Representation of coupled potential energy surfaces for multiple electronic states has been advanced by means of progress on diabatization methods, which have been reviewed recently. Diabatization enables the study of nonadiabatic processes with nuclear quantum dynamics or with large ensembles of long-time semiclassical nonadiabatic dynamics. Two methods are competing for adoption, namely neural networks and multilinear regression with high-order polynomials. From a supervised-learning perspective, although both are universal, neural networks are gaining a stronger foothold in the field due to their high convenience. However, a notorious drawback for machine-learned potentials is their unreliable behavior when applied to data quite different from that used for training. For example, it's easy for neural-network potentials to acquire unphysical holes or unphysical barriers and/or to have the wrong asymptotic behavior.