Numerical modeling and optimization of advanced composite materials can require huge computational effort when considering their heterogeneous mesostructure and interactions between different material phases within the framework of multiscale modeling. Employing machine learning methods for computational homogenization enables the reduction of computational effort for the evaluation of the mesostructural behavior while retaining high accuracy. Classically, one unit cell with representative characteristics of the material is chosen for the description of the heterogeneous structure, which presents a simplification of the actual composite. This contribution presents a neural network-based approach for computational homogenization of composite materials with the ability to consider arbitrary compositions of the mesostructure. Therefore, various statistical volume elements and their respective constitutive responses are evaluated. Thereby, the naturally occurring fluctuation within the composition of the phases can be considered. Different approaches using distinct metrics to represent the arbitrary mesostructures are investigated in terms of required computational effort and accuracy.