Reconstructing unsaturated infiltration behavior with sparse data via physics-informed deep learning

In this paper, we propose a novel framework, physics-informed deep learning (PIDL), which combines a set of data- and physics-driven modeling methods along with an uncertainty assessment technique, to solve the ill-posed inverse problems in unsaturated infiltration and make plausible moisture field predictions. Specifically, PIDL integrates three methods: physics-informed neural network (PINN), multi-fidelity PINN (MF-PINN), and Monte Carlo dropout (MC-dropout). Firstly, we accurately predict the unsaturated infiltration behaviors using a PINN model, based on the Richards equation (RE) and a specific set of sparse and noisy observation data. Besides, in the presence of undetermined parameters within the soil–water characteristic curve, it is plausible to simultaneously ascertain those parameters. Subsequently, in cases where the available high-fidelity (HF) observation data are excessively sparse, the MF-PINN method can serve as an alternative to the PINN method for accurately predicting infiltration behavior by assimilating a certain quantity of easily accessible low-fidelity (LF) data. Finally, we apply the MC-dropout to investigate the uncertainty of the PINN and MF-PINN predicted results, and provide the corresponding credible intervals. We demonstrate the PIDL’s efficacy with three unsaturated infiltration models and an on-site drainage case. This study offers a fresh perspective on addressing the inverse problems of unsaturated infiltration.