arXiv：cs.LG· Alessandro Coretti, Nico Unglert, Sebastian Falkner, Georg K. H. Madsen, Christoph Dellago·· 6 小时前AI 评分38
NS-Flows：用生成式归一化流加速原子尺度热力学嵌套采样
Generative Nested Sampling of Atomistic Thermodynamic Landscapes
AI 导读
研究者提出 NS-Flows，用单个条件归一化流替代 MCMC 完成嵌套采样中活集去相关，流以 NS 能量界为条件并在近期活集滑动窗口上训练，活集自洽供数无需结构化先验或预置数据集。在周期性边界条件下的 Lennard-Jones 圆盘系统中，该方法可将能量评估次数减少两个数量级、墙钟时间降低约 30%，且势能计算成本越高优势越明显。
正文
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.
| Comments: | Revised version: numerical results remeasured and updated throughout; conditioning comparison extended to ten independently trained networks; Supplementary Material added, including run-to-run variability of reported costs; figures improved; link to the public code and data repository provided |
| Subjects: | Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG); Computational Physics (physics.comp-ph) |
| Cite as: | arXiv:2609.03193 [cond-mat.stat-mech] |
| (or arXiv:2609.03193v2 [cond-mat.stat-mech] for this version) | |
| https://doi.org/10.48550/arXiv.2609.03193 arXiv-issued DOI via DataCite |
Submission history
From: Alessandro Coretti [view email]
[v1]
Wed, 2 Sep 2026 22:21:10 UTC (5,690 KB)
[v2]
Wed, 7 Oct 2026 12:51:46 UTC (11,494 KB)
来源：arXiv：cs.LG · arxiv.org