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. Our DNNCS is trained on a coastal simulation dataset and uses it for model optimization and evaluation. Our method shows superior downscaling quality and fast computation compared to the state-of-the-art methods.