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<p>Based on data time-frequency analysis theory and nonlinear spatiotemporal sequence modeling, in this study, the spatiotemporal interactions between different sites were evaluated while removing noise effects. Moreover, by integrating wavelet analysis with recurrent neural networks, we developed a wavelet-denoised, Huber loss function-enhanced spatiotemporal sequence multi-value, multistep prediction model employing an extended gated recurrent unit (RNN-BiGRU), termed WD-HRNN-BiGRU. The selected study area was Minqin County, which faces water overextraction and declining water levels. Based on monthly groundwater-level (GWL) data spanning over 240 months from 61 local monitoring stations, we established the WD-HRNN-BiGRU model. The model’s core is a multisite collaborative forecasting unit that takes the historical time series of 50 stations as input and outputs 20-month-ahead GWL predictions for the other 11 stations. The model achieved simultaneous 20-month-ahead predictions for all 61 stations. Further, the flexible iterative framework enabled the model to infer sequences for any site in the study region through learned spatiotemporal dependencies from other sites. Moreover, the results of comparative experiments demonstrate the model’s superiority. It demonstrated marked improvements in the mean squared error, coefficient of determination (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R^2\)</EquationSource> </InlineEquation>), and mean absolute error. Compared with baseline models using conventional time series methods, WD-HRNN-BiGRU achieved a 422% improvement in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(R^2\)</EquationSource> </InlineEquation> predictive performance. When benchmarked against wavelet-denoised multi-variable and multistep prediction models (e.g., LSTM, BiGRU), it achieved an average <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(R^2\)</EquationSource> </InlineEquation> performance gain of 28.3%. Thus, it possesses marked advantages in prediction accuracy and robustness, and its future extensions framework can support large-scale clustered multisite prediction to achieve more efficient, precise forecasting systems.</p>

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WD-HRNN-BiGRU: A Novel Spatiotemporal Sequence Multi-Value Prediction Model

  • 期刊论文

  • 发表日期：

    2026年2月26日

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  • Zhongrong Zhang,
  • Junyan Sun,
  • Yulin Shen,
  • Kang Lin,
  • Yijia Liu,
  • Jisheng Li

摘要

Based on data time-frequency analysis theory and nonlinear spatiotemporal sequence modeling, in this study, the spatiotemporal interactions between different sites were evaluated while removing noise effects. Moreover, by integrating wavelet analysis with recurrent neural networks, we developed a wavelet-denoised, Huber loss function-enhanced spatiotemporal sequence multi-value, multistep prediction model employing an extended gated recurrent unit (RNN-BiGRU), termed WD-HRNN-BiGRU. The selected study area was Minqin County, which faces water overextraction and declining water levels. Based on monthly groundwater-level (GWL) data spanning over 240 months from 61 local monitoring stations, we established the WD-HRNN-BiGRU model. The model’s core is a multisite collaborative forecasting unit that takes the historical time series of 50 stations as input and outputs 20-month-ahead GWL predictions for the other 11 stations. The model achieved simultaneous 20-month-ahead predictions for all 61 stations. Further, the flexible iterative framework enabled the model to infer sequences for any site in the study region through learned spatiotemporal dependencies from other sites. Moreover, the results of comparative experiments demonstrate the model’s superiority. It demonstrated marked improvements in the mean squared error, coefficient of determination ( \(R^2\) ), and mean absolute error. Compared with baseline models using conventional time series methods, WD-HRNN-BiGRU achieved a 422% improvement in \(R^2\) predictive performance. When benchmarked against wavelet-denoised multi-variable and multistep prediction models (e.g., LSTM, BiGRU), it achieved an average \(R^2\) performance gain of 28.3%. Thus, it possesses marked advantages in prediction accuracy and robustness, and its future extensions framework can support large-scale clustered multisite prediction to achieve more efficient, precise forecasting systems.