# A Hybrid Deep Learning Model Based on FFT-STL Decomposition for Ocean Wave Height Prediction
## 1 Introduction
However, the practical effectiveness of RNNs is constrained by gradient pathology issues during backpropagation through time, which manifests itself as vanishing gradients suppressing long-range memory or explosion gradients destabilizing training [15]. These critical limitations were systematically addressed by long short-term memory (LSTM) networks through innovative gated cell architectures, which explicitly regulate information flow via forget/input/output gates to preserve multi-scale temporal dependencies essential for wave evolution modeling. [PERSON] et al. (2025) predicted wave height by establishing an LSTM model [16]. [PERSON] et al. (2021) applied an LSTM-based hybrid model to predict wave height and period under near-ideal wave growth conditions in Lake Erie [17]. In ocean data modeling, the traditional unidirectional long short-term memory network can capture the lagged effects of historical wave heights, but has limitations in explaining the delayed effects of future meteorological changes on current wave conditions [18]. To overcome this limitation, this study uses the BiLSTM model for trend component forecasting, which can capture the forward and backward temporal dependencies in the time series. In order to improve the accuracy of the calculation, two independent LSTMs are combined. One model processes the sequence forwards in chronological order, and the other model processes the sequence in reverse chronological order to form a new model BiLSTM. [PERSON] et al. (2024) [19] proposed an innovative ocean wave height prediction model, RIME-CNN-BiLSTM. The model combines the RIME algorithm, CNN and BiLSTM. Compared with traditional models, the model can more accurately grasp the complex nonlinear characteristics between these factors and wave height, and it shows stronger generalization performance in different sea areas. [PERSON] and [PERSON] (2024) used a bidirectional long short-term memory network to process forward and reverse time-series data, in order to more comprehensively extract the temporal dynamic characteristicsof wave height [20]. This bidirectional architecture breaks through the limitation that the traditional unidirectional long short-term memory model can only capture the temporal dependency in a single direction, thus helping to more accurately understand the change of wave height over time. Although traditional methods for the prediction of wave height have achieved certain results, recent research has achieved significant breakthroughs in model accuracy and applicability by adopting innovative technical means. Numerous studies have shown that hybrid modeling methods that incorporate prior knowledge, such as fluid dynamics equations, into a machine learning framework exhibit powerful wave height prediction capabilities [21; 22]. However, due to the inherent multi-scale characteristics of complex ocean systems, these models still face significant limitations in capturing high-frequency fluctuations and long-range temporal dependencies. In addition, some other methods, such as the design of new neural network architecture, feature enhancement technology based on integrated signal processing and so on. Some scholars have proposed a new deep learning model. This model uses the variable importance measure of random forests and the ability of graph neural networks to extract long-term temporal features to construct an adaptive weight matrix to capture potential spatial dependencies and long-term temporal patterns in input data [23]. [PERSON] et al. (2023) applied empirical mode decomposition to wave signals and merged the resulting intrinsic mode functions into the original dataset, using a feature extraction module combined with a self-attention network to improve the prediction of significant wave height [24]. However, the prediction performance of this model on small-scale datasets may not be well generalized to large-scale scenarios. Its scalability and effectiveness in capturing complex spatiotemporal dependencies under large-scale data conditions still need to be verified.