Novel physics informed-neural networks for estimation of hydraulic conductivity of green infrastructure as a performance metric by solving Richards–Richardson PDE

Green infrastructure (GI) is an ecologically informed approach to stormwater management that is potentially sustainable and effective. Infiltration-based GI systems, including rain gardens, permeable pavements, green roofs infiltrate surface water and stormwater run-off to recharge ground water systems. However, these systems are susceptible to clogging and deterioration of their function, and we have limited understanding of the evolution of their function due to the lack of long-term monitoring. The ability of these systems to infiltrate water depends on the unsaturated hydraulic conductivity function K of the soil. We introduce a novel approach based on physics informed neural networks (PINNs) to estimate K of a homogeneous column of soil using data from volumetric water content sensors and by solving the Richards–Richardson partial differential equation (RRE). We introduce and compare two different deep neural network architectures to solve RRE and estimate K. To generate the ground truth, we simulate three types of soil water dynamics using HYDRUS-1D and compare the results of these two neural network architectures in terms of the estimation of K. We investigate the effect of inter-sensor placement on the estimation of K. Both architectures show satisfactory performance on homogeneous soil with three volumetric water content sensors with different advantages. PINN-based estimation of K can be used fundamental tool for assessment of the evolution of the performance of GI over time, while requiring as input only the data from simple soil moisture sensors that are easily installed at the time of GI construction or even retrofitted.