  The usage of numerical homogenization to obtain structure-property relations
using the finite element method at both the micro and macroscale has gained
much interest in the research community. However the computational cost of this
so called FE$^2$ method is so high that algorithmic modifications and reduction
methods are essential. Currently the authors proposed a monolithic algorithm.
Now this algorithm is combined with ROM and ECM hyper integration, applied at
finite deformations and complemented by a clustered training strategy, which
lowers the training effort and the number of necessary ROM modes immensely. The
applied methods are modularly combinable as aimed in finite element approaches.
An implementation in terms of an extension for the already established
MonolithFE$^2$ code is provided. Numerical examples show the efficiency and
accuracy of the monolithic hyper ROM FE$^2$ method and the advantages of the
clustered training strategy. Online times of below $1\%$ of the conventional
FE$^2$ method could be gained. In addition the training stage requires around
$3\%$ of that time, meaning that no extremely expensive offline stage is
necessary as in many Neural Network approaches, which only pay off when a lot
of online simulations will be conducted.
