An auxetic lattice structure with a negative Poisson's ratio has excellent energy absorption and high fracture toughness.Unlike conventional metamaterials with Poisson's ratio, the auxetic lattice structure has been used in various fields from biomechanics to industrial structural applications to improve mechanical properties.We aim to optimize the design parameters of the auxetic unit cell to minimize the stress concentrations on the surface of the metamaterial based on the analysis of the compressive mechanical behavior of the auxetic lattice structure.After parametrizing the design variables for three types of re-entrant structures, the maximum stress on the structure surface and the Poisson's ratio of the structure was measured through a finite element (FE) parametric study.The results of the FE parametric study were used as training and prediction data to construct an artificial neural network (ANN)-based FE surrogate model.Using the design optimization with a deep neural network (DNN)-based surrogate model, we proposed insights into the design parameters of the auxetic unit cell that minimize the surface stress concentrations.