Abstract:

Classical many-body systems comprise everyday liquids, colloidal systems or almost everything in the realm of soft matter. In equilibrium, all properties can be deduced from the one-body density profile (the space-dependent probability for finding a particle). This is guaranteed by the therorems of Density Functional Theory (DFT), but one needs the functional of the free energy to put DFT to work. For many systems, even very simple ones, this functional is not known.
I discuss recent advances and perspectives on finding these functionals using methods of Machine Learning (ML) and try to build a bridge also to the quantum DFT problem where similar developments are in progress. Also, the general classical nonequilibrium problem can be put in a functional form (power functional theory), and the likewise unknown functional of dissipated power should be learnable by ML methods.