  Lattice models are abundant in theoretical and condensed-matter physics.
Generally, lattice models contain time-independent hopping and interaction
parameters that are derived from the Wannier functions of the noninteracting
problem. Here, we present a new concept based on time-dependent Wannier
functions and the variational principle that leads to optimal time-dependent
lattice models. As an application, we use the Bose-Hubbard model with
time-dependent Wannier functions to study a quench scenario involving higher
bands. We find a separation of times scales in the dynamics and show that under
some circumstances the multi-band nonequilibrium dynamics of a quantum system
can be obtained essentially at the cost of a single-band model.
