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\begin{document}

\title{Effective Characterization of Fractured Media with PEDL: A Deep
Learning-Based Data Assimilation Approach}



\author[1]{Tongchao Nan}%
\author[1]{Jiangjiang Zhang}%
\author[1]{Yifan Xie}%
\author[1]{Chenglong Cao}%
\author[2]{Jichun Wu}%
\author[1]{Chunhui Lu}%
\affil[1]{Hohai University}%
\affil[2]{Nanjing University}%


\vspace{-1em}



  
  \date{May 17, 2024}


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\begin{abstract}
In various research fields such as hydrogeology, environmental science
and energy engineering, geological formations with fractures are
frequently encountered. Accurately characterizing these fractured media
is of paramount importance when it comes to tasks that demand precise
predictions of liquid flow and the transport of solute and energy within
them. Since directly measuring fractured media poses inherent
challenges, data assimilation (DA) techniques are typically employed to
derive inverse estimates of media properties using observed state
variables like hydraulic head, concentration, and temperature.
Nonetheless, the considerable difficulties arising from the strong
heterogeneity and non-Gaussian nature of fractured media have diminished
the effectiveness of existing DA methods. In this study, we formulate a
novel DA approach known as PEDL (parameter estimator with deep learning)
that harnesses the capabilities of DL to capture nonlinear relationships
and extract non-Gaussian features. To evaluate PEDL's performance, we
conduct two numerical case studies with increasing complexity. Our
results unequivocally demonstrate that PEDL outperforms three popular DA
methods: ensemble smoother with multiple DA (ESMDA), iterative local
updating ES (ILUES), and ES with DL-based update (ESDL). Sensitivity
analyses confirm PEDL's validity and adaptability across various
ensemble sizes and DL model architectures. Moreover, even in scenarios
where structural difference exists between the accurate reference model
and the simplified forecast model, PEDL adeptly identifies the primary
characteristics of fracture networks.%
\end{abstract}%



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