The main idea of potential energy surface fits, and the way in which they go beyond conventional force fields, is that the potential energy is explicitly written as a generic function of all atomic degrees of freedom, without making assumptions about separability (e.g. into body ordered terms such as bond and angle potentials). Thus the fit to the potential energy is high dimensional. The basis functions for the fit have to be of a kind that allow systematic convergence to the a priori unknown target potential energy surface, and this has consequences for the attainable accuracy as a function of the amount of input data, for transferability to configurations far away from the distribution from which the training configurations were drawn, as well as for the overall cost of evaluation of the potential energy fit. Typically the high dimensional fits are significantly more expensive to evaluate than the short range terms of a conventional force field, though they are still of course much cheaper than a QM calculation, or the evaluation of the electrostatic potential of a large system that includes a protein and explicit solvent molecules.