  For the past several decades, numerous attempts have been made to model the
climate of Mars with extensive studies focusing on the planet's dynamics and
the understanding of its climate. While physical modeling and data assimilation
approaches have made significant progress, uncertainties persist in
comprehensively capturing and modeling the complexities of Martian climate. In
this work, we propose a novel approach to Martian climate modeling by
leveraging machine learning techniques that have shown remarkable success in
Earth climate modeling. Our study presents a deep neural network designed to
accurately model relative humidity in Gale Crater, as measured by NASA's Mars
Science Laboratory ``Curiosity'' rover. By utilizing simulated meteorological
variables produced by the Mars Planetary Climate Model, a robust Global
Circulation Model, our model accurately predicts relative humidity with a mean
error of 3\% and an $R^2$ score of 0.92. Furthermore, we present an approach to
predict quantile ranges of relative humidity, catering to applications that
require a range of values. To address the challenge of interpretability
associated with machine learning models, we utilize an interpretable model
architecture and conduct an in-depth analysis of its internal mechanisms and
decision making processes. We find that our neural network can effectively
model relative humidity at Gale crater using a few meteorological variables,
with the monthly mean surface H$_2$O layer, planetary boundary layer height,
convective wind speed, and solar zenith angle being the primary contributors to
the model predictions. In addition to providing a fast and efficient method to
modeling climate variables on Mars, this modeling approach can also be used to
expand on current datasets by filling spatial and temporal gaps in
observations.
