Preprints

2024

1. 

   Physics-constrained Active Learning for Soil Moisture Estimation and Optimal Sensor Placement

   Jianxin Xie, Bing Yao, and Zheyu Jiang

   2024

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   Soil moisture is a crucial hydrological state variable that has significant importance to the global environment and agriculture. Precise monitoring of soil moisture in crop fields is critical to reducing agricultural drought and improving crop yield. In-situ soil moisture sensors, which are buried at pre-determined depths and distributed across the field, are promising solutions for monitoring soil moisture. However, high-density sensor deployment is neither economically feasible nor practical. Thus, to achieve a higher spatial resolution of soil moisture dynamics using a limited number of sensors, we integrate a physics-based agro-hydrological model based on Richards equation in a physics-constrained deep learning framework to accurately predict soil moisture dynamics in the soil’s root zone. This approach ensures that soil moisture estimates align well with sensor observations while obeying physical laws at the same time. Furthermore, to strategically identify the locations for sensor placement, we introduce a novel active learning framework that combines space-filling design and physics residual-based sampling to maximize data acquisition potential with limited sensors. Our numerical results demonstrate that integrating Physics-constrained Deep Learning (P-DL) with an active learning strategy within a unified framework–named the Physics-constrained Active Learning (P-DAL) framework - significantly improves the predictive accuracy and effectiveness of field-scale soil moisture monitoring using in-situ sensors.

   @misc{jianxin2024pdl,
     title = {Physics-constrained Active Learning for Soil Moisture Estimation and Optimal Sensor Placement},
     author = {Xie, Jianxin and Yao, Bing and Jiang, Zheyu},
     year = {2024},
     eprint = {2403.07228},
     archiveprefix = {arXiv},
     primaryclass = {eess.SP},
     doi = {https://doi.org/10.48550/arXiv.2403.07228},
   }

2023

1. 

   A Novel Data-driven Numerical Method for Hydrological Modeling of Water Infiltration in Porous Media

   Zeyuan Song, and Zheyu Jiang

   2023

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   Root-zone soil moisture monitoring is essential for sensor-based smart irrigation and agricultural drought prevention. Modeling the spatiotemporal water flow dynamics in porous media such as soil is typically achieved by solving an agro-hydrological model, the most important of which being the Richards equation. In this paper, we present a novel data-driven solution algorithm named the DRW (Data-driven global Random Walk) algorithm, which holistically integrates adaptive linearization scheme, neural networks, and global random walk in a finite volume discretization framework. We discuss the need and benefits of introducing these components to achieve synergistic improvements in solution accuracy and numerical stability. We show that the DRW algorithm can accurately solve n-dimensional Richards equation with guaranteed convergence under reasonable assumptions. Through examples, we also demonstrate that the DRW algorithm can better preserve the underlying physics and mass conservation of the Richards equation compared to state-of-the-art solution algorithms and commercial solver.

   @misc{song2023datafacilitated,
     title = {A Novel Data-driven Numerical Method for Hydrological Modeling of Water Infiltration in Porous Media},
     author = {Song, Zeyuan and Jiang, Zheyu},
     year = {2023},
     eprint = {2310.02806},
     archiveprefix = {arXiv},
     primaryclass = {math.NA},
     doi = {https://doi.org/10.48550/arXiv.2310.02806},
   }