  Machine Learning (ML) has become a promising tool for improving the quality
of atomistic simulations. Using formaldehyde as a benchmark system for
intramolecular interactions, a comparative assessment of ML models based on
state-of-the-art variants of deep neural networks (NN), reproducing kernel
Hilbert space (RKHS+F), and kernel ridge regression (KRR) is presented.
Learning curves for energies and atomic forces indicate rapid convergence
towards excellent predictions for B3LYP, MP2, and CCSD(T)-F12 reference results
for modestly sized (in the hundreds) training sets. Typically, learning curve
off-sets decay as one goes from NN (PhysNet) to RKHS+F to KRR (FCHL).
Conversely, the predictive power for extrapolation of energies towards new
geometries increases in the same order with RKHS+F and FCHL performing almost
equally. For harmonic vibrational frequencies, the picture is less clear, with
PhysNet and FCHL yielding respectively flat learning at $\sim$ 1 and $\sim$ 0.2
cm$^{-1}$ no matter which reference method, while RKHS+F models level off for
B3LYP, and exhibit continued improvements for MP2 and CCSD(T)-F12.
Finite-temperature molecular dynamics (MD) simulations with the same initial
conditions yield indistinguishable infrared spectra with good performance
compared with experiment except for the high-frequency modes involving hydrogen
stretch motion which is a known limitation of MD for vibrational spectroscopy.
For sufficiently large training set sizes all three models can detect
insufficient convergence (``noise'') of the reference electronic structure
calculations in that the learning curves level off. Transfer learning (TL) from
B3LYP to CCSD(T)-F12 with PhysNet indicates that additional improvements in
data efficiency can be achieved.
