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

Computer Science > Machine Learning [Submitted on 26 Mar 2026] Pure and Physics-Guided Deep Learning Solutions for Spatio-Temporal Groundwater Level Prediction at Arbitrary Locations Matteo Salis, Gabriele Sartor, Rosa Meo, Stefano Ferraris, Abdourrahmane M. Atto 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. Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI) Cite as: arXiv:2603.25779 [cs.LG]   (or arXiv:2603.25779v1 [cs.LG] for this version)   https://doi.org/10.48550/arXiv.2603.25779 Focus to learn more Submission history From: Matteo Salis [view email] [v1] Thu, 26 Mar 2026 15:57:08 UTC (71,687 KB) Access Paper: HTML (experimental) view license Current browse context: cs.LG < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.AI References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)