  We develop a flow renormalization approach for periodically-driven quantum
systems, which reveals prethermal dynamical regimes and associated timescales
via direct correspondence between real time and flow time behavior. In this
formalism, the dynamical problem is recast in terms of coupling constants of
the theory flowing towards an attractive fixed point that represents the
thermal Floquet Hamiltonian at long times, while narrowly avoiding a series of
unstable fixed points which determine distinct prethermal regimes at
intermediate times. We study a class of relevant perturbations that trigger the
onset of heating and thermalization, and demonstrate that the renormalization
flow has an elegant representation in terms of a flow of matrix product
operators. Our results permit microscopic calculations of the emergence of
distinct dynamical regimes directly in the thermodynamic limit in an efficient
manner, establishing a new computational tool for driven non-equilibrium
systems.
