用于采样分子晶体结构的刚体流
Rigid Body Flows for Sampling Molecular Crystal Structures
AI总结：
提出面向晶体中分子位置与取向的刚体归一化流，利用单位四元数流及其双重覆盖性质建模旋转，并在四面体系统和 TIP4P ice XI 的玻尔兹曼生成器中验证。
摘要：
Normalizing flows（NF，归一化流）是一类强大的生成模型，近年来因其能够以高度灵活性和表达能力建模复杂分布而受到欢迎。在本工作中，我们引入了一种新型归一化流，专门用于建模三维空间中多个对象（例如晶体中的分子）的位置和取向。我们的方法基于两个关键思想：首先，我们在单位四元数群上定义平滑且富有表达能力的流，这使我们能够捕捉刚体的连续旋转运动；其次，我们利用单位四元数的双重覆盖性质，在旋转群上定义恰当的密度。这确保了我们的模型可以使用标准的基于似然的方法进行训练，或者相对于热力学目标密度进行变分推断。我们通过为两个分子示例训练 Boltzmann generators（玻尔兹曼生成器）来评估该方法，即外场中四面体系统的多峰密度，以及 TIP4P 水模型中的 ice XI 相。我们的流可以与作用于分子内部自由度的流相结合，并构成了朝建模许多相互作用分子的分布迈出的重要一步。
英文摘要：
Normalizing flows (NF) are a class of powerful generative models that have gained popularity in recent years due to their ability to model complex distributions with high flexibility and expressiveness. In this work, we introduce a new type of normalizing flow that is tailored for modeling positions and orientations of multiple objects in three-dimensional space, such as molecules in a crystal. Our approach is based on two key ideas: first, we define smooth and expressive flows on the group of unit quaternions, which allows us to capture the continuous rotational motion of rigid bodies; second, we use the double cover property of unit quaternions to define a proper density on the rotation group. This ensures that our model can be trained using standard likelihood-based methods or variational inference with respect to a thermodynamic target density. We evaluate the method by training Boltzmann generators for two molecular examples, namely the multi-modal density of a tetrahedral system in an external field and the ice XI phase in the TIP4P water model. Our flows can be combined with flows operating on the internal degrees of freedom of molecules and constitute an important step towards the modeling of distributions of many interacting molecules.
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