Self-attention hierarchical kernel reservoir state network for inland water level prediction

Waterway transportation sustainably facilitates global trade through eco-efficient cargo movement, where accurate water level forecasting is critical for ensuring navigational safety and operational continuity. To develop a highly accurate prediction model, it is essential to consider the periodic characteristics of water level data, which often emerge in real-world datasets. This study introduces a novel reservoir state structure based on reservoir computing theory, the Self-attention Hierarchical Kernel Reservoir State Network (SHK-RSN). It employs three primary mechanisms. First, a hierarchical feature extraction method groups training data and extracts high-dimensional features from these groups using the kernel trick in a hierarchical manner. Second, a self-attention weight selection approach is introduced to replace the random weights in the Hierarchical Kernel Reservoir State Network (HK-RSN), improving the rationale for hidden neuron connections and enhancing the interpretability of weight selection. Third, a novel reservoir state structure is proposed to capture periodic information and extract temporal features across periods, enabling the model to capture richer temporal information and identify relationships among periods. Experiments are conducted on one artificial and five real-world time series datasets, with forecast performance evaluated over 1–7 steps. Our proposed model, SHK-RSN, is compared with models based on randomization, the kernel trick, and deep learning. The experimental results demonstrate that SHK-RSN exhibits superior forecasting ability relative to the baselines. It achieves the best Symmetric Mean Absolute Percentage Error (SMAPE) across all datasets in the 1–7 period average among baseline methods, demonstrating a relative improvement of 25.7% to 46.9% over the conventional Echo State Network.