  Periodic driving of optical lattices has enabled the creation of novel
bandstructures not realizable in static lattice systems, such as topological
bands for neutral particles. However, especially driven systems of interacting
bosonic particles often suffer from strong heating. We have systematically
studied heating in an interacting Bose-Einstein condensate in a driven
one-dimensional optical lattice. We find interaction-dependent heating rates
that depend both on the scattering length and the driving strength and identify
the underlying resonant intra- and interband scattering processes. By comparing
experimental data and theory, we find that for driving frequencies well above
the trap depth, the heating rate is dramatically reduced by the fact that
resonantly scattered atoms leave the trap before dissipating their energy into
the system. This mechanism of Floquet evaporative cooling offers a powerful
strategy to minimize heating in Floquet engineered quantum gases.
