Optimization of Smooth Isotropic Pair Potentials for the Self Assembly of Complex Structures*

The synthesis of complex materials through the self-assembly of particles at the nanoscale provides opportunities for the realization of novel material properties. However, the inverse design process to create these materials is uniquely challenging. Standard methods for the optimization of isotropic pair potentials tend toward overfitting, resulting in solutions with too many features and length scales that are challenging to map to mechanistic models. Here we demonstrate how to effectively regularize the optimization of pair potential functions toward smooth and simple solutions by selectively amplifying relevant frequencies within the Fourier spectrum. Such simpler functions not only should be more readily realized experimentally, but also can be shown to be critical for robust self-assembly processes.