Scaling atom-by-atom inverse design with nano-topology optimization and diffusion models

TL;DR

This paper introduces an atom-by-atom inverse design framework combining Nano-Topology Optimization with diffusion models to optimize metallic nanostructures considering surface physics and crystal symmetry.

Contribution

It develops a novel atomistic inverse design method that incorporates surface physics, enabling the creation of large, stable nanostructures with diverse high-performance designs.

Findings

Atomistic optimization outperforms continuum methods in nanopillars.

Surface-physics-driven topology selection rules identified for aluminum nanocantilevers.

Diffusion models generate diverse high-performance nanostructure candidates.

Abstract

The mechanical properties of metallic nanostructures are governed not only by topology but also by crystal symmetry and face-specific surface physics, which are typically absent from continuum topology optimization. We develop an atom-by-atom inverse design framework that combines Nano-Topology Optimization (Nano-TO) with conditional denoising diffusion probabilistic models. Nano-TO treats each atom as a discrete design variable and evaluates stiffness from the symmetric curvature of the total energy, removing residual surface-stress bias. A crystallography-aligned multi-shell sensitivity filter stabilizes the optimization and enables designs containing more than 6.5 x 10^5 atoms. Using aluminum nanocantilevers, we identify a surface-physics-driven topology selection rule: thickness-periodic beams favor brace-dominated trusses, whereas finite-thickness beams favor nearly closed walls that provide efficient shear paths and reduce surface penalties. At sufficiently small scales, these walls become mechanically unstable, and truss-like layouts reappear. In nanopillar studies, atomistic optimization outperforms continuum topology-optimized designs. Finally, conditional diffusion models trained on Nano-TO data generate diverse high-performance candidates near the optimization frontier. These results establish nanoscale inverse design as a coupled problem of topology and surface physics.