This work focuses on the development of machine learning strategies for modeling mechanical metamaterials designed to absorb and dissipate energy in vibrating structures. The dissipation mechanism is driven by the elastic buckling of periodic lattice microstructures, which are modeled using beam elements under the assumptions of small strains and large displacements. By capturing these complex instabilities, the metamaterial can effectively mitigate vibrations transmitted from external sources. To bypass the prohibitive computational costs of traditional multiscale strategies, we implement a surrogate modeling framework to perform data-driven homogenization. Using Gaussian Processes (GP), the surrogate model successfully captures the nonlinear behavior of the microstructure, predicting the Piola-Kirchhoff stress tensor directly from the macroscopic strain tensor. A significant advantage of this approach is the ability to obtain the tangent stiffness matrix through analytical derivation of the surrogate model. This allows the homogenized microstructural response to be seamlessly integrated into macro-scale simulations, ensuring high-fidelity results without the need for costly computational multiscale iterations. Furthermore, replacing the expensive microscopic simulations with an ML surrogate facilitates microstructure topology optimization to maximize macroscopic energy dissipation at a feasible computational cost. The precision of the Gaussian Process model is rigorously controlled by evaluating the uncertainty of the posterior distribution of the energy function relative to the strain tensor. This uncertainty quantification enables an active learning approach, where sampling points are strategically added to the training set in regions where the model’s confidence is lowest. Finally, a comparative analysis between different machine learning architectures, including Artificial Neural Networks, demonstrates that Gaussian Processes offer a more robust and straightforward implementation for this class of nonlinear mechanical problems.