The research introduces DU-NO, a double U-shaped neural operator designed for phase-resolving wave modeling. The model utilizes a multiscale U-shaped spectral operator with convolutional U-Net branches attached only at the two shallowest encoder and decoder levels. This placement focuses computational resources on high-wavenumber content, which primarily exists on finer grids. The model achieves a parameter count of 3.64 million, representing a reduction of approximately one order of magnitude compared to U-FNO.
Evaluations on the publicly released FUNWAVE-TVD benchmark demonstrate DU-NO’s effectiveness, achieving the best autoregressive rollout error among six identically trained architectures. The model improved upon U-FNO by 14.9% with a 10.8x reduction in parameters. Frequency-band analysis confirms this improvement across all bands, including the high-wavenumber band where truncated-spectral operators typically degrade.
Parameter-matched controls confirmed that the architectural advantage is the primary driver of the performance gains. Rescaling the model to a 3.6 million parameter budget still resulted in DU-NO outperforming the strongest baseline by 28.6%. Beyond nearshore waves, DU-NO performed strongly on 2D Navier-Stokes simulations and achieved a clear win on the PDEBench shallow-water rollout benchmark.
Code, trained models, and evaluation artifacts are available for public use. The research addresses the limitations of large spectral-convolutional operators by offering a more efficient solution for operational forecasting and related applications. Source: https://arxiv.org/abs/2609.12115
