Downscaling Neural Network for Coastal Simulations

TL;DR

This paper presents DNNCS, a spatiotemporal downscaling neural network for coastal shallow-water simulations that converts coarse DG-SWE outputs into high-resolution representations while preserving mass and momentum. The model uses grid-aware spatiotemporal attention, learnable positional encodings, and a frequency-domain feature reconstruction to jointly upscale in space and time. Physics-informed losses complemented by a diffusion-like residual framework substantially improve temporal coherence and accuracy, achieving state-of-the-art metrics on Bahamas and Galveston tidal scenarios and demonstrating robustness to changing forcing data and real-world storm surge conditions such as Hurricane Ike. The work also introduces a dedicated coastal simulation dataset, highlights model transferability, and discusses deployment considerations and future graph-based extensions for irregular meshes. Overall, DNNCS offers a fast, physically consistent pathway to obtain high-resolution coastal predictions from coarse simulations, with clear implications for real-time warning and hazard assessment.

Abstract

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.

Figures (15)

• Figure 1: The overall deep learning pipeline for coastal ocean downscaling. We use the numerical model to simulate the coarse solution representation as $U, V, \xi$. We stack them as RGB channels to form a low-resolution (LR) image, which will be taken as input to the proposed DNNCS for spatiotemporal upsampling. The obtained downscaling coastal images seamlessly enhance the spatial and temporal details, which will be useful for coastal ocean simulation and visualization.
• Figure 2: The overall structure of the proposed DNNCS . We show the complete architecture of our proposed DNNCS. Given two consecutive coastal simulations, we take them as input to first extract the deep feature representation via multiple RCAB (Residual Channel Attention Block) blocks. Then we use spatiotemporal attention to learn the pixel correlations across space and time. Finally, we split the features into three channels for temporal interpolation and spatial downscaling.
• Figure 3: The spatiotemporal correlation of the water movement. We visualize the water movement as a 3D heatmap, and we can see that the particle at the same coordinate can relate to neighborhood particles and to itself in the next step.
• Figure 4: Computational domain, bathymetry (in meters), and the coarse mesh for Bahamas (left, 1696 elements) and Galveston (right, 3397 elements) test cases. The x-axis points East and the y-axis points North.
• Figure 5: Visual comparison among different methods on Bahamas dataset. We show the ground truth from resolution 1696, order 0 at time $t_{15}$ and $t_{30}$, and the corresponding residual maps between prediction and ground truth (U, V, and $\xi$ planes -- we multiply the residuals by factor 50 to highlight the differences), and the residual map between the ground truths at times $t_{30}$ and $t_{15}$ (we multiply the residuals by factor 20 for visualization).