Physics-informed neural networks (PINNs) with unsaturated water flow models for inverse analysis of soil hydraulic parameters of layered soil profiles

Information about the spatial distribution of soil hydraulic parameters is necessary for the accurate prediction of soil water flow and coupled movement of chemicals and heat at the field scale using a process-based model. Physics-informed neural networks (PINNs), which can provide physical constraints in deep learning to obtain a mesh-free solution, can be used to inversely estimate the soil hydraulic parameters from less and noisy training data. Previous studies using PINNs have successfully estimated soil hydraulic parameters for homogeneous soil but estimating such parameters of layered soil profiles where the interface depth and the parameters are unknown still has some difficulties. The objective of this study was to develop PINNs to inversely estimate the distribution of soil hydraulic parameters, such as saturated hydraulic conductivity and α and n, of the Mualem-van Genuchten model directly within layered soil profiles by predicting changes in pressure head from training data based on simulation results at given depths during infiltration. The impact of factors affecting PINNs performance, such as the weights assigned to each component of the loss function, the time range used in error computations, and the number of samples used to assess physical constraint was investigated. By assigning a larger weight to the physical constraint and excluding the earlier stage of infiltration in the loss function, the changes in pressure head and the three soil hydraulic parameter distributions within the layered soil profiles were successfully estimated. The developed PINNs can be further applied to more complex soils and can be improved.