Inverse Design of Strongly Localized Topological $\pi$ Modes in One-Dimensional Nonperiodic Systems

This study investigates the spatial confinement of topological $\pi$-modes in one-dimensional chiral-symmetric systems. In conventional periodic and quasiperiodic structures, edge-mode wave functions inevitably penetrate the bulk. To suppress this, inverse design of a potential sequence is performed using a generative model under a global topological constraint. The generated sequence reveals a characteristic structure consisting of a topological boundary layer and a macroscopic S-dense domain, leading to enhanced confinement ($\xi=0.85$) while preserving topology. Based on the physical principle extracted from this result, a minimal heterostructure composed of only two S-blocks is manually constructed, which further reduces the localization length to $\xi=0.75$. These results provide a compact design principle for strongly localized topological states.