Inverse Design for Self Assembly via On-the-Fly Optimization

Inverse methods of statistical mechanics have facilitated the discovery of pair potentials that stabilize a wide variety of targeted lattices at zero temperature. However, such methods are complicated by the need to compare, within the optimization framework, the energy of the desired lattice to all possibly relevant competing structures, which are not generally known in advance. Furthermore, ground-state stability does not guarantee that the target will readily assemble from the fluid upon cooling from higher temperature. Here, we introduce a molecular dynamics simulation-based, optimization design strategy that iteratively and systematically refines the pair interaction according to the fluid and crystalline structural ensembles encountered during the assembly process. We successfully apply this probabilistic, machine-learning approach to the design of repulsive, isotropic pair potentials that assemble into honeycomb, kagome, square, rectangular, truncated square, and truncated hexagonal lattices.