# A Hybrid Deep Learning Model Based on FFT-STL Decomposition for Ocean Wave Height Prediction
## 1 Introduction  
Wave height is closely related to various human activities [1]. On the one hand, wave height plays a vital role in marine operations, directly affecting the safety and efficiency of ship navigation and marine operations [2, 3]. Accurate prediction of wave height is essential to ensure navigation safety and optimize marine operations [4]. Therefore, in-depth research on wave height dynamics and improving forecast accuracy is of great significance to improving the safety and efficiency of marine activities. On the other hand, waves are a promising renewable energy source that helps alleviate energy shortages [5]. Reliable wave height forecasting is essential to optimize wave energy conversion and ensure the stability and efficiency of wave energy utilization. Therefore, based on the two pressing issues of protecting human activities and promoting renewable energy, the study of wave height prediction is urgent. Over the years, various methodologies have been developed to enhance the accuracy and reliability of wave height forecasting. Traditional approaches, such as numerical wave models and hydrodynamic models, have been widely used for their ability to simulate wave dynamics based on meteorological and oceanographic data. [PERSON] and [PERSON] (2024) developed a numerical wave model, experimentally verified the collinear wave-current interaction, and extended it to the non-collinear scenario through theoretical verification, while studying the orthogonal interaction observation region [6]. [PERSON] et al. (2025) systematically verified and validated the numerical wave pool based on momentum source and quantified the numerical modeling errors under 13 sea states [7]. To investigate the hydrodynamics ofthe main channel, Khenifiss lagoon, [PERSON] and [PERSON] (2024) integrated hydrodynamic models with existing hydrological data and utilized them as a comprehensive tool in the flood modeling process [8]. Although these models can effectively simulate complex fluid dynamics to predict ocean wave height variations, their accuracy in capturing local wave behavior is often limited by the quality of input data and computational limitations. To overcome the limitations of traditional numerical wave models, which depend on high-quality input data, researchers have increasingly adopted data-driven approaches for wave height prediction. In particular, autoregressive models, neural networks, and ensemble learning methods have emerged as prominent techniques in this field. Autoregressive (AR) models, which employ linear combinations of historical observations to predict future values, have served as fundamental tools in wave height forecasting due to their mathematical transparency and computational efficiency [9; 10]. Many scholars have applied the SARIMA model to make long-term predictions of significant wave height and achieved good prediction performance [11; 12]. However, these methods are fundamentally affected by the strict assumption of stationarity and linear parameterization, which in turn limits their ability to effectively capture the nonlinear dynamics and nonstationary properties inherent in complex ocean processes. Neural networks have the ability to learn and extract complex patterns from large amounts of data. Through training, neural networks can identify the inherent laws and associations in data, provide model-free solutions for data prediction, and improve tolerance to data errors [13]. This understanding has promoted the application and development of neural networks, among which recurrent neural networks (RNNs) are similar to autoregressive (AR) models in time-series modeling in terms of recursive characteristics, but have stronger nonlinear expression capabilities. Many scholars have used RNN models to predict changes in ocean wave height. Studies have found that wave prediction using RNNs produces better results than previous neural network methods [14].