Multi-objective Optimization for Targeted Self-assembly among Competing Polymorphs

While inverse approaches for designing crystalline materials typically focus on the thermodynamic stability of a target polymorph, the outcome of a self-assembly process is often controlled by kinetic pathways. A prototypical example is the design of an isotropic pair potential to efficiently guide the self-assembly of a two-dimensional honeycomb lattice, which is a challenging problem at low densities due to the existence of competing crystal polymorphs. Here we present a machine-learning guided approach to explore pair potentials that maximizes both the thermodynamic stability and kinetic accessibility of the honeycomb polymorph. We find that the optimal pair potentials exist along a convex Pareto front, indicating a trade-off between these objectives at a low density. Furthermore, we show that the physical origin of this trade-off lies in competition between the honeycomb and triangular polymorphs: specifically, potentials that favor the honeycomb polymorph on short timescales, thus kinetically optimal, instead stabilize the triangular polymorph at long times. We also present a computationally inexpensive optimization method for finding kinetically optimal pair potentials using an ensemble of short trajectories. Our results show that this algorithm can find pair potentials close to the kinetically optimal region of the Pareto front, offering an efficient method for designing fast-assembling metastable honeycomb structures. Our work suggests that in presence of competing polymorphs, optimization for kinetic feasibility may be a better strategy for obtaining Pareto-optimal designs for targeted self-assembly.