用自编码器分析多模态概率测度
Analyzing multimodal probability measures with autoencoders
AI总结：
本文研究基于自编码器的神经网络方法，用于发现描述物理系统亚稳态的集体变量，分析了损失函数的数学性质，并通过条件方差和最小能量路径提供物理解释，扩展了鞍点信息及多解码器以描述多个过渡路径，在二维系统和丙氨酸二肽上验证了效果。
摘要：
寻找集体变量来描述物理系统中的某些重要粗粒化信息，特别是亚稳态，仍然是分子动力学中的一个关键问题。近年来，机器学习技术被大量用于补充甚至可能绕过专家知识，以构建集体变量。我们在此关注基于自编码器的神经网络方法。我们研究了用于训练自编码器的损失函数的一些相关数学性质，并基于条件方差和最小能量路径提供了物理解释。我们还考虑了各种扩展，以便通过纳入鞍点处过渡态的更多信息，和/或允许多个解码器来描述多个过渡路径，从而更好地描述物理系统。我们的结果在二维玩具系统和丙氨酸二肽上得到了展示。
英文摘要：
Finding collective variables to describe some important coarse-grained information on physical systems, in particular metastable states, remains a key issue in molecular dynamics. Recently, machine learning techniques have been intensively used to complement and possibly bypass expert knowledge in order to construct collective variables. Our focus here is on neural network approaches based on autoencoders. We study some relevant mathematical properties of the loss function considered for training autoencoders, and provide physical interpretations based on conditional variances and minimum energy paths. We also consider various extensions in order to better describe physical systems, by incorporating more information on transition states at saddle points, and/or allowing for multiple decoders in order to describe several transition paths. Our results are illustrated on toy two dimensional systems and on alanine dipeptide.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
