The complex nanostructure of open-porous materials presents a significant challenge for simulating their mechanical properties. Traditional computational methods that explicitly account for the nanostructured morphology and subsequent numerical simulations are computationally expensive. To overcome this limitation, multiscale numerical homogenization approaches are commonly employed to account for the coupling effects of a heterogeneous nanostructure and macroscopic deformations. Based on the well-established FE^2 method [1] we apply a homogenization approach which couples the nanostructure with a finite element solver at the macroscopic scale. For open-porous materials, such as aerogels, modelling the representative volume element (RVE) as a beam frame model has proven to be suitable [2]. However, computing the microscopic problem for typical nanostructures requires solving many large systems of equations. Replacing the microscopic beam frame model with a computationally cheaper surrogate model yields significant potential for reducing the computational effort of the homogenization method. Machine learning techniques are used to train a model which predicts the resulting average stress in an RVE for a given macroscopic deformation [3]. The independence of the individual microscopic problems from one another allows for simple parallelization of the computations on the microscopic scale.