DU-NO：一种用于相位解析波浪建模的参数高效双U形神经算子
DU-NO: A Parameter-Efficient Double U-Shaped Neural Operator for Phase-Resolving Wave Modeling
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- Canizaro-Livingston Gulf States Center for Environmental Informatics, LSU New Orleans（卡尼萨罗-利文斯顿海湾国家环境信息学中心，路易斯安那州立大学新奥尔良分校）
- U.S. Naval Research Laboratory（美国海军研究实验室）
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中文总结 AI 辅助
针对相位解析波浪建模中神经算子参数过多的问题，提出参数高效的DU-NO模型，通过浅层附加卷积分支和深度衰减模式调度，以364万参数实现比U-FNO低14.9%的误差，并在多个基准上验证了其优越性。
中文摘要 AI 辅助
相位解析波浪模型（如FUNWAVE-TVD）是近岸动力学精度标准的代表，能够解析单个波浪的浅化、折射和破碎过程，但其计算成本使其无法用于业务预报所需的集合预报、不确定性量化和实时预警。神经算子有望以极低的成本实现求解器级别的精度，然而在波浪主导的场域中，高精度的神经算子往往规模庞大：混合谱卷积算子如U-FNO（本研究中除DU-NO外的最强基线）以数千万参数换取其保真度。我们提出了DU-NO（双U形神经算子），一种多尺度U形谱算子，仅在编码器和解码器最浅的两层附加轻量级卷积U-Net分支。该放置遵循采样论证：高波数内容仅存在于细网格上，因此局部全频带通路被放置在该内容所在之处，而粗网格带限层级则保持纯谱形式。深度衰减模式调度将模型参数控制在364万，比U-FNO低一个数量级。在我们公开发布的FUNWAVE-TVD基准上，DU-NO在六个相同训练架构中取得了最佳自回归滚动误差，相比U-FNO提升了14.9%，同时参数减少了10.8倍；频带分析表明，该增益在所有频带中均成立，包括截断谱算子失效的高波数频带。参数匹配对照实验证实该增益源于架构本身：将最佳基线缩放到相同的360万参数预算后，其误差仍比DU-NO高28.6%。该优势不仅限于近岸波浪：DU-NO在二维Navier-Stokes方程上匹配了最强基线，并在PDEBench浅水方程滚动预测中明显胜出。代码、训练模型和评估工件可在https URL获取。
英文摘要
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 our study after DU-NO) buy their fidelity with tens of millions of parameters. We 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. The placement follows a sampling argument: high-wavenumber content exists only on fine grids, so the local, full-band pathways go where that content lives, while the coarse, band-limited levels stay purely spectral. A depth-decaying mode schedule holds the model to 3.64M parameters, an order of magnitude below U-FNO. On our publicly released FUNWAVE-TVD benchmark, DU-NO attains the best autoregressive rollout error of six identically trained architectures, improving on U-FNO by 14.9% with 10.8x fewer parameters, and a frequency-band analysis shows the gain holds across all bands, including the high-wavenumber band where truncated-spectral operators collapse. Parameter-matched controls confirm the gain is architectural: rescaled to the same 3.6M budget, the best baseline still trails DU-NO by 28.6%. The advantage carries beyond nearshore waves: DU-NO matches the strongest baselines on 2D Navier-Stokes and wins clearly on PDEBench shallow-water rollouts. Code, trained models, and evaluation artifacts are available at https://anonymous.4open.science/r/duno-code-5A7B/.
