  Progress in machine learning has facilitated the development of potentials
that offer both the accuracy of first-principles techniques and vast increases
in the speed of evaluation. Recently,"$\Delta$-machine learning" has been used
to elevate the quality of a potential energy surface (PES) based on low-level,
e.g., density functional theory (DFT) energies and gradients to close to the
gold-standard coupled cluster level of accuracy. We have demonstrated the
success of this approach for molecules, ranging in size from H$_3$O$^+$ to
15-atom acetyl-acetone and tropolone. These were all done using the B3LYP
functional. Here we investigate the generality of this approach for the PBE,
M06, M06-2X, and PBE0+MBD functionals, using ethanol as the example molecule.
Linear regression with permutationally invariant polynomials is used to fit
both low-level and correction PESs. These PESs are employed for standard RMSE
analysis for training and test datasets, and then general fidelity tests such
as energetics of stationary points, normal mode frequencies, and torsional
potentials are examined. We achieve similar improvements in all cases.
Interestingly, we obtained significant improvement over DFT gradients where
coupled cluster gradients were not used to correct the low-level PES. Finally,
we present some results for correcting a recent molecular mechanics force field
for ethanol and comment on the possible generality of this approach.
