A machine learning based multi-scale method is proposed for modeling anisotropic damage in quasi-brittle composite structures. This approach uses the results of damage simulations on Representative Volume Elements (RVEs), at the microscopic scale, as data to build a surrogate model describing the behavior law and macroscopic internal variables evolution. Damage computations on the scale of the RVE are carried out in a preliminary stage (off-line calculations) using the Phase field method [1]. At each loading increment, a numerical homogenization technique [2] is applied to evaluate the effective elastic tensor of the RVE. A harmonic analysis of the elastic tensor evolution during crack propagation simulations in the RVE (DDHAD method - Data Driven Harmonic Analysis of Damage [3, 4]) is used to define the macroscopic internal variables. Their evolution is modeled by an appropriate machine-learning-based surrogate model. Machine learning is applied to construct the behavior law and the internal variables evolution, as a surrogate model to be used, at the macroscopic scale. Applications to periodic quasi-brittle composites with strongly anisotropic microstructures are presented.