Designing an appropriate set of collective variables is crucial to the success of several enhanced sampling methods. Here we focus on how to obtain such variables from information limited to the metastable states. We characterize these states by a large set of descriptors and employ neural networks to compress this information in a lower-dimensional space, using Fisher's linear discriminant as an objective function to maximize the discriminative power of the network. We test this method on alanine dipeptide, using the nonlinearly separable data set composed by atomic distances. We then study an intermolecular aldol reaction characterized by a concerted mechanism. The resulting variables are able to promote sampling by drawing nonlinear paths in the physical space connecting the fluctuations between metastable basins. Lastly, we interpret the behavior of the neural network by studying its relation to the physical variables. Through the identification of its most relevant features, we are able to gain chemical insight into the process.

中文翻译：

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数据驱动的集合变量，用于增强采样。

设计适当的集合变量集对于几种增强采样方法的成功至关重要。在这里，我们专注于如何从限于亚稳态的信息中获取此类变量。我们通过大量的描述符来描述这些状态，并使用神经网络将这些信息压缩在低维空间中，并使用Fisher线性判别作为目标函数来最大化网络的判别能力。我们使用由原子距离组成的非线性可分离数据集在丙氨酸二肽上测试该方法。然后，我们研究以协同机制为特征的分子间羟醛反应。通过在连接亚稳盆地之间波动的物理空间中绘制非线性路径，所得变量能够促进采样。最后，我们通过研究神经网络与物理变量的关系来解释神经网络的行为。通过识别其最相关的功能，我们可以对过程进行化学分析。