Accurate modeling of water flow and solute transport in unsaturated soils is of significant importance for precision agriculture, environmental protection and aquifer management. Traditional modeling approaches are considerably challenging since they require well-defined boundaries and initial conditions. Physics-informed neural networks (PINNs) have recently been developed to learn and solve forward and inverse problems also constrained to a set of partial differential equations and are more flexible than traditional modeling approaches. However, hydrological applications of PINNs used so far spatial measurements of hydraulic head, water content and/or solute concentrations, which were well distributed in the subsurface for training the system. Such measurements are hard to obtain in real-world applications. Here, we propose to train PINNs with non-invasive geoelectrical tools for simulating two-dimensional water flow and solute transport during infiltration and redistribution processes with unknown initial conditions. Two-dimensional flow and transport numerical simulations were used as benchmarks to examine the suitability of the described approach. Results have shown that the trained PINNs system was able to reproduce the spatiotemporal distribution of both water content and pore-water salinity during both processes with high accuracy, using five time-lapse geoelectrical measurements and matric head measurements at a single location. The trained PINNs system reconstructed the initial conditions of both state parameters at both processes. It was also able to separate the measured electrical signal into its two components, that is, water content and pore-water salinity. The subsurface geoelectrical tomograms were significantly improved compared to those obtained from a classical inversion of the raw geoelectrical data.
- electrical resistivity tomography
- physics-informed neural networks
- unsaturated flow and transport