## Physics-informed neural networks with monotocnicity constraints for Richardson-Richards equation–Estimation of constitutive relationships and soil water flux density from volumetric water content measurements.

#### Bandai, Toshiyuki and Ghezzehei, Teamrat

Water Resources Research, volume 57(2), pp. e2020WR027642 , 2021.

### Abstract

Water retention curve (WRC) and hydraulic conductivity function (HCF) are essential information to model the movement of water in the soil using the Richardson-Richards equation (RRE). Although laboratory measurement methods of WRC and HCF have been well established, the lab-based WRC and HCF can not be used to model soil moisture dynamics in the field because of the scale mismatch. Therefore, it is necessary to derive the inverse solution of the RRE and estimate WRC and HCF from field measurement data. We are proposing a physics-informed neural networks (PINNs) framework to obtain the inverse solution of the RRE and estimate WRC and HCF from only volumetric water content measurements. The PINNs was constructed using three feedforward neural networks, two of which were constrained to be monotonic functions to reflect the monotonicity of WRC and HCF. The PINNs was trained using noisy synthetic volumetric water content data derived from the simulation of soil moisture dynamics for three soils with distinct textures. The PINNs could reconstruct the true soil moisture dynamics from the noisy data. As for WRC, the PINN could not precisely determine the WRCs. However, it was shown that the PINNs could estimate the HCFs from only the noisy volumetric water content data without specifying initial and boundary conditions and assuming any information about the HCF (e.g., saturated hydraulic conductivity). Additionally, we showed that the PINNs framework could be used to estimate soil water flux density with a broader range of estimation than the currently available methods.

## Citations

#### Cite as:

Bandai, Toshiyuki and Ghezzehei, Teamrat, Physics-informed neural networks with monotocnicity constraints for Richardson-Richards equation–Estimation of constitutive relationships and soil water flux density from volumetric water content measurements., Water Resources Research, 57(2):e2020WR027642, 2021.

#### BibTex

@article{2020-Bandai,
author = {Bandai, Toshiyuki and Ghezzehei, Teamrat},
title = {Physics-informed neural networks with monotocnicity constraints for Richardson-Richards equation--Estimation of constitutive relationships and soil water flux density from volumetric water content measurements.},
journal = {Water Resources Research},
volume = {57},
number = {2},
pages = {e2020WR027642},
year = {2021},
doi = {10.1029/2020WR027642},
status = {published}
}