Phase-resolving wave models such as FUNWAVE-TVD resolve individual waves shoaling, refracting and breaking, but the preprint says their cost rules them out for ensembles, uncertainty quantification and real-time warning. Neural operators are proposed as a cheaper substitute, yet the accurate ones on wave-dominated fields are large: the preprint puts hybrid spectral-convolutional operators such as U-FNO at tens of millions of parameters.

DU-NO is described as a multiscale U-shaped spectral operator that attaches lightweight convolutional U-Net branches only at its two shallowest encoder and decoder levels, holding the model to 3.64M parameters. On the authors' publicly released FUNWAVE-TVD benchmark, the preprint reports the best autoregressive rollout error of six identically trained architectures, improving on U-FNO by 14.9% with 10.8x fewer parameters. The preprint also reports gains on 2D Navier-Stokes and PDEBench shallow-water rollouts.