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Estimating Soil Hydraulic Parameters for Unsaturated Flow Using Physics-Informed Neural Networks

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Computational Science – ICCS 2024 (ICCS 2024)

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Abstract

Water movement in soil is essential for weather monitoring, prediction of natural disasters, and agricultural water management. Richardson-Richards’ equation (RRE) is the characteristic partial differential equation for studying soil water movement. RRE is a non-linear PDE involving water potential, hydraulic conductivity, and volumetric water content. This equation has underlying non-linear parametric relationships called water retention curves (WRCs) and hydraulic conductivity functions (HCFs). This two-level non-linearity makes the problem of unsaturated water flow of soils challenging to solve. Physics-Informed Neural Networks (PINNs) offer a powerful paradigm to combine physics in data-driven techniques. From noisy or sparse observations of one variable (water potential), we use PINNs to learn the complete system, estimate the parameters of the underlying model, and further facilitate the prediction of infiltration and discharge. We employ training on RRE, WRC, HCF, and measured values to resolve two-level non-linearity directly instead of explicitly deriving water potential or volumetric water content-based formulations. The parameters to be estimated are made trainable with initialized values. We take water potential data from simulations and use this data to solve the inverse problem with PINN and compare estimated parameters, volumetric water content, and hydraulic conductivity with actual values. We chose different types of parametric relationships and wetting conditions to show the approach’s effectiveness.

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Notes

  1. 1.

    The code is available at https://github.com/cvjena/InverseRRE.

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Acknowledgements

This research is funded by the Federal Ministry for Economic Affairs and Climate Actions (BMWK) for the project titled LuFo VI-2 Melodi 20E2115B. We also thank Bandai et al. [3] and Ireson et al. [12] for their open-source simulation codes.

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Authors and Affiliations

  1. Computer Vision Group, Friedrich Schiller University Jena, 07743, Jena, Germany

    Sai Karthikeya Vemuri, Tim Büchner & Joachim Denzler

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  1. Sai Karthikeya Vemuri
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Correspondence to Sai Karthikeya Vemuri .

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Editors and Affiliations

  1. University of Malaga, Malaga, Spain

    Leonardo Franco

  2. University of Amsterdam, Amsterdam, The Netherlands

    Clélia de Mulatier

  3. AGH University of Science and Technology, Krakow, Poland

    Maciej Paszynski

  4. University of Amsterdam, Amsterdam, The Netherlands

    Valeria V. Krzhizhanovskaya

  5. University of Tennessee, Knoxville, TN, USA

    Jack J. Dongarra

  6. University of Amsterdam, Amsterdam, The Netherlands

    Peter M. A. Sloot

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Vemuri, S.K., Büchner, T., Denzler, J. (2024). Estimating Soil Hydraulic Parameters for Unsaturated Flow Using Physics-Informed Neural Networks. In: Franco, L., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2024. ICCS 2024. Lecture Notes in Computer Science, vol 14834. Springer, Cham. https://doi.org/10.1007/978-3-031-63759-9_37

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