  The average energy curvature as a function of the particle number is a
molecule-specific quantity, which measures the deviation of a given functional
from the exact conditions of density functional theory (DFT). Related to the
lack of derivative discontinuity in approximate exchange-correlation
potentials, the information about the curvature has been successfully used to
restore the physical meaning of Kohn-Sham orbital eigenvalues and to develop
non-empirical tuning and correction schemes for density functional
approximations. In this work, we propose the construction of a machine-learning
framework targeting the average energy curvature between the neutral and the
radical cation state of thousands of small organic molecules (QM7 database).
The applicability of the model is demonstrated in the context of
system-specific gamma-tuning of the LC-$\omega$PBE functional and validated
against the molecular first ionization potentials at equation-of-motion (EOM)
coupled-cluster references. In addition, we propose a local version of the
non-linear regression model and demonstrate its transferability and predictive
power by determining the optimal range-separation parameter for two large
molecules relevant to the field of hole-transporting materials. Finally, we
explore the underlying structure of the QM7 database with the t-SNE
dimensionality-reduction algorithm and identify structural and compositional
patterns that promote the deviation from the piecewise linearity condition.
