Abstract: Soil moisture is a key hydrological parameter that has significant importance to human society and environment. Accurate modeling and monitoring of soil moisture in crop fields, especially in the root zone (top 100 cm of soil), is essential for improving agricultural production and crop yield with the help of precision irrigation and farming tools. Unfortunately, state-of-the-art soil moisture modeling and monitoring practices face several technical challenges. For instance, existing lab-based soil property measurement techniques are not applicable for modeling and monitoring soil moisture dynamics in the crop field due to scale mismatch. Furthermore, directly solving the complex hydrological models (e.g., Richards equation) for soil moisture dynamics characterization is computationally demanding and has not found a way to be integrated with actual soil moisture sensor measurements. To tackle these challenges, in this work, we propose a physics-constrained deep learning (P-DL) framework to achieve 1) an efficient solution of the Richards equation, 2) effective reconstruction of the soil moisture dynamics, and 3) accurate recovery of soil properties in a nonparametric form. We adopt three different optimizers, namely Adam, RMSprop, and SGD, to minimize the loss function of P-DL during the training process. In an illustrative case study, we demonstrate the empirical convergence of these optimizers and compare their effectiveness in minimizing the loss function.
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