10

    Fourier neural operators trained on 2D projected views of 3D astrophysical simulations can forecast subsequent projected density and velocity snapshots with 5-25% RMS error, though a constant hidden magnetic field mea...

  7. LaDEEP: A Deep Learning-based Surrogate Model for Large Deformation of Elastic-Plastic Solids

    cs.LG 2025-06 conditional novelty 6.0 of 10

    A two-stage Transformer surrogate trained on finite element data predicts stretch-bending final shapes with about 0.17 mm mean absolute distance and over 10,000 times speedup versus FEM.

  8. Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems

    cs.AI 2025-05 conditional novelty 6.0 of 10

    HEAP, a hierarchical autoencoder with a predictor that advances multiple scale layers in sync, achieves several-fold lower long-term rollout error than flat ResNet baselines on Hasegawa-Wakatani turbulence.

  9. Feature Interaction Modeling for Physics-Informed Neural Networks and Neural Operators

    cs.LG 2026-07 conditional novelty 5.0 of 10

    Adding NFM-style bi-interaction layers to PINNs and DeepONets improves accuracy on several high-dimensional smooth PDEs and shock-dominated conservation laws, but not on low-dimensional smooth problems.

  10. GFocal: A Global-Focal Neural Operator for Solving PDEs on Arbitrary Geometries

    cs.LG 2025-08 conditional novelty 5.0 of 10

    GFocal, a global-focal Transformer neural operator, achieves state-of-the-art relative L2 errors on five of six PDE benchmarks by fusing Nystrom attention and slice-based local tokens.

  11. Latent Mamba Operator for Partial Differential Equations

    cs.LG 2025-05 conditional novelty 5.0 of 10

    LaMO replaces attention in latent-token neural operators with bidirectional state-space models and reports consistent accuracy gains on six PDE benchmarks.

  12. DPNO: A Dual Path Architecture For Neural Operator

    math.NA 2025-07 conditional novelty 4.0 of 10

    Applying a ResNet-like plus DenseNet-like dual path to DeepONet and FNO reduces relative L2 error on Burgers, Darcy flow, and 2D Navier-Stokes benchmarks compared with the original single-path models.

  13. Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning

    cs.LG 2025-06 conditional novelty 4.0 of 10

    A practical recipe to convert common neural architectures into discretization-agnostic neural operators, validated by Navier-Stokes experiments showing cross-resolution generalization of FNO-style models.

  14. A Neural Operator based on Dynamic Mode Decomposition

    cs.LG 2025-07 reject novelty 3.0 of 10

    A DMD-enhanced branch-trunk neural operator is proposed and tested on three 2D PDEs, but the claimed comparative results and key theoretical bound are not supported.

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