Inverse Design of Simple Pair Potentials for the Self-Assembly of Complex Structures

TL;DR

This paper presents a new inverse design method for simple pair potentials that enhances the self-assembly of complex structures by focusing on relevant length scales and filtering high-frequency components, leading to more robust and feasible interactions.

Contribution

The authors introduce a filtering-based iterative optimization approach that produces simpler, smoother pair potentials for targeted self-assembly, improving robustness over traditional methods.

Findings

Filtered potentials assemble target structures more reliably.

Method reduces complexity of interaction potentials.

Enhanced robustness compared to unfiltered optimization.

Abstract

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 experimentally feasible interparticle interaction strategies 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 introduce a method for the optimization of simple pair potentials that minimizes the relative entropy of the complex target structure while directly considering only those length scales most relevant for self-assembly. Our approach maximizes the relative information of a target pair distribution function with respect to an ansatz distribution function via an iterative update process. During this process, we filter high frequencies from the Fourier spectrum of the pair potential, resulting in interaction potentials that are smoother and simpler in real space, and therefore likely easier to make. We show that pair potentials obtained by this method assemble their target structure more robustly with respect to optimization method parameters than potentials optimized without filtering.