发表机构
Helmholtz Institute Mainz; Johannes Gutenberg University Mainz; Institute of Molecular Biology (IMB) Mainz（美因茨亥姆霍兹研究所; 美因茨约翰内斯古腾堡大学; 美因茨分子生物学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究从非归一化玻尔兹曼密度采样问题，提出神经非平衡哈密顿蒙特卡罗方法，通过学习哈密顿路径并校正，可用于估计归一化常数等，在双阱等目标上实验，重叠足够时有效，不佳时有问题，还进行了分子内坐标可行性研究。
AI 中文摘要
从非归一化玻尔兹曼密度进行采样需要能全局移动概率质量并保留足够路径概率信息以进行统计校正的提议。我们引入神经非平衡哈密顿蒙特卡罗（NHMC），一种先训练后校正的学习哈密顿采样器。从一个易处理的基础分布开始，NHMC学习朝向目标的随机哈密顿风格路径。训练完成后，固定学习到的提议参数；提议随后生成完整路径和端点配置，使用记录的非平衡功进行统计校正。这个无量纲广义功由正向提议路径和反向参考路径之间的概率比确定。在训练期间，最小化其均值可减少路径空间KL散度并控制端点不匹配的上限。在评估期间，相同的量定义路径上自归一化重要性采样（path - SNIS）的权重，估计归一化常数或自由能差，并给出路径空间独立的梅特罗波利斯 - 黑斯廷斯（path - IMH）接受率。相同的正向 - 反向定律还定义共享桥往返梅特罗波利斯核，直接作用于配置并保持玻尔兹曼目标。在双阱和有限体积晶格\(\phi^4\)目标上，当路径重叠足够时，NHMC构造给出校正估计；当重叠不佳时，权重退化、低接受率和长自相关表明提议失败。我们还报告了使用分子动力学先验和学习力路径提议的分子内坐标可行性研究。
英文摘要
Learned dynamical proposals can generate configurations without providing a tractable endpoint density. Nonequilibrium path probabilities offer a way to correct such proposals, but correction alone does not determine their ability to connect separated regions. We introduce Neural Non-Equilibrium Hamiltonian Monte Carlo (NHMC), which combines conditional momentum distributions with reversible, volume-preserving dynamics. The forward--reverse path ratio gives the work used for training, importance weighting, normalizer estimation, and Metropolis correction. We then construct a configuration-space round-trip kernel whose reverse and forward paths share an intermediate configuration. Conditional on that configuration, its path-record update is independence Metropolis--Hastings. We compare its stationary inter-region flow with the flow obtained under exact conditional matching and bound their difference by the conditional path mismatch. This separates errors in the conditional proposal from dependence between the endpoint region and the intermediate configuration. Many-well experiments test normalizers and mode probabilities; a controlled lattice $ϕ^4$ experiment relates inter-sector flow to sector relaxation. Two-dimensional $U(1)$, $\mathrm{SU}(2)$, and $\mathrm{SU}(3)$ experiments compare four proposal constructions sharing a structured reference, including paths with analytic and learned forces.
Comments65 pages, 30 figures, including appendices
