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\begin{document}

\title{Interpretable Framework of Physics-guided Neural Network for Water
temperature Simulation}



\author[1]{Wenpeng Xie}%
\author[2]{Masaomi Kimura}%
\author[3]{Xiaowei Jia}%
\author[1]{Kyoji Takaki}%
\affil[1]{The University of Tokyo}%
\affil[2]{Kindai University}%
\affil[3]{University of Pittsburgh}%


\vspace{-1em}



  
  \date{May 18, 2024}


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\selectlanguage{english}
\begin{abstract}
With the development of large-scale rice cultivation management
initiatives in East Asia, there is concern that a reduction in the
number of human cultivators per unit area may lead to poor water
management, which could result in decreased land productivity, owing to
abnormal high- and low-temperature damage to crops. Accurate simulation
of paddy field water temperature is important for studying its impact on
crops and for providing timely information to aid in decision making for
more efficient management under limited resources. We propose a
neural-network framework that considers the heat transfer by the
vegetation canopy and applies physical-theory constraints in its
training. A novel tuning method is proposed to cope with the trade-off
between water temperature accuracy and physical consistency during
training to ensure that the calculated water temperature variations in a
paddy field enjoy high accuracy and physical consistency. In the
experiments, the proposed framework outperforms (with RMSE 0.78\selectlanguage{ngerman}°C) both
physical process models (with RMSE 1.06°C) and pure neural-network
models (with RMSE 0.9°C) while maintaining high accuracy in the case of
sparse datasets. Furthermore, an attention-mechanism input layer is
integrated into the model to rank feature importance, providing global
interpretation to the proposed framework. We also perform sensitivity
analysis on the physical process and propose models to compare their
different strategies of feature ranking. The results show that the two
methods have different sensitivities to different types of feature
patterns, but they complement each other. In summary, the proposed model
is credible and stable for practical applications and has the potential
to guide more efficient paddy management.%
\end{abstract}\selectlanguage{ngerman}%



\sloppy


\textbf{Interpretable Framework of Physics-guided Neural Network for
Water temperature Simulation}

With the development of large-scale rice cultivation management
initiatives in East Asia, there is concern that a reduction in the
number of human cultivators per unit area may lead to poor water
management, which could result in decreased land productivity, owing to
abnormal high- and low-temperature damage to crops. Accurate simulation
of paddy field water temperature is important for studying its impact on
crops and for providing timely information to aid in decision making for
more efficient management under limited resources. We propose a
neural-network framework that considers the heat transfer by the
vegetation canopy and applies physical-theory constraints in its
training. A novel tuning method is proposed to cope with the trade-off
between water temperature accuracy and physical consistency during
training to ensure that the calculated water temperature variations in a
paddy field enjoy high accuracy and physical consistency. In the
experiments, the proposed framework outperforms (with RMSE 0.78\selectlanguage{ngerman}°C) both
physical process models (with RMSE 1.06°C) and pure neural-network
models (with RMSE 0.9°C) while maintaining high accuracy in the case of
sparse datasets. Furthermore, an attention-mechanism input layer is
integrated into the model to rank feature importance, providing global
interpretation to the proposed framework. We also perform sensitivity
analysis on the physical process and propose models to compare their
different strategies of feature ranking. The results show that the two
methods have different sensitivities to different types of feature
patterns, but they complement each other. In summary, the proposed model
is credible and stable for practical applications and has the potential
to guide more efficient paddy management.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/essoar/essoar}

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\end{figure}

\selectlanguage{english}
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