  Active systems, which are driven by non-conservative forces acting
independently on individual particles, exhibit a variety of unique behaviors
and structures, with potential applications in the design of novel materials.
Towards designing such materials, an important open challenge is to precisely
connect the structure of active systems to the dissipation of energy induced by
the local driving. We approach this problem by developing a perturbative
mean-field theory which predicts the static structure with good accuracy, even
for strongly interacting systems. Significantly, this theory requires only
equilibrium measurements of the structure to deduce, systematically, how
driving forces shape the structure out-of-equilibrium. Second, based on this
theory, we derive an expression for the rate of dissipation and we show that
there exists a robust relation between dissipation and structure, which holds
even as the system approaches an activity-induced phase transition far from
equilibrium. Finally, we construct a neural network which maps static
configurations of active particles to their dissipation rate, thus showing that
the dissipation of energy can be inferred from purely static structural
information, without any prior knowledge of the underlying dynamics.
