Learning the fine-scale details of a coastal ocean simulation from a coarse representation is a challenging task. For real-world applications, high-resolution simulations are necessary to advance understanding of many coastal processes, specifically, to predict flooding resulting from tsunamis and storm surges. We propose a Downscaling Neural Network for Coastal Simulation (DNNCS) for spatiotemporal enhancement to learn the high-resolution numerical solution. Given images of coastal simulations produced on low-resolution computational meshes using low polynomial order discontinuous Galerkin discretizations and a coarse temporal resolution, the proposed DNNCS learns to produce high-resolution free surface elevation and velocity visualizations in both time and space. To model the dynamic changes over time and space, we propose grid-aware spatiotemporal attention to project the temporal features to the spatial domain for non-local feature matching. The coordinate information is also utilized via positional encoding. For the final reconstruction, we use the spatiotemporal bilinear operation to interpolate the missing frames and then expand the feature maps to the frequency domain for residual mapping. Besides data-driven losses, the proposed physics-informed loss guarantees gradient consistency and momentum changes, leading to a 24% reduction in root-mean-square error compared to the model trained with only data-driven losses. To train the proposed model, we propose a coastal simulation dataset and use it for model optimization and evaluation. Our method shows superior downscaling quality and fast computation compared to the state-of-the-art methods.

翻译：从粗粒度表示中学习海岸海洋模拟的精细尺度细节是一项具有挑战性的任务。在实际应用中，高分辨率模拟对于深化理解众多海岸过程至关重要，特别是用于预测海啸和风暴潮引发的洪水。我们提出了一种用于海岸模拟的下采样神经网络，用于时空增强以学习高分辨率数值解。给定使用低多项式阶间断伽辽金离散化在低分辨率计算网格上生成且时间分辨率较粗的海岸模拟图像，所提出的DNNCS能够学习生成时间和空间上均具有高分辨率的自由表面高程和速度可视化结果。为了模拟随时间和空间的动态变化，我们提出了网格感知的时空注意力机制，将时序特征投影到空间域以进行非局部特征匹配。坐标信息也通过位置编码得以利用。在最终重建阶段，我们使用时序双线性操作对缺失帧进行插值，然后将特征图扩展至频域以进行残差映射。除了数据驱动的损失函数外，所提出的物理信息损失保证了梯度一致性和动量变化，与仅使用数据驱动损失训练的模型相比，均方根误差降低了24%。为了训练所提出的模型，我们构建了一个海岸模拟数据集，并将其用于模型优化和评估。与现有先进方法相比，我们的方法展现出更优的下采样质量和更快的计算速度。