This study introduces a deep learning framework to accelerate multiscale finite element analysis (FE2) based on the data-driven mechanics and data augmentation [1]. To overcome inefficiency of conventional concurrent FE2 [2] induced by repetitive analysis at each macroscopic integration point, a distance-minimizing data-driven computational mechanics approach [3] is adopted within the proposed deep learning framework. The key innovation lies in leveraging a neural network for adaptive sampling points without prior knowledge of the mechanical problem. Specifically, the sparse offline database (the macroscopic stress and strain) is directly obtained using nonlinear finite element homogenization analysis of the representative volume element (RVE). Using the distance-minimizing algorithm, macroscopic strain and stress solutions are derived, representing the closest dataset to mechanistic constraints (i.e., equilibrium and compatibility equations) within the neural network constitutive dataset of macroscopic strain and stress. The proposed deep learning framework plays a key role in identifying suitable solution points, guiding the data augmentation process to minimize constraints and perform RVE calculations selectively for those strains. Consequently, the iterative process discovers solution points beyond the initial data, facilitating improved prediction performance for specific mechanical problems.