Pure and Physics-Guided Deep Learning Solutions for Spatio-Temporal Groundwater Level Prediction at Arbitrary Locations
Groundwater is a crucial component of the water cycle, yet its modeling presents significant challenges due to its intricate and context-dependent relationships. Traditional theory-based models have long served as the foundation of scientific understanding in this field. However, these models often come with high computational demands, simplifying assumptions, and a need for extensive calibration, which can limit their practical application.
In recent years, the emergence of data-driven models has provided powerful alternatives for groundwater level prediction. Among these, deep learning has gained prominence due to its design flexibility and capacity to learn complex relationships from data. In this context, we introduce an innovative attention-based deep learning model, named STAINet, specifically designed to predict weekly groundwater levels across an arbitrary and variable number of locations. This model utilizes both spatially sparse groundwater measurements and spatially dense weather information to enhance prediction accuracy.
Physics-Guided Strategies for Enhanced Model Trustworthiness
To further bolster the model’s reliability and generalization capabilities, we explored various physics-guided strategies aimed at integrating the groundwater flow equation into the deep learning framework. The following approaches were developed:
- STAINet-IB: This variant introduces an inductive bias to the model, allowing it to estimate key components of the governing groundwater flow equation.
- STAINet-ILB: By adopting a learning bias strategy, this model is trained with additional loss terms that provide supervision on the estimated equation components, enhancing its predictive performance.
- STAINet-ILRB: This approach leverages expert-estimated information about the groundwater body recharge zones, further refining the model’s predictions.
Results and Implications
Among these models, the STAINet-ILB emerged as the most effective, achieving remarkable test performance in a rollout setting with a median Mean Absolute Percentage Error (MAPE) of 0.16% and a Kling-Gupta Efficiency (KGE) of 0.58. Furthermore, the model successfully predicted physically sensible equation components, which provided valuable insights into its physical validity.
The integration of physics-guided approaches represents a significant advancement in the field of groundwater modeling, offering promising opportunities to enhance both the generalization ability and trustworthiness of deep learning models. This innovative methodology paves the way for the development of a new generation of disruptive hybrid deep learning Earth system models, which can potentially transform our understanding and management of groundwater resources.
As the demand for accurate groundwater predictions continues to grow amidst changing climate conditions and increasing human activity, the STAINet models may serve as critical tools for researchers and policymakers alike, facilitating more effective water resource management and sustainability efforts.