Water flow analysis in unsaturated soils using physics-informed neural networks

Abstract

Conventional deep learning models do not always follow physical conditions such as governing equations in their predictions. Physics-Informed Neural Networks (PINNs) add physical loss terms to the loss function to evaluate whether the predictions are satisfied with the governing equations and initial and boundary conditions, in addition to a prediction loss term to evaluate the error between the predictions and the training data when learning deep learning models. Conventional numerical inverse analysis to estimate soil hydraulic properties requires appropriate settings for boundary and initial conditions. One novel example that allows more flexible condition setting than process-based models is an inverse analysis method using PINNs. PINNs, given training data on pressure head and/or volumetric water content and the Richards equation as a governing equation, can predict changes in pressure head over time and the soil hydraulic property profiles. This paper describes examples of PINNs used both in forward and inverse analysis of variably saturated water flow in soils. Finally, we summarize some recent studies using PINNs in the field of soil physics and future issues.