  Inverse engineering of electric fields has been recently proposed to achieve
fast and robust spin control in a single-electron quantum dot with spin-orbit
coupling. In this paper we design, by inverse engineering based on
Lewis-Riesenfeld invariants, time-dependent electric fields to realize fast
transitions in the selected singlet-triplet subspace of a two-electron double
quantum dot. We apply two-mode driving schemes, directly employing the
Lewis-Riesenfeld phases, to minimize the electric field necessary to design
flexible protocols and perform spin manipulation on the chosen timescale.
