Before revision:  Rather than constructing a low-dimensional subspace for the entire state space in a monolithic fashion---which would be infeasible for extreme-scale systems and decomposable models---the methodology constructs separate subspaces for the different subdomains/components characterizing the original model.
After revision:  Rather than constructing a low-dimensional subspace for the entire state space in a monolithic fashion, the methodology constructs separate subspaces for the different subdomains/components characterizing the original model.