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\begin{document}

\title{Can Machine Learning Extract Useful Information about Energy Dissipation
and Effective Hydraulic Conductivity from Gridded Conductivity Fields?}



\author[1]{Mohammad A Moghaddam}%
\author[1]{Ty Ferre}%
\author[1]{JEFFREY KLAKOVICH}%
\author[1]{Hoshin Vijai Gupta}%
\author[1]{Mohammad Reza Ehsani}%
\affil[1]{University of Arizona}%


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  \date{May 04, 2024}


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\begin{abstract}
We confirm that energy dissipation weighting provides the most accurate
approach to determining the effective hydraulic conductivity
(K\textsubscript{eff}) of a binary K grid. Machine learning and deep
learning algorithms of varying complexity (decision tree, vanilla CNN,
UNET) can infer K\textsubscript{eff} with extremely high accuracy
(R\textsuperscript{2} \textgreater{} 0.99), even given only the fraction
of the grid occupied by the high K medium. Adding information derived
from the energy dissipation distribution improved each algorithm.
However, all methods failed to infer K\textsubscript{eff} accurately for
outlier cases, all of which were inferred accurately using energy
dissipation weighting directly. The UNET architecture could be trained
to infer the energy dissipation weighting pattern from an image of the K
distribution with high fidelity, although it was less accurate for cases
with highly localized structures that controlled flow. Furthermore, the
UNET architecture learned to infer the energy dissipation weighting even
if it was not trained on this information. However, the weights were
represented within the UNET in a way that was not immediately
interpretable by a human user. This reiterates the idea that even if
ML/DL algorithms are trained to make some hydrologic predictions
accurately, they must be designed and trained to provide each
user-required output if their results are to be used to improve our
understanding of hydrologic systems most effectively.%
\end{abstract}%



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