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Physics-informed neural networks with monotonicity constraints for Richardson-Richards equation: Estimation of constitutive relationships and soil water flux density from volumetric water content measurements
  • Toshiyuki Bandai,
  • Teamrat Ghezzehei
Toshiyuki Bandai
University of California, Merced, University of California, Merced

Corresponding Author:[email protected]

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Teamrat Ghezzehei
University of California Merced, University of California Merced
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Water retention curves (WRCs) and hydraulic conductivity functions (HCFs) are critical soil-specific characteristics necessary for modeling the movement of water in soils using the Richardson-Richards equation (RRE). Well-established laboratory measurement methods of WRCs and HCFs are not usually unsuitable for simulating field-scale soil moisture dynamics because of the scale mismatch. Hence, the inverse solution of the RRE is used to estimate WRCs and HCFs from field measured data. Here, we propose a physics-informed neural networks (PINNs) framework for the inverse solution of the RRE and the estimation of WRCs and HCFs from only volumetric water content (VWC) measurements. Unlike conventional inverse methods, the proposed framework does not need initial and boundary conditions. The PINNs consists of three linked feedforward neural networks, two of which were constrained to be monotonic functions to reflect the monotonicity of WRCs and HCFs. Alternatively, we also tested PINNs without monotonicity constraints. We trained the PINNs using synthetic VWC data with artificial noise, derived by a numerical solution of the RRE for three soil textures. The PINNs were able to reconstruct the true VWC dynamics. The monotonicity constraints prevented the PINNs from overfitting the training data. We demonstrated that the PINNs could recover the underlying WRCs and HCFs in non-parametric form, without a need for initial guess. However, the reconstructed WRCs at near-saturation–which was not fully represented in the training data–was unsatisfactory. We additionally showed that the trained PINNs could estimate soil water flux density with a broader range of estimation than the currently available methods.
Feb 2021Published in Water Resources Research volume 57 issue 2. 10.1029/2020WR027642