With this contribution, the aim is to incorporate and evaluate the uncertainty in multiscale structural analyses. The material properties of composites (e.g., concrete, spinoidal structures) consequently depend on structural parameters and actual realizations of the composite mesostructures. Uncertainties on the mesoscale lead to uncertain behavior on the macroscale. Based on scale separation and following the current homogenization methods, a surrogate model is introduced, which enables the uncertainty quantification of macroscopic structures based on uncertainties at the mesoscale. Through the usage of Neural Networks (NN)s as surrogate models for the composite material, sampling-based uncertainty quantification schemes are enabled in large elastic deformations. A formulation of NNs that incorporates physical information of hyperelastic materials in the network structure is used and expanded with uncertain parameters to further reduce the information needed for the training of the NN. The proposed procedure enables the consideration of aleatoric, epistemic, and polymorphic uncertainty. For the training of the NN, a domain separation is proposed, which allows the efficient pre-training of the neural network.