Abstract
Soil moisture is an essential variable for many applications, such as agricultural irrigation, water resources management, and natural disasters, such as landslides and droughts. With the advancement of measurement technology, a vast amount of soil moisture date is available from ground-based sensors and remote sensing. How can we extract information from such big data? My perspective is that soil moisture data should be analyzed based on a known physical model through the framework of inverse modeling. In the dissertation, I explored the inverse modeling of soil moisture dynamics based on the Richardson-Richards equation (RRE) via techniques recently developed in applied mathematics. I investigated the application of a neural network-based inverse method called physics-informed neural networks (PINNs). I demonstrated that PINNs with domain decomposition could approximate the solution to the RRE for layered soils by comparing PINNs with the analytical solutions. Secondly, I conducted the inverse modeling of soil hydraulic properties from upward infiltration experiments using the Peters-Durner-Iden (PDI) model. I demonstrated that the PDI model better captured soil moisture dynamics for dry conditions than the commonly used van Genuchten-Mualem model. Finally, I discuss the estimation of surface water flux from soil moisture measurements through an adjoint method. I compared the adjoint method with PINNs and demonstrated that both methods gave comparable results for small scale problems, while the adjoint method was more robust than PINNs for a data-limited case.

Biography
Toshiyuki Bandai is a Ph.D. candidate in the Environmental Systems graduate group at University of California, Merced. He joined Professor Teamrat A. Ghezzehei's soil physics lab in 2018 and worked on inverse modeling of soil moisture dynamics. He received his B.Sc. and M.Sc. in Biological and Environmental Engineering from the University of Tokyo, Japan. He was a summer intern at the Lawrence Berkeley National Laboratory in 2022. He is interested in both biological and artificial neural networks.