Physics-Guided Spatiotemporal Learning for Coastal Wave Peak Period Estimation from Video

High deployment cost, poor spatial coverage and susceptibility to storm conditions are all challenges faced by traditional in-situ methods. This paper presents a video-based and high performance computing (HPC) enabled deep learning framework for joint sensor free estimation of five coastal wave parameters, namely significant wave height (Hs), maximum wave height (Hmax), peak period (Tp), zero upcrossing period (Tz) and wave direction (theta) from monocular coastal video. The proposed architecture comprises of a V-JEPA (self supervised) ViT Small backbone for robust spatiotemporal feature extraction in visually challenging scenarios, a dual-stream SlowFast temporal encoder for broad bandwidth representation of wave motion in both hydrodynamic breaking and swell regimes, an optical flow stream based on Farneback optical flow algorithm for adding saliency information to the structure with emphasis on hydrodynamically active wavelength bands of waves, and a multi-task regression layer with dispersion constraints (Airy wave dispersion lambda_p = 0.1). The model was trained on an NVIDIA DGX A100 cluster and was early stopped at epoch 31 and achieved Pearson correlation coefficients of 0.451, 0.578, 0.643, 0.680 and 0.832 for Hs, Hmax, Tp, Tz and wave direction respectively, with generalization ability to geographically diverse held out test data sites. While operating in a data-limited regime (6 annotated training scenes), the framework demonstrates statistically significant temporal correlations (PCC of 0.451 to 0.832), confirming proof of concept feasibility; R2 values (max 0.246) indicate that variance capture will improve with larger annotated datasets.

Rip currents are recurrent coastal natural hazards that threaten beachgoers and create operational challenges for lifeguards and coastal managers. Reliable monitoring from standard RGB (red-green-blue) imagery acquired by unmanned aerial vehicles (UAVs) remains difficult because hazardous channels often appear as subtle gaps in breaking waves, foam texture, or sediment patterns, and these signatures are affected by illumination, sea state, and environmental noise. This study presents a physically informed coastal environmental monitoring workflow for detecting visually expressed rip-current indicators that integrates wavelet-derived spatial-frequency texture features with deep learning. We evaluate multiple strategies for incorporating Discrete Wavelet Transform features into convolutional architectures, from computationally efficient channel replacement to dual-stream fusion with attention mechanisms. Performance is assessed against a standard RGB baseline using a task specific convolutional neural network for image-level presence classification and a YOLOv8 model for object-level localization. Under the evaluated dataset conditions, integrating wavelet derived texture features improves performance over RGB-only models. The dual-stream architecture achieves the strongest classification performance, exceeding 95% accuracy with high recall, while channel replacement is most effective for YOLOv8 object detection, reaching 94% mAP@50 for localization. Explainable artificial intelligence analyses provide qualitative evidence that the models attend to visually plausible wave-gap regions associated with rip currents. These results suggest that under the conditions of the evaluated dataset, physically informed wavelet integration may support UAV-based decision-support tools for interpretable beach-safety risk mitigation.

Performance of deep learning models is strongly governed by architectural capacity, with width and depth as primary controls. However, in physical-science applications, models are often compared at a single fixed size or by separating accuracy and computational cost, which can be misleading since architectures exhibit different accuracy-cost scaling as width and depth vary. This issue is particularly relevant for U-Net-type encoder-decoder models, widely used for multi-scale gas, fluid, and plasma dynamics due to their ability to represent features across spatial scales. A U-Net constructs a multi-resolution representation via an encoder that progressively reduces spatial resolution, followed by a decoder that restores it for prediction. Skip connections link corresponding encoder and decoder features, preserving fine-scale information and improving optimization. In practice, U-Net width is routinely tuned, while depth is typically kept fixed (a set number of down/up-sampling stages with few convolutions per stage), limiting systematic exploration of depth for improving the accuracy-cost trade-off. We address this limitation by increasing effective depth through stacking multiple encoder-decoder "waves" in series, with skip connections both within and across waves to enable progressive cross-scale refinement. We call this architecture a Deep Wave Network (DW-Net). Training data, optimization, and schedules are kept identical across models. Instead of evaluating single configurations, we train multiple width variants of each architecture and compare accuracy vs. GPU time Pareto fronts. Across several 2D and 3D flow benchmarks, DW-Net models consistently improve the Pareto frontier over single-wave U-Nets, achieving higher accuracy at matched cost or similar accuracy at reduced cost, and reaching low-error regimes with up to 3x less training time under identical training settings.