  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 guide the self-assembly
of a two-dimensional honeycomb lattice, which is a challenging problem due to
the existence of competing crystal polymorphs. Here we present a
machine-learning-guided approach to explore potentials that maximize both the
thermodynamic stability and kinetic accessibility of the honeycomb polymorph.
Optimal pair potentials exist along a Pareto front, indicating a trade-off
between these objectives. We show that this trade-off is density-dependent and
arises from a competition between crystal polymorphs: Kinetically optimal
potentials that favor the honeycomb polymorph on short timescales tend to
stabilize a triangular polymorph at long times. Finally, we explore the
fundamental limits of optimization algorithms based on ensembles of short
trajectories, which can find potentials close to the kinetically optimal region
of the Pareto Front. Our work reveals fundamental trade-offs between
crystallization speed and accuracy in the presence of competing polymorphs and
suggests guiding principles for the development of materials design algorithms
that optimize for kinetic accessibility.
