  Driving an inertial many-body system out of equilibrium generates complex
dynamics due to memory effects and the intricate relationships between the
external driving force, internal forces, and transport effects. Understanding
the underlying physics is challenging and often requires carrying out
case-by-case analysis. To systematically study the interplay between all types
of forces that contribute to the dynamics, a method to generate prescribed flow
patterns could be of great help. We develop a custom flow method to numerically
construct the external force field required to obtain the desired time
evolution of an inertial many-body system, as prescribed by its one-body
current and density profiles. We validate the custom flow method in a Newtonian
system of purely repulsive particles by creating a slow motion dynamics of an
out-of-equilibrium process and by prescribing the full time evolution between
two distinct equilibrium states. The method can also be used with thermostat
algorithms to control the temperature.
