Deep-Learning-Empowered Programmable Topolectrical Circuits

Topolectrical circuits provide a versatile platform for exploring and simulating modern physical models. However, existing approaches suffer from incomplete programmability and ineffective feature prediction and control mechanisms, hindering the investigation of physical phenomena on an integrated platform and limiting their translation into practical applications. Here, we present a deep-learning-empowered programmable topolectrical circuits (DLPTCs) platform for physical modeling and analysis. By integrating fully independent, continuous tuning of both on-site and off-site terms of the lattice Hamiltonian, physics-graph-informed inverse state design, and immediate hardware verification, our system bridges the gap between theoretical modeling and practical realization. Through flexible control and adiabatic path engineering, we experimentally observe the boundary states without global symmetry in higher-order topological systems, their adiabatic phase transitions, and the flat-band-like characteristic corresponding to Landau levels in the circuit. Incorporating a physics‑graph‑informed mechanism with a generative AI model for physics exploration, we realize arbitrary, position-controllable on-board Anderson localization, surpassing conventional random localization. Utilizing this unique capability with high‑fidelity hardware implementation, we further demonstrate a compelling cryptographic application: hash-based probabilistic information encryption by leveraging Anderson localization with extensive disorder configurations, enabling secure delivery of full ASCII messages.