  We construct Landau-Ginzburg models for numerically effective complete
intersections in toric manifolds as partial compactifications of families of
Laurent polynomials. We show a mirror statement saying that the quantum
D-module of the ambient part of the cohomology of the submanifold is isomorphic
to an intersection cohomology D-module defined from this partial
compactification and we deduce Hodge properties of these differential systems.
