HS-FNO lifts the state to include history and decomposes updates into a learned future-slice predictor plus an exact shift-append transport, yielding lower rollout errors than standard or lag-stack FNO baselines on five non-Markovian PDE families.
Transformer for partial differential equations’ operator learning
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
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2026 6representative citing papers
CATO learns a continuous latent chart for efficient axial attention on PDE meshes and adds derivative-aware supervision to improve accuracy and reduce oversmoothing on general geometries.
QuadNorm uses quadrature-based moments instead of uniform averaging in normalization layers, achieving O(h²) consistency across resolutions and better cross-resolution transfer in neural operators.
Physics-informed Fourier neural operators recover plasmoid formation in sparse SRRMHD vortex data where data-only models fail, and transformer operators approximate AMR jet evolution, marking first reported uses in these relativistic MHD settings.
Scale-autoregressive modeling (SAR) samples fluid flow distributions hierarchically from coarse to fine resolutions on meshes, achieving lower distributional error and 2-7x faster runtime than diffusion or flow-matching baselines.
RETO achieves relative L2 errors of 0.063 on ShapeNet and 0.089/0.097 on DrivAerML surface pressure/velocity, outperforming Transolver and other baselines.
citing papers explorer
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HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations
HS-FNO lifts the state to include history and decomposes updates into a learned future-slice predictor plus an exact shift-append transport, yielding lower rollout errors than standard or lag-stack FNO baselines on five non-Markovian PDE families.
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CATO: Charted Attention for Neural PDE Operators
CATO learns a continuous latent chart for efficient axial attention on PDE meshes and adds derivative-aware supervision to improve accuracy and reduce oversmoothing on general geometries.
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QuadNorm: Resolution-Robust Normalization for Neural Operators
QuadNorm uses quadrature-based moments instead of uniform averaging in normalization layers, achieving O(h²) consistency across resolutions and better cross-resolution transfer in neural operators.
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Learning Neural Operator Surrogates for the Black Hole Accretion Code
Physics-informed Fourier neural operators recover plasmoid formation in sparse SRRMHD vortex data where data-only models fail, and transformer operators approximate AMR jet evolution, marking first reported uses in these relativistic MHD settings.
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One Scale at a Time: Scale-Autoregressive Modeling for Fluid Flow Distributions
Scale-autoregressive modeling (SAR) samples fluid flow distributions hierarchically from coarse to fine resolutions on meshes, achieving lower distributional error and 2-7x faster runtime than diffusion or flow-matching baselines.
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RETO: A Rotary-Enhanced Transformer Operator for High-Fidelity Prediction of Automotive Aerodynamics
RETO achieves relative L2 errors of 0.063 on ShapeNet and 0.089/0.097 on DrivAerML surface pressure/velocity, outperforming Transolver and other baselines.