Modeling Water Flow and Contaminant Transport in Unsaturated Soil by Artificial Intelligence

Abstract

The water flow in unsaturated soil is typically represented by Richardson-Richards Equation (RRE), while solute transport is often described by Advection-Diffusion Equation (ADE). These two equations are fundamental for addressing problems in water and waste resources management but are challenging to solve because of their input-data requirements and inherent non-linearities. RRE's nonlinearity arises from the strong dependence of material properties (hydraulic conductivity and gradient of water retention curve) on state variables (soil water content and pore pressure), which can cause convergence issues in numerical solutions. Additionally, solving RRE requires water retention curve (WRC), which is time-consuming and difficult to measure. While pedo-transfer functions (PTF) for estimating WRC from easily measurable soil properties have been developed, uncertainties remain about the most relevant soil properties required. ADE, for its part, depends on output from the RRE (water content and seepage velocities) and is challenging to solve under advection-dominated scenarios (high Peclet number) in which spurious numerical oscillations may occur. Recent advances in AI offer potentially innovative solutions to these challenges. The universal approximation capabilities of AI provide a new approach to estimating complex relationships. Furthermore, machine learning methods can incorporate physics-based constraints, enabling models to perform well even with limited data. This new class of machine learning algorithm is called Physics-Informed Neural Networks (PINN) and has been shown to be effective in solving complex partial differential equations. Very recently, new hard-constraint PINN approaches based on strict enforcement of boundary conditions, have been proposed but are yet to be explored in the context of this thesis. This thesis advances the modeling of water flow and solute transport in unsaturated soils through the application of the above AI techniques.