  A key challenge for soft materials design and coarse-graining simulations is
determining interaction potentials between components that give rise to desired
condensed-phase structures. In theory, the Ornstein-Zernike equation provides
an elegant framework for solving this inverse problem. Pioneering work in
liquid state theory derived analytical closures for the framework. However,
these analytical closures are approximations, valid only for specific classes
of interaction potentials. In this work, we combine the physics of liquid state
theory with machine learning to infer a closure directly from simulation data.
The resulting closure is more accurate than commonly used closures across a
broad range of interaction potentials. We show for two examples of a
prototypical inverse design problem, fitting a coarse-grained simulation
potential, that our approach leads to improved one-step inversion.
