Generative Surrogates for Stochastic Lattice Dynamics: How Close to the Bayes-Optimal Ceiling?

Kinetic Monte Carlo (KMC) resolves a catalyst's site dynamics event by event—adsorption, desorption, hopping, reaction, and the coking that deactivates it. A learned surrogate for such stochastic lattice dynamics cannot be judged the way a deterministic emulator is: the next frame is sampled from a conditional distribution, so asking which site changes is asking about a die roll. Such a surrogate can be trained to generate the dynamics directly, but a harder question remains: how good is good enough? The Bayes-optimal ceiling on per-site accuracy is well defined yet has no closed form, so restarting the KMC simulator from held-out frames estimates the best ranking any model with the same inputs can reach (Neyman–Pearson). A layered check then tests macroscopic equivalence, ordering the target statistics by strictness. Our surrogate matches the Bayes ceiling on arrival, reaches 99.1% of it on departure, and saturates the coking channel at its random ceiling of 0.5. Within a single step, the occupancy deviation remains at or below 2.30%. Over 60,000 events, the occupancy bias stays within +0.26%. The model reproduces not only the mean occupancy but the size of its fluctuations: particle-number standard deviations average 0.98× the paired-KMC value, with no individual condition statistically distinguishable from it by a Bonferroni-corrected F-test. Spatially, the anisotropy and clustering statistics remain within 0.93–1.10× their paired-KMC references, and the coking-irreversibility violation rate stays at or below 0.59%. The protocol needs only a restartable simulator and a hierarchy of statistical targets, so it transfers to other Markovian lattice processes.