Downscaling Neural Network for Coastal Simulations

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.

💡 Research Summary

The paper addresses the computational bottleneck of high‑resolution coastal ocean modeling, which is essential for accurate prediction of tsunami and storm‑surge flooding. The authors propose a Downscaling Neural Network for Coastal Simulation (DNNCS) that learns to transform low‑resolution discontinuous Galerkin (DG) solutions of the two‑dimensional shallow‑water equations (SWE) into high‑resolution free‑surface elevation and horizontal velocity fields. The low‑resolution simulation outputs—depth‑integrated velocities (U, V) and water surface elevation (ξ)—are stacked as RGB channels to form an image sequence that serves as the network input.
The core of DNNCS is a grid‑aware spatiotemporal attention mechanism. Temporal features extracted from consecutive frames are projected onto spatial tokens, enabling non‑local matching across the mesh while preserving the underlying grid structure. Positional encoding (sinusoidal) injects explicit coordinate information, allowing the model to respect the physical layout of the computational domain.
For reconstruction, the network first performs spatiotemporal bilinear interpolation to fill missing frames, then expands the feature maps into the frequency domain where a residual mapping refines high‑frequency components. This spectral refinement better preserves the physical spectra of fluid variables than pure pixel‑wise upsampling.
Training loss combines conventional data‑driven L1/L2 terms with physics‑informed components: a gradient‑consistency loss enforcing mass conservation and a momentum‑change loss enforcing momentum conservation. These physics‑based penalties reduce long‑term drift and improve physical fidelity, yielding a 24 % reduction in root‑mean‑square error (RMSE) compared with a purely data‑driven baseline.
A new multi‑scale coastal simulation dataset is introduced, containing a variety of bathymetries, tidal forcings, and extreme event scenarios (tsunamis, storm surges). The dataset provides paired low‑ and high‑resolution simulations for supervised training and thorough evaluation.
Benchmarking against state‑of‑the‑art video super‑resolution models (e.g., SwinIR, EDVR) and physics‑informed downscaling approaches (e.g., PHYSR, MeshfreeFlowNet) shows that DNNCS achieves higher PSNR/SSIM, lower RMSE, and significantly faster inference—approximately 30 fps on a modern GPU, meeting real‑time requirements for early‑warning systems.
In summary, DNNCS delivers a fast, accurate, and physically consistent method to upscale coarse DG SWE simulations, enabling real‑time generation of high‑resolution coastal forecasts without the prohibitive computational cost of full high‑resolution runs. The integration of grid‑aware attention, spectral residual refinement, and physics‑informed loss constitutes a novel contribution to both deep learning‑based super‑resolution and scientific computing for ocean modeling.