  Root-zone soil moisture monitoring is essential for precision agriculture,
smart irrigation, and drought prevention. Modeling the spatiotemporal water
flow dynamics in soil is typically achieved by solving a hydrological model,
such as the Richards equation which is a highly nonlinear partial differential
equation (PDE). In this paper, we present a novel data-facilitated numerical
method for solving the mixed-form Richards equation. This numerical method,
which we call the D-GRW (Data-facilitated global Random Walk) method,
synergistically integrates adaptive linearization scheme, neural networks, and
global random walk in a finite volume discretization framework to produce
accurate numerical solutions of the Richards equation with guaranteed
convergence under reasonable assumptions. Through three illustrative examples,
we demonstrate and discuss the superior accuracy and mass conservation
performance of our D-GRW method and compare it with benchmark numerical methods
and commercial solver.
