A Comparative Analysis of Numerical Inversion and Physics-Informed Neural Networks for Estimating Soil Hydraulic Properties in Peatlands

Understanding soil hydraulic properties is essential for accurately modelling water flow and storage in peatlands, where hydrological processes mainly driven by the shallow water table play a critical role in carbon dynamics and ecosystem functions. However, conventional laboratory methods for determining these properties often face significant challenges due to the highly compressible, heterogeneous, and anisotropic nature of peat. These limitations motivate the use of inverse modelling approaches, where effective hydraulic parameters are estimated by fitting models to observed field data. In this study, we focused on a historically drained peatland site in the Hautes Fagnes (Belgium), utilizing in-situ TDR sensors to monitor water content. Given the limited information of field data in nearly saturated conditions, we first applied a global optimization approach using HYDRUS-1D – which solves Richards' equation coupled with the van Genuchten-Mualem (vGM) model – employing the Shuffled Complex Evolution algorithm (SCE-UA) to estimate three key effective hydraulic parameters (α, n and Ks). Building on this, we explored a novel Physics-Informed Neural Network (PINN) method, embedding Richards' equation directly into the network architecture to integrate physical process knowledge with data-driven learning. The PINN architecture was initially validated with synthetic data and subsequently applied to real-world measurements to assess its performance under practical constraints. Current results indicate that the SCE-UA approach provides accurate parameter estimates within an acceptable range, demonstrating robustness even with limited data. While the PINN method shows promise, particularly without knowledge of initial and boundary conditions, further fine-tuning is needed to fully leverage its potential. This study highlights both the reliability of traditional numerical inversion and the exciting opportunities offered by machine learning frameworks for advancing peatland hydrological modelling.