Clusters, also known as ultra-fine clusters, belong to the scale concept of nanomaterials and represent the initial state of condensed matter. Cluster science is a very important research direction in the field of condensed matter physics. In this paper, for the gold cluster $Au_{20}$ with known structural data, the energy prediction of different structures of $Au_{20}$ is realized by establishing a CatBoost regression prediction model. At the same time, the L-J potential energy function is used to obtain the energy of different structures of $Au_{32}$. Finally, the global maximum between $Au_{20}$ and $Au_{32}$ is obtained by genetic algorithm.