  In this paper we investigate the cosmological effects of modified gravity
with string curvature corrections added to Einstein-Hilbert action in the
presence of a dynamically evolving scalar field coupled to Riemann invariants.
The scenario exhibits several features of cosmological interest for late
universe. It is shown that higher order stringy corrections can lead to a class
of dark energy models consistent with recent observations. The model can give
rise to quintessence, deSitter or phantom dark energy, in last case without
recourse to negative kinetic energy field. The detailed treatment of
reconstruction program for general scalar-Gauss-Bonnet gravity is presented for
any given cosmology. The explicit examples of reconstructed scalar potentials
are given for accelerated (quintessence, cosmological constant or phantom)
universe. Finally, the relation with modified $F(G)$ gravity is established on
classical level and is extended to include third order terms on curvature.
