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

The mechanical properties of metallic nanostructures are governed not only by topology but also by crystal symmetry and facet-dependent 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 × 10⁵ 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.