Serravalle Reis Rodrigues Vitor Hugo, de Melo Barros Junior Paulo Roberto, Dos Santos Marinho Euler Bentes, Lima de Jesus Silva Jose Luis
Geological Survey of Brazil - SGB, Avenida Ulysses Guimarães, 2862 Centro Administrativo da Bahia, Salvador, BA, 1649-026, Brazil.
Petrobras, Petróleo Brasileiro S.A, Av. Repúlica do Chile, No 65 Centros, Rio de Janeiro, 20031-912, Brazil.
Sci Rep. 2023 Aug 5;13(1):12726. doi: 10.1038/s41598-023-39688-0.
Developing accurate models for groundwater control is paramount for planning and managing life-sustaining resources (water) from aquifer reservoirs. Significant progress has been made toward designing and employing deep-forecasting models to tackle the challenge of multivariate time-series forecasting. However, most models were initially taught only to optimize natural language processing and computer vision tasks. We propose the Wavelet Gated Multiformer, which combines the strength of a vanilla Transformer with the Wavelet Crossformer that employs inner wavelet cross-correlation blocks. The self-attention mechanism (Transformer) computes the relationship between inner time-series points, while the cross-correlation finds trending periodicity patterns. The multi-headed encoder is channeled through a mixing gate (linear combination) of sub-encoders (Transformer and Wavelet Crossformer) that output trending signatures to the decoder. This process improved the model's predictive capabilities, reducing Mean Absolute Error by 31.26 % compared to the second-best performing transformer-like models evaluated. We have also used the Multifractal Detrended Cross-Correlation Heatmaps (MF-DCCHM) to extract cyclical trends from pairs of stations across multifractal regimes by denoising the pair of signals with Daubechies wavelets. Our dataset was obtained from a network of eight wells for groundwater monitoring in Brazilian aquifers, six rainfall stations, eleven river flow stations, and three weather stations with atmospheric pressure, temperature, and humidity sensors.
开发精确的地下水控制模型对于规划和管理含水层水库中维持生命的资源（水）至关重要。在设计和应用深度预测模型以应对多变量时间序列预测挑战方面已经取得了重大进展。然而，大多数模型最初仅被训练用于优化自然语言处理和计算机视觉任务。我们提出了小波门控多变换器，它将普通变换器的优势与采用内部小波互相关块的小波交叉变换器相结合。自注意力机制（变换器）计算内部时间序列点之间的关系，而互相关则找到趋势周期性模式。多头编码器通过子编码器（变换器和小波交叉变换器）的混合门（线性组合）进行引导，这些子编码器将趋势特征输出到解码器。这一过程提高了模型的预测能力，与评估的第二好的类变换器模型相比，平均绝对误差降低了31.26%。我们还使用了多重分形去趋势互相关热图（MF-DCCHM），通过用Daubechies小波对一对信号进行去噪，从多重分形区域的成对站点中提取周期性趋势。我们的数据集来自巴西含水层中用于地下水监测的八口井、六个降雨站、十一个河流流量站以及三个配备气压、温度和湿度传感器的气象站组成的网络。
