Modeling water flow in unsaturated soils through physics-informed neural network with principled loss function

Modeling water flow in unsaturated soils is crucial in geotechnical practice. Nowadays, the physics informed neural network (PINN) is gaining popularity in solving the Richardson Richards equation (RRE) thanks to its mesh-free, physics-constrained, and data-driven properties. Despite several successful applications in modelling 1D infiltration problems, its capability and stability to deal with more complicated boundary conditions and multidimensional problems still need to be examined. This paper investigates the impacts of the loss weights and random state on the performance of the RRE-solving PINNs and possible solutions to mitigate such impacts. Two loss-balanced PINNs, GN-PINN and PLF-PINN, were compared to the baseline PINN in modelling three unsatu-rated groundwater flow problems. The results show that the performance of the baseline PINN severely depends on the loss weight configurations and random states. While GN-PINN's tendency to ignore the train loss term makes it infeasible for solving RRE, PLF-PINN can strike a good balance between loss terms and hence enhance PINN's robustness against loss weight initialization and random state greatly.