标题： 学习尊重置换对称性的集体变量 显示英文标题

标题： Learning collective variables that respect permutational symmetry

摘要： 除了平移和旋转对称性外，相同相互作用粒子的团簇具有置换对称性。 对于这类系统，粗粒化模型在识别亚稳态、提供其动力学的有效描述以及估计跃迁速率方面至关重要。 我们提出了一种数值框架，用于学习尊重平移、旋转和置换对称性的集体变量，并估计跃迁速率和驻留时间。 它结合了基于种类的特征提取，在特征空间中进行驻留流形学习，并使用损失函数利用正交关系（Legoll和Lelievre，2010）的自编码器来学习集体变量。 所得简化模型的传递概率被用作前向通量采样中的反应坐标，并用于设计采样过渡路径过程的控制。 我们提供了两个案例研究，即二维的Lennard-Jones-7和三维的Lennard-Jones-8。 借助简化模型计算出的跃迁速率和驻留时间与通过暴力方法获得的结果一致。 显示英文摘要

摘要： In addition to translational and rotational symmetries, clusters of identical interacting particles possess permutational symmetry. Coarse-grained models for such systems are instrumental in identifying metastable states, providing an effective description of their dynamics, and estimating transition rates. We propose a numerical framework for learning collective variables that respect translational, rotational, and permutational symmetries, and for estimating transition rates and residence times. It combines a sort-based featurization, residence manifold learning in the feature space, and learning collective variables with autoencoders whose loss function utilizes the orthogonality relationship (Legoll and Lelievre, 2010). The committor of the resulting reduced model is used as the reaction coordinate in the forward flux sampling and to design a control for sampling the transition path process. We offer two case studies, the Lennard-Jones-7 in 2D and the Lennard-Jones-8 in 3D. The transition rates and residence times computed with the aid of the reduced models agree with those obtained via brute-force methods.