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\begin{document}

\title{Physics-Informed Neural Networks with New Activation Function and
Multi-Objective Optimization for Improving Estimation of Soil Hydraulic
Properties}



\author[1]{Jize Fan}%
\author[2]{Xiaofei Yan}%
\author[1]{Qiang Cheng}%
\affil[1]{China Agricultural University}%
\affil[2]{Beijing Forestry University}%


\vspace{-1em}



  
  \date{June 16, 2024}


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\selectlanguage{english}
\begin{abstract}
While physics-informed neural networks (PINNs) can solve the problem
pertaining to the absence of boundary conditions in soil water systems,
their results exhibit low accuracy primarily due to insufficient
utilization of the available prior knowledge regarding soil hydraulic
parameters. In this research, an improved PINNs framework is proposed,
which introduces an optimizable saturated hydraulic conductivity into
the activation function, and an advanced optimization strategy is
developed to identify the optimal superparameters for the
multi-objective loss function. The PINNs was trained using synthetic
volumetric soil water content (VSWC) and soil matric potential (SMP)
data generated by a numerical solution of the Richardson-Richards
equation (RRE) for three soil types (silt loam, loam and sandy loam).
The results show that the proposed framework increases the accuracy of
SMP estimations in the unsaturated soil system. The results reveal that
the relative error achieved by the proposed framework in loam or silt
loam has been reduced by two orders of magnitude in comparison with that
achieved by the framework introduced by Bandai and Ghezzehei (2020),
indicating a significant improvement. While there is a slight reduction
in the accuracy of volumetric soil water content estimation, this minor
reduction has minimal practical significance. Both the soil water
retention curve and the soil hydraulic conductivity exhibit superior
performance at the near-saturation scale. For unsaturated flow in
homogeneous soil, the proposed PINNs framework provides accurate
estimations of soil hydraulic parameters and holds significant potential
for the practical application and widespread adoption of PINNs in the
realm of soil hydrodynamics.%
\end{abstract}%



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\textbf{Hosted file}

\verb`Physics-Informed Neural Networks with New Activation Function and Multi-Objective Optimization for Improving Estimation of Soil Hydraulic Properties.docx`  available at \url{https://authorea.com/users/771743/articles/856073-physics-informed-neural-networks-with-new-activation-function-and-multi-objective-optimization-for-improving-estimation-of-soil-hydraulic-properties}

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