Pure and Physics-Guided Deep Learning Solutions for Spatio-Temporal Groundwater Level Prediction at Arbitrary Locations

2026-03-26

AI Summary

Groundwater level prediction is governed by complex spatiotemporal processes, posing challenges for traditional physics-based models—often computationally expensive and overly simplified—and purely data-driven approaches, which frequently lack physical consistency. To address this, this work proposes the STAINet family of hybrid models that integrate sparse groundwater observations with dense meteorological data to enable weekly-scale predictions at arbitrary locations via an attention mechanism. Crucially, the groundwater flow equation is incorporated into the deep learning framework through three novel strategies: inductive bias (IB), learnable physics-informed loss (ILB), and expert-delineated recharge zone constraints (ILRB). Experimental results demonstrate that STAINet-ILB achieves the best performance in rolling forecasts, attaining a median test-set MAPE of 0.16% and a KGE of 0.58, while faithfully reproducing components of the governing physical equations, thereby ensuring both high accuracy and physical plausibility.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Natural Language Processing: Language Grounding & Multi-modal NLP
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Web Mining and Content Analysis: Large pretrained models with web data
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Groundwater represents a key element of the water cycle, yet it exhibits intricate and context-dependent relationships that make its modeling a challenging task. Theory-based models have been the cornerstone of scientific understanding. However, their computational demands, simplifying assumptions, and calibration requirements limit their use. In recent years, data-driven models have emerged as powerful alternatives. In particular, deep learning has proven to be a leading approach for its design flexibility and ability to learn complex relationships. We proposed an attention-based pure deep learning model, named STAINet, to predict weekly groundwater levels at an arbitrary and variable number of locations, leveraging both spatially sparse groundwater measurements and spatially dense weather information. Then, to enhance the model's trustworthiness and generalization ability, we considered different physics-guided strategies to inject the groundwater flow equation into the model. Firstly, in the STAINet-IB, by introducing an inductive bias, we also estimated the governing equation components. Then, by adopting a learning bias strategy, we proposed the STAINet-ILB, trained with additional loss terms adding supervision on the estimated equation components. Lastly, we developed the STAINet-ILRB, leveraging the groundwater body recharge zone information estimated by domain experts. The STAINet-ILB performed the best, achieving overwhelming test performances in a rollout setting (median MAPE 0.16%, KGE 0.58). Furthermore, it predicted sensible equation components, providing insights into the model's physical soundness. Physics-guided approaches represent a promising opportunity to enhance both the generalization ability and the trustworthiness, thereby paving the way to a new generation of disruptive hybrid deep learning Earth system models.

Problem

• groundwater level prediction
• spatio-temporal modeling
• physics-guided deep learning
• data-driven modeling
• hydrological modeling

Innovation

• physics-guided deep learning
• attention mechanism
• groundwater level prediction
• hybrid modeling
• spatio-temporal modeling