Structure–Curvature Proposal Learning for Potential-Energy-Landscape Graph Construction

Potential-energy-landscape (PEL) graphs connect local minima through saddle-mediated transitions, but random initialization of the activation--relaxation technique nouveau (ARTn) can spend searches without adding a new graph connection. We introduce a structure--curvature proposal framework for a 1,000-atom Kob--Andersen model glass. An invariant site model and an E(3)-equivariant multi-vector model generate atomically resolved displacement fields from the source structure, while a parameter-free source-Hessian representation organizes these fields in a 320-mode physical eigenspace using a population spectral prior. ARTn then recovers the physically resolved minimum--saddle--minimum connections. At the structural level, prospective searches on 120 source minima from ten new parent liquids produce 1.518 times as many distinct verified transition channels as global-random initialization under the same 48 ARTn attempts per source, with positive mean gains in all ten parents. For this structural benchmark, observed throughput in channels per CPU core-hour is 1.254 times that of the control. At the curvature level, evaluation on 77 verified transitions from six additional parent liquids shows that the Hessian spectral representation achieves 2.37 times the mean directional overlap of the original structural fields and 1.67 times that of direct Hessian projection, with improvement in all 18 model--parent evaluations. Together, these results show that atomic structure and local curvature contribute complementary information to proposal formation for physically resolved PEL graphs and further scientific probes. The spectral result is directional; its prospective graph yield and end-to-end cost remain to be measured.