Predicting water movement in unsaturated soil using physics-informed deep operator networks

Accurate modeling of soil water movement in the unsaturated zone is essential for effective soil and water resources management. Physics-informed neural networks (PINNs) offer promising potential for this purpose, but necessitate retraining upon changes in initial or boundary conditions, posing a challenge when adapting to variable natural conditions. To address this issue, inspired by the operator learning with more universal applicability than function learning, we develop a physics-informed deep operator network (PI-DeepONet), integrating physical principles and observed data, to simulate soil water movement under variable boundary conditions. In the numerical case, PI-DeepONet achieves the best performance among three modeling strategies when predicting soil moisture dynamics across different testing areas, especially for the extrapolation one. Guided by both data and physical mechanisms, PI-DeepONet demonstrates greater accuracy than HYDRUS in capturing spatio-temporal moisture variations in real-world scenario. Furthermore, PI-DeepONet successfully infers constitutive relationships and reconstructs missing boundary flux condition from limited data by incorporating known prior physical information, providing a unified solution for both forward and inverse problems. This study is the first to develop a PI-DeepONet specifically for modeling real-world soil water movement, highlighting its potential to improve predictive accuracy and reliability in vadose zone modeling by combining data-driven approaches with physical principles.