Recent advances in Scientific Machine Learning, particularly Physics-Informed Neural Networks (PINNs), have greatly improved our ability to model complex dynamical systems like groundwater flow as described by Richards' equation. This study focuses on the use of PINNs to robustly estimate soil hydraulic parameters and accurately simulate moisture content distributions under conditions of measurement noise and data uncertainty. We use a coupled PINN approach to solve Richards' hydrological equations while incorporating observational constraints. The explicit integration of noise modeling into the training process, which employs both static and time-dependent noise generation methods, is an important aspect of this study. This strategy ensures that the PINN model is robust and reliable even in noisy and uncertain data. In addition, petrophysical relationships (such as Archie's law) are used as constraints to improve the physical consistency and stability of parameter estimation. This integrated neural network architecture, combined with advanced noise handling methods, significantly improves groundwater modeling accuracy and reliability over traditional computational methods. The developed methodologies and codes, which use TensorFlow and DeepXDE frameworks, provide practical tools for environmental monitoring and groundwater management, significantly improving our ability to deal with real-world uncertainties and noise in hydrological modeling.