Preprints
https://doi.org/10.5194/hess-2022-73
https://doi.org/10.5194/hess-2022-73
 
25 Feb 2022
25 Feb 2022
Status: this preprint is currently under review for the journal HESS.

Forward and inverse modeling of water flow in unsaturated soils with discontinuous hydraulic conductivities using physics-informed neural networks with domain decomposition

Toshiyuki Bandai and Teamrat A. Ghezzehei Toshiyuki Bandai and Teamrat A. Ghezzehei
  • Life and Environemental Science Department, University of California, Merced, Merced, CA, USA

Abstract. Modeling water flow in unsaturated soils is vital for describing various hydrological and ecological phenomena. Soil water dynamics is described by well-established physical laws (Richardson-Richards equation (RRE)). Solving the RRE is difficult due to the inherent non-linearity of the processes, and various numerical methods have been proposed to solve the issue. However, applying the methods to practical situations is very challenging because they require well-defined initial and boundary conditions. Recent advances in machine learning and the growing availability of soil moisture data provide new opportunities for addressing the lingering challenges. Specifically, physics-informed machine learning allows taking advantage of both the known physics and data-driven modeling. Here, we present a physics-informed neural networks (PINNs) method that approximates the solution to the RRE using neural networks while concurrently matching available soil moisture data. Although the ability of PINNs to solve partial differential equations, including the RRE, has been demonstrated previously, its potential applications and limitations are not fully known. This study conducted a comprehensive analysis of PINNs and carefully tested the accuracy of the solutions by comparing them with analytical solutions and accepted traditional numerical solutions. We demonstrated that the solutions by PINNs with adaptive activation functions are comparable with those by traditional methods. Furthermore, while a single neural network (NN) is adequate to represent a homogeneous soil, we showed that soil moisture dynamics in layered soils with discontinuous hydraulic conductivities are correctly simulated by PINNs with domain decomposition (using separate NNs for each unique layer). A key advantage of PINNs is the absence of the strict requirement for precisely prescribed initial and boundary conditions. In addition, unlike traditional numerical methods, PINNs provide an inverse solution without repeatedly solving the forward problem. We demonstrated the application of these advantages by successfully simulating infiltration and redistribution constrained by sparse soil moisture measurements. As a free by-product, we gain knowledge of the water flux over the entire flow domain, including the unspecified upper and bottom boundary conditions. Nevertheless, there remain challenges that require further development. Chiefly, PINNs are sensitive to the initialization of NNs and are significantly slower than traditional numerical methods.

Toshiyuki Bandai and Teamrat A. Ghezzehei

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2022-73', Silvio Gumiere, 24 Mar 2022
    • AC1: 'Reply on RC1', Toshiyuki Bandai, 30 Mar 2022
      • AC3: 'Reply on AC1', Toshiyuki Bandai, 07 Apr 2022
  • RC2: 'Comment on hess-2022-73', Anonymous Referee #2, 04 Apr 2022
    • AC2: 'Reply on RC2', Toshiyuki Bandai, 07 Apr 2022
      • AC4: 'Reply on AC2', Toshiyuki Bandai, 07 Apr 2022
  • RC3: 'Comment on hess-2022-73', Anonymous Referee #3, 22 Apr 2022
    • AC5: 'Reply on RC3', Toshiyuki Bandai, 21 May 2022

Toshiyuki Bandai and Teamrat A. Ghezzehei

Data sets

DD-PINNS-RRE Toshiyuki Bandai and Teamrat A. Ghezzehei https://doi.org/10.5281/zenodo.6030635

Model code and software

DD-PINNS-RRE Toshiyuki Bandai and Teamrat A. Ghezzehei https://doi.org/10.5281/zenodo.6030635

Toshiyuki Bandai and Teamrat A. Ghezzehei

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Short summary
Scientists use a physics-based equation to simulate water dynamics that influence hydrological and ecological phenomena. We present hybrid physics-informed neural networks (PINNs) to leverage the growing availability of soil moisture data and advances in machine learning. We showed that PINNs perform comparably to traditional methods and enable estimating rainfall rates from soil moisture. However, PINNs are challenging to train and significantly slower than traditional methods.