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Self-attention hierarchical kernel reservoir state network for inland water level prediction
(2026-01-15)
Liu, Zongying
;
Xu, Xiaohan
;
Pasupa, Kitsuchart
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Loo, Chu Kiong
;
Wei, Yang
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.
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MS-PatchTST: Leveraging Multi-Scale Temporal Features for Water Level Forecasting
(2025-01-01)
Zhang, Dong
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Pasupa, Kitsuchart
;
Liu, Zongying
;
Pan, Mingyang
Accurate water level forecasting is essential for navigation, enabling safe sailing, effective drought management, optimized route planning, and efficient port operations. However, traditional statistical approaches and conventional machine learning models often struggle to capture adaptive, multi-scale temporal features, thereby limiting forecasting accuracy. In recent years, patch-based forecasting methods have demonstrated strong capabilities in modeling consecutive temporal features. Building on this foundation, we propose Multi-Scale PatchTST (MS-PatchTST), a framework designed to enhance the perception of multi-scale information. The model incorporates a newly developed multi-scale parallel convolutional network (Multi-Scale ConvNet) to extract interaction features across different time scales. These features are then fused through a Transformer Encoder with relative positional encoding to capture temporal dependencies more effectively. Finally, the kernel mean squared error loss function is employed in place of the conventional mean squared error loss, improving the optimization process and enhancing overall training performance. Experiments on four real-world water level datasets demonstrate that MS-PatchTST consistently outperforms state-of-the-art baselines, achieving an average reduction of approximately 13% in both MAE and SMAPE compared with PatchTST.
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Weighted error-output recurrent Xavier echo state network for concept drift handling in water level prediction
(2024-11-01)
Liu, Zongying
;
Zhang, Wenru
;
Pan, Mingyang
;
Loo, Chu Kiong
;
Pasupa, Kitsuchart
Water level holds utmost significance in maritime domains. Precise water level predictions furnish indispensable insights for safe maritime navigation, guiding ships and vessels through passages, harbors, and waterways. This paper introduces a novel approach: the Weighted Error-Output Recurrent Xavier Echo State Network with Adaptive Forgetting Factor (WER-XESN-AFF). One of the contributions of this study is the introduction of the Xavier weights selection method, which replaces random weight selection from the Echo State Network (ESN). This method not only enhances forecasting performance but also reduces uncertainty in predictions. Additionally, two modified concept drift detectors, the Early Drift Detection Method and the Adaptive Forgetting Factor, are employed to address concept drift challenges. Another notable contribution is the introduction of a novel weighted error-output recurrent multi-step algorithm. This algorithm successfully overcomes the error accumulation problem by using past forecast errors to update current output weights. This study performs extensive experiments to evaluate the effectiveness of our approach in multi-step prediction in synthetic and real datasets. It compares the performance between the conventional randomization-based models and the ESN with the new weights selection approach and also tests the ability of concept drift detectors and the weighted error-output multi-step algorithm. Empirical findings and statistical analyses demonstrate that our proposed methods achieve expected effects, and the proposed model has better prediction ability than baselines. A significant improvement rate of 75.39% in Mean Squared Error is evident within the Jiujiang water level dataset when contrasting the performance of WER-XESN-AFF against the baseline model R-ESN across the 1–5 period.

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