One way of achieving moduli stabilization for KK-compactifications of string theory backgrounds is to consider higher gauge fields in the compact space. Their higher field strength/curvature forms parameterize mass terms for the compactification moduli and hence can, under suitable conditions, stabilize them.
A good survey of the story of flux compactifications in F-theory is in
Barton Zwiebach, A first course in string theory
R. Blumenhagen, A. Deser, E. Plauschinn, F. Rennecke, Bianchi identities for non-geometric fluxes: from quasi-Poisson structures to Courant algebroids, arXiv:1205.1522