Extracting consistent statistics between relevant free-energy minima of a molecular system is essential for physics, chemistry and biology. Molecular dynamics (MD) simulations can aid in this task but are computationally expensive, especially for systems that require quantum accuracy. To overcome this challenge, we develop an approach combining enhanced sampling with deep generative models and active learning of a machine learning potential (MLP). We introduce an adaptive Markov chain Monte Carlo framework that enables the training of one Normalizing Flow (NF) and one MLP per state, achieving rapid convergence towards the Boltzmann distribution. Leveraging the trained NF and MLP models, we compute thermodynamic observables such as free-energy differences or optical spectra. We apply this method to study the isomerization of an ultrasmall silver nanocluster, belonging to a set of systems with diverse applications in the fields of medicine and catalysis.

翻译：从分子体系相关自由能极小值间提取一致统计量是物理学、化学与生物学的基础。分子动力学模拟可辅助完成此任务，但计算成本高昂，尤其对于需要量子精度的体系。为克服这一挑战，我们提出一种将增强采样、深度生成模型与机器学习势能主动学习相结合的方法。引入自适应马尔可夫链蒙特卡洛框架，该框架支持为每个状态训练一个归一化流模型和一个机器学习势能，实现向玻尔兹曼分布的快速收敛。利用训练好的归一化流与机器学习势能模型，可计算自由能差或光谱等热力学可观测量。我们应用该方法研究超小银纳米团簇的异构化过程，此类体系在医学和催化领域具有广泛应用前景。