We propose a simple scheme to estimate the potential energy surface (PES) for which the accuracy can be easily controlled and improved. It is based on model selection within the framework of linear regression using the least absolute shrinkage and selection operator (LASSO) technique. Basis functions are selected from a systematic large set of candidate functions. The sparsity of the PES significantly reduces the computational cost of evaluating the energy and force in molecular dynamics simulations without losing accuracy. The usefulness of the scheme for describing the elemental metals Na and Mg is clearly demonstrated.