Generative Nested Sampling of Atomistic Thermodynamic Landscapes

Abstract

Nested sampling (NS) resolves the thermodynamics of an atomistic system from a single simulation, but its practical reach is limited by the Markov-chain updates needed to decorrelate walkers within each likelihood-constrained ensemble. Flow-based NS has removed this bottleneck for gravitational-wave (GW) inference, yet its transfer to atomistic systems is not merely a change of application. Comparing a GW150914-like binary-black-hole likelihood with an eight-particle two-dimensional Lennard-Jones (LJ) system of comparable dimensionality, we show that the two landscapes differ fundamentally: atomistic multimodality is discrete and combinatorial, generated by particle permutations separated by hard collision walls, and its coordinate coupling is dense and collective, whereas the GW posterior exhibits smooth degeneracies and localized parameter coupling. Guided by this diagnosis, we introduce NS-Flows: a single conditional normalizing flow, conditioned on the NS energy bound and trained on a sliding window of recent live sets, that replaces MCMC by direct parallel draws corrected by importance-weighted rejection resampling. Live sets supply data self-consistently, allowing flow training without structured priors or a pre-existing dataset. For LJ disks in PBC, the algorithm reduces energy evaluations by over two orders of magnitude and wall-clock time by roughly one third, an advantage that becomes increasingly favorable as the cost of the potential grows. The flow's generation efficiency further acts as a physical diagnostic: it varies non-monotonically along the annealing trajectory, is lowest in the dense disordered regime, and is quantitatively captured by the constrained ensemble's internal mode complexity together with target drift across the training window, identifying liquid-like ensembles, rather than prior-target separation, as the hard case for current flow architectures.