  Spectral lines allow us to probe the thermodynamics of the solar atmosphere,
but the shape of a single spectral line may be similar for different
thermodynamic solutions. Multiline analyses are therefore crucial, but
computationally cumbersome. We investigate correlations between several
chromospheric and transition region lines to restrain the thermodynamic
solutions of the solar atmosphere during flares. We used machine-learning
methods to capture the statistical dependencies between 6 spectral lines
sourced from 21 large solar flares observed by NASA's Interface Region Imaging
Spectrograph (IRIS). The techniques are based on an information-theoretic
quantity called mutual information (MI), which captures both linear and
nonlinear correlations between spectral lines. The MI is estimated using both a
categorical and numeric method, and performed separately for a collection of
quiet Sun and flaring observations. Both approaches return consistent results,
indicating weak correlations between spectral lines under quiet Sun conditions,
and substantially enhanced correlations under flaring conditions, with some
line-pairs such as Mg II and C II having a normalized MI score as high as 0.5.
We find that certain spectral lines couple more readily than others, indicating
a coherence in the solar atmosphere over many scale heights during flares, and
that all line-pairs are correlated to the GOES derivative, indicating a
positive relationship between correlation strength and energy input. Our
methods provide a highly stable and flexible framework for quantifying
dependencies between the physical quantities of the solar atmosphere, allowing
us to obtain a three-dimensional picture of its state.
