  We argue in favour of developing a comprehensive dynamical theory for
rationalizing, predicting, designing, and machine learning nonequilibrium
phenomena that occur in soft matter. To give guidance for navigating the
theoretical and practical challenges that lie ahead, we discuss and exemplify
the limitations of dynamical density functional theory. Instead of the implied
adiabatic sequence of equilibrium states that this approach provides as a
makeshift for the true time evolution, we posit that the pending theoretical
tasks lie in developing a systematic understanding of the dynamical functional
relationships that govern the genuine nonequilibrium physics. While static
density functional theory gives a comprehensive account of the equilibrium
properties of many-body systems, we argue that power functional theory is the
only present contender to shed similar insights into nonequilibrium dynamics,
including the recognition and implementation of exact sum rules that result
from the Noether theorem. As~a~demonstration of the power functional point of
view, we consider an idealized steady sedimentation flow of the
three-dimensional Lennard-Jones fluid and machine-learn the kinematic map from
the mean motion to the internal force field. The trained model is capable of
both predicting and designing the steady state dynamics universally for various
target density modulations. This demonstrates the significant potential of
using such techniques in nonequilibrium many-body physics and overcomes both
the conceptual constraints of dynamical density functional theory as well as
the limited availability of its analytical functional approximations.

Soft Condensed Matter;Statistical Mechanics