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Active systems, which are driven out of equilibrium by local non-conservativeforces, can adopt unique behaviors and configurations. An important challengein the design of novel materials which utilize such properties is to preciselyconnect the static structure of active systems to the dissipation of energyinduced by the local driving. Here, we use tools from liquid-state theories andmachine learning to take on this challenge. We first demonstrate analyticallyfor an isotropic active matter system that dissipation and pair correlationsare closely related when driving forces behave like an active temperature. Wethen extend a nonequilibrium mean-field framework for predicting these paircorrelations, which unlike most existing approaches is applicable even forstrongly interacting particles and far from equilibrium, to predictingdissipation in these systems. Based on this theory, we reveal a robust analyticrelation between dissipation and structure which holds even as the systemapproaches a nonequilibrium phase transition. Finally, we construct a neuralnetwork which maps static configurations of particles to their dissipation ratewithout any prior knowledge of the underlying dynamics. Our results open novelperspectives on the interplay between dissipation and organizationout-of-equilibrium.

From predicting to learning dissipation from pair correlations of active liquids