用深度算子网络替代传统波浪模型，提速一万倍且精度高。
Operator Learning for Predicting Bulk Wave Parameters of Spectral Wave Models
- 用DeepONet学习连续波浪算子，不依赖网格，可高效推断。
- 在杜克海滩案例中计算效率提升10000倍，误差低于2%~11%。
- 适合需要快速波浪参数预测的海洋模拟与风暴潮预警场景。
波浪引起的强迫对平均水位和近岸流的影响通常通过辐射应力及其空间梯度建模。准确的风暴潮预测需耦合潮流与波浪模型，但数值波浪模型计算成本高，限制了时间分辨率。本文探索使用深度算子网络（DeepONets）作为模拟近岸波浪（SWAN）模型的代理模型。不同于依赖网格的代理模型，DeepONets学习底层连续算子，实现高效预测并支持无关离散化的推理。所提代理模型在两个不同的一维和二维稳态数值案例中评估，边界波况和风场变化多样。应用于北卡罗来纳州杜克海滩的真实稳态波浪模拟时，DeepONet代理模型将计算效率提升四个数量级。此外，该模型在所有未见测试场景中均保持高精度，显著波高及辐射应力梯度的x、y分量相对L₂误差分别控制在1.91%、10.98%和6.88%以内。
原文摘要 · Abstract (English)
The impact of wave-induced forcing on the mean water level and nearshore currents is typically modeled through excess momentum fluxes, also known as radiation stresses, and their spatial gradients. Accurate storm surge prediction requires coupled circulation and wave models, but the high computational cost of numerical wave models limits their temporal resolution. In this work, we explore a proof-of-concept application of Deep Operator Networks (DeepONets) as a surrogate for the Simulating WAves Nearshore (SWAN) numerical wave model. Unlike grid-dependent surrogate models, DeepONets learn the underlying continuous operator, and thus, can provide highly efficient prediction while enabling discretization-invariant inference. The proposed surrogate model is evaluated using two distinct 1-D and 2-D steady-state numerical examples with variable boundary wave conditions and wind fields. When applied to a realistic numerical example of steady-state wave simulation in Duck, NC, the DeepONet surrogate improves computational efficiency by four orders of magnitude. Furthermore, the model demonstrates consistently high accuracy in predicting the significant wave height and the x- and y- components of the radiation stress gradient, by achieving relative L_2 errors bounded by 1.91%, 10.98%, and 6.88%, respectively, across all unseen test scenarios.
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