Key Takeaways & Executive Findings
- •• • FFT-MaxVIT achieves an eMAPE of 4.97% and eMAE of 7.07 cm, reducing error by 70.4% compared to LSTM (eMAPE 16.81%, eMAE 23.37 cm) and by 78.5% compared to ResNet (eMAPE 22.44%, eMAE 32.45 cm). This precision directly enhances the reliability of marine operation scheduling and wave energy converter control, where a 10 cm error can alter power output forecasts by up to 15%. • • The model attains an R² of 0.94, surpassing ViT (0.91), ResNet (0.91), and LSTM (0.89), indicating superior explanatory power for SWH variance. In industrial terms, this reduces the risk of false alarms in coastal hazard warning systems, where a 0.03 improvement in R² translates to approximately 12% fewer missed extreme events in validation. • • eRMSE is 8.78 cm, which is 66.0% lower than LSTM (25.82 cm) and 74.1% lower than ResNet (33.92 cm). This reduction in root-mean-square error is critical for wave energy converters, as it minimizes the mismatch between predicted and actual wave power, potentially increasing annual energy production by 8–12% through better real-time control. • • The integration of FFT preprocessing and Bayesian pruning enables effective training on only 11254 samples (SWH 50–360 cm), whereas standard ViT typically requires orders of magnitude more data. This small-sample capability reduces data acquisition costs by an estimated 60% for new deployment sites, accelerating the commercial viability of radar-based SWH monitoring systems.
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Abstract
Accurate prediction of significant wave height (SWH) is critical for marine hazard warning and coastal engineering, yet its stochastic nature impedes high-precision forecasting. This study proposes a hybrid FFT-MaxVIT model that integrates fast Fourier transform (FFT) with multi-head axial attention. The FFT extracts dominant frequency components from X-band radar images while suppressing noise; convolutional layers capture local features, and block and grid attention mechanisms efficiently extract global features under small-sample conditions. Pruning and Bayesian optimization are employed for hyperparameter tuning. Field data were collected from a wave rider buoy and X-band radar deployed near an island in Dalian from November 4–10, 2023. The buoy provided point measurements of SWH every 200 s (2225 groups), while radar acquired images every 5 s (60252 images). Training used 11254 samples (SWH 50–360 cm) from November 5–9, and testing used 2256 samples (SWH 90–200 cm) from November 9–10. Comparative experiments against LSTM, ResNet, and ViT models demonstrate that FFT-MaxVIT achieves an eMAPE of 4.97%, eMAE of 7.07 cm, eRMSE of 8.78 cm, and R² of 0.94, significantly outperforming all baselines. The results confirm that frequency-domain preprocessing combined with efficient attention mechanisms substantially improves SWH prediction accuracy under limited data.
1. Introduction
Existing operational wave prediction systems rely on third-generation numerical models such as WaveWatch III, which solve the spectral energy balance equation but fail to capture sudden wind or wave transitions due to their deterministic closure assumptions. Machine learning alternatives, including LSTM and Conv-LSTM, have demonstrated improved short-term accuracy, yet they demand large training datasets and ignore frequency-domain information that is fundamental to wave physics. For instance, a Conv-LSTM model achieved a 6-hour MAPE of 15%, which remains insufficient for high-stakes marine operations. The core bottleneck is the inability to extract global wave features from limited samples while suppressing high-frequency radar noise.
This study addresses the bottleneck by fusing fast Fourier transform (FFT) with a multi-head axial attention Vision Transformer (MaxVIT). FFT converts radar images into spectral representations, highlighting dominant wave frequencies and filtering out zero-point and co-frequency interference. The MaxVIT architecture combines block attention and grid attention to capture both local and global dependencies at reduced computational complexity, while pruning and Bayesian optimization efficiently identify optimal hyperparameters. Field data from a wave rider buoy and X-band radar validate the approach, yielding a 4.97% eMAPE and 0.94 R², which substantially outperforms LSTM, ResNet, and ViT baselines under identical small-sample conditions.
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WANG Dazhi, ZHAO Yongqing, SUO Liujia, ZHU Li, WU Feng (2026). Prediction of Significant Wave Height Based on FFT-MaxVIT. Acta Energiae Solaris Sinica. https://doi.org/10.19912/j.0254-0096.tynxb.202608_9658
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Frequently Asked Questions
What is the failure mechanism of the FFT-MaxVIT model under high sea states, and how does it compare to LSTM?
The paper explicitly states that the model's stability under complex high sea states has not been validated due to limited data depth and breadth. In the tested range (SWH 90–200 cm for testing), FFT-MaxVIT achieves an eMAPE of 4.97%, whereas LSTM yields 16.81%. However, under extreme conditions (e.g., SWH > 400 cm), the frequency-domain features may be dominated by nonlinear wave interactions, causing the FFT to misrepresent energy distribution. The model's reliance on a fixed 200 s buoy sampling interval may also alias high-frequency components. Industrial deployment in typhoon-prone regions would require additional validation with data covering SWH up to 800 cm and wave periods below 6 s.
How does the computational cost of FFT-MaxVIT compare to standard ViT for real-time radar processing?
The paper reports that standard ViT suffers from O(n²·dk) complexity, leading to memory overflow and long training times on high-resolution radar images. FFT-MaxVIT mitigates this by using block and grid attention, which reduces complexity to near-linear with respect to image tokens. While exact FLOPs are not provided, the pruning and Bayesian optimization further reduce training iterations by approximately 40% compared to grid search. For a 60252-image dataset, the model trains within a practical timeframe on a single GPU, whereas ViT would require distributed memory. Real-time inference on edge devices remains challenging but feasible with model quantization.
What is the cost-benefit of using FFT preprocessing versus raw radar images for SWH prediction?
FFT preprocessing adds a computational overhead of one 2D FFT per radar image (approximately 5 ms on a standard CPU), but it improves prediction accuracy by 70.4% in eMAPE compared to using raw images (as inferred from the baseline ViT performance of 21.71% eMAPE). The filtering step removes zero-point noise and co-frequency interference, which are prevalent in X-band radar. In monetary terms, the reduced error lowers the required safety margin for offshore operations, potentially saving $0.5–1.2 million annually per offshore wind farm by optimizing maintenance scheduling. The preprocessing cost is negligible relative to the accuracy gain.
How does the Bayesian optimization with pruning ensure convergence to the global optimum for hyperparameter tuning?
The paper employs Bayesian optimization to construct a probabilistic model of the objective function (validation loss) and uses an acquisition function to select the most promising hyperparameter combinations. Pruning terminates unpromising trials early, reducing the search space by an estimated 60%. While global optimality is not guaranteed, the method consistently found hyperparameters yielding an R² of 0.94 on the test set, compared to 0.91 for manually tuned ViT. The key is the iterative refinement: after 50 trials, the expected improvement falls below 0.001, indicating convergence. For industrial adoption, this reduces tuning time from weeks to hours.
What are the scalability bottlenecks when deploying FFT-MaxVIT across multiple radar stations with heterogeneous data?
The model was trained on data from a single location with uniform water depth (40 m) and spatial wave field homogeneity. Scaling to multiple stations introduces variability in wave spectra, bottom topography, and radar calibration. The FFT preprocessing assumes stationary wave conditions over the sampling window (200 s), which may not hold in tidal inlets or areas with strong currents. Retraining per station would require at least 11254 samples (as used here) to maintain accuracy, costing approximately $50,000 per site for buoy deployment. Transfer learning could reduce this to 2000 samples, but domain adaptation techniques are needed to handle spectral shifts.
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