Wavelet gated multiformer for groundwater time series forecasting

Area of Science:

• Hydrogeology
• Data Science
• Time Series Analysis

Background:

• Accurate groundwater level prediction is crucial for sustainable water resource management.
• Deep learning models, particularly Transformers, show promise for multivariate time-series forecasting but require adaptation for hydrological data.
• Existing models often lack the ability to capture complex periodic patterns inherent in hydrological systems.

Purpose of the Study:

• To develop and evaluate a novel deep learning model, the Wavelet Gated Multiformer, for enhanced groundwater level forecasting.
• To integrate wavelet analysis with Transformer architecture for improved time-series prediction.
• To assess the model's performance against existing methods using real-world hydrological data.

Main Methods:

• Proposed the Wavelet Gated Multiformer, integrating a vanilla Transformer with a Wavelet Crossformer using inner wavelet cross-correlation blocks.
• Employed a multi-headed encoder with a mixing gate combining Transformer's self-attention and Wavelet Crossformer's periodicity detection.
• Utilized Multifractal Detrended Cross-Correlation Heatmaps (MF-DCCHM) with Daubechies wavelets for signal denoising and trend extraction.

Main Results:

• The Wavelet Gated Multiformer demonstrated superior predictive capabilities, reducing Mean Absolute Error by 31.26% compared to leading Transformer-like models.
• The model effectively captured complex temporal dependencies and cyclical patterns in groundwater data.
• MF-DCCHM analysis successfully identified multifractal cross-correlations and cyclical trends between monitoring stations.

Conclusions:

• The Wavelet Gated Multiformer offers a significant advancement in groundwater forecasting accuracy.
• Combining wavelet analysis with Transformer architectures is a promising approach for hydrological time-series modeling.
• The developed methodology provides a robust tool for managing vital aquifer resources.