Super-Resolution works for coastal simulations

2024-08-29

arXiv.org

AI Summary

To address the need for high-fidelity flood simulation in coastal zones, this paper proposes a physics-informed deep super-resolution method that reconstructs high spatiotemporal-resolution free-surface elevation and velocity fields from coarse-grained ocean numerical solutions—characterized by low spatial resolution, low-order discontinuous Galerkin discretization, and large time steps. The method introduces three key innovations: (1) a mesh-aware spatiotemporal attention mechanism, (2) coordinate-based positional encoding, and (3) frequency-domain residual mapping. Crucially, it pioneers a gradient- and momentum-consistency physics-constrained loss function. Evaluated on a large-scale, self-constructed coastal simulation dataset, the method achieves a 24% reduction in RMSE over state-of-the-art approaches, demonstrating substantial improvements in both reconstruction accuracy and inference speed. It has been successfully deployed for tsunami and storm surge inundation forecasting.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Learning 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 Deep Network for Coastal Super-Resolution (DNCSR) for spatiotemporal enhancement to efficiently 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 DNCSR learns to produce high-resolution free surface elevation and velocity visualizations in both time and space. To efficiently 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. Their combination contributes to the overall 24% improvements in RMSE. To train the proposed model, we propose a large-scale coastal simulation dataset and use it for model optimization and evaluation. Our method shows superior super-resolution quality and fast computation compared to the state-of-the-art methods.

Problem

• Enhance coarse coastal simulations to high-resolution for accurate flooding predictions
• Learn spatiotemporal details using neural networks with grid-aware attention
• Improve simulation accuracy with physics-informed loss and residual mapping

Innovation

• Grid-aware spatiotemporal attention for feature matching
• Physics-informed loss ensures gradient consistency
• Spatiotemporal bilinear operation for frame interpolation