Paper Overview
Field: ML Authors: Enrique Hernandez Noguera, Md Meftahul Ferdaus, Nathan Cooper, Elias Ioup, Mahdi Abdelguerfi Published: 2026-09-15 arXiv: 2609.12115
Summary
Phase-resolving wave models such as FUNWAVE-TVD are the accuracy standard for nearshore dynamics, resolving the shoaling, refraction, and breaking of individual waves — but their cost rules them out for the ensembles, uncertainty quantification, and real-time warning that operational forecasting demands. Neural operators promise solver-level accuracy at a fraction of that cost, yet on wave-dominated fields the accurate ones are large: hybrid spectral-convolutional operators such as U-FNO (the strongest baseline in this study after DU-NO) buy their fidelity with tens of millions of parameters.
The authors introduce DU-NO (Double U-shaped Neural Operator), a multiscale U-shaped spectral operator that attaches lightweight convolutional U-Net branches only at its two shallowest encoder and decoder levels. This placement follows a sampling argument: high-wavenumber content exists only on fine grids, so the local full-band pathway belongs where that content lives, while coarse band-limited levels remain purely spectral. A depth-decaying pattern schedule keeps the model at 3.64 million parameters — an order of magnitude below U-FNO.
Key Results
- On a publicly released FUNWAVE-TVD benchmark, DU-NO achieves the best autoregressive rollout error among six identically trained architectures.
- It improves over U-FNO by 14.9% with 10.8x fewer parameters.
- Band-wise analysis shows the gains hold across all frequency bands, including the high-wavenumber bands where truncated spectral operators collapse.
- Parameter-matched controls confirm the gains are architectural: rescaled to the same 3.6M-parameter budget, the best baseline still trails DU-NO by 28.6%.
- Beyond nearshore waves, DU-NO matches the strongest baseline on 2D Navier-Stokes and clearly wins on PDEBench shallow-water rollouts.
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