Determine the origin of the ML correction’s size-dependent contribution

Determine whether the size-dependent contribution produced by the semilocal machine-learning correction is primarily determined by compensation of parent-functional errors or by the semilocal form learned by the neural network.

Background

The paper applies the same global-loss semilocal machine-learning correction to PBE, B3LYP, SCAN, and r²SCAN. Along the n-alkane series, the correction contributes an approximately linear change in atomization-energy error for every parent functional, with nearly perfect Pearson correlations. For PBE and B3LYP, the learned contribution partially compensates for the parent functional’s size-dependent error, whereas for SCAN and r²SCAN it introduces a substantially larger size-dependent contribution than is present in the parent functional.

The authors compare the correction slopes with training-set biases and find essentially no correlation between the magnitude of the learned slope and either the magnitude of the training-set error or the reduction in training loss. Because only four parent functionals are studied, the data do not resolve whether the observed size dependence reflects parent-error compensation or an intrinsic consequence of the semilocal neural-network representation.