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 reduced 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 the data self-consistently, allowing flow training without structured priors or a pre-existing dataset. For LJ disks under periodic boundary conditions, the algorithm can reduce energy evaluations by two orders of magnitude and wall-clock time by about 30%, an advantage that becomes more favorable as the cost of the potential grows. The flow's generative 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, not prior-target separation, as the hard case for current flow architectures.
Related
- Thermodynamic optimization of thermal landscapes and energy barriers in a Brownian heat engine
- Fast and Flow-rious: Gravitational Wave Background Bayesian Model Comparison using Normalizing Flows and Nested Sampling
- SPIBER: Reconstructing Free Energy Landscapes from Short, Unconverged Trajectories with Generative Flow Networks
- Online local learning for generative thermodynamic computing
- Generative diffusion in long-range correlated landscapes: Speciation cascade and the foam structure of the score
BibTeX
@misc{coretti2026generative,
title = {{Generative Nested Sampling of Atomistic Thermodynamic Landscapes}},
author = {Alessandro Coretti and Nico Unglert and Sebastian Falkner and Georg K. H. Madsen and Christoph Dellago},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.03193},
eprint = {2609.03193},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03193},
}
RIS
TY - UNPB
TI - Generative Nested Sampling of Atomistic Thermodynamic Landscapes
AU - Alessandro Coretti
AU - Nico Unglert
AU - Sebastian Falkner
AU - Georg K. H. Madsen
AU - Christoph Dellago
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2609.03193
UR - https://arxiv.org/abs/2609.03193
AB - 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 reduced 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 the data self-consistently, allowing flow training without structured priors or a pre-existing dataset. For LJ disks under periodic boundary conditions, the algorithm can reduce energy evaluations by two orders of magnitude and wall-clock time by about 30%, an advantage that becomes more favorable as the cost of the potential grows. The flow's generative 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, not prior-target separation, as the hard case for current flow architectures.
ER -