🤖 AI Summary
Solving the Richards equation in unsaturated soils faces challenges including strong nonlinearity, high computational cost, and difficulty in ensuring mass conservation. To address these, this paper proposes a Data-driven Random Walk (DRW) numerical method. Within a finite-volume framework, DRW innovatively integrates adaptive linearization, physics-informed neural networks, and global random-walk sampling to achieve efficient and stable solutions. Theoretical analysis establishes convergence of DRW in n-dimensional domains. Experiments demonstrate that DRW significantly outperforms state-of-the-art algorithms and commercial solvers in solution accuracy, physical fidelity, and mass conservation, while maintaining exceptional stability and computational robustness. As a result, DRW provides a highly reliable modeling tool for dynamic monitoring of root-zone soil moisture.
📝 Abstract
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.