原子模拟中的流形学习：概念性综述
Manifold Learning in Atomistic Simulations: A Conceptual Review
AI总结：
本综述聚焦于原子模拟中基于马尔可夫转移概率的无监督流形学习方法，旨在通过低维流形表征复杂过程，支持长时间尺度采样与自由能估计，并讨论了其理论框架与局限性。
摘要：
分析大量高维数据需要降维：即在它们的高维观测中寻找有意义的低维结构。这种实践在复杂系统的原子模拟中是必要的，因为即使数千个自由度也会被采样。如此丰富的数据使得深入了解特定物理问题变得困难。本综述的主要目标是关注可用于模拟数据的无监督机器学习方法，以找到一个低维流形，从而对所研究过程提供集体且信息丰富的表征。这样的流形可用于长时间尺度过程的采样和自由能估计。我们描述了能够处理来自标准和增强采样原子模拟数据集的方法。与近期关于原子模拟中流形学习的综述不同，我们仅考虑基于高维样本之间的马尔可夫转移概率来构建低维流形的方法。我们从概念的角度讨论这些技术，包括它们的基本理论框架和可能的局限性。
英文摘要：
Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of complex systems where even thousands of degrees of freedom are sampled. An abundance of such data makes gaining insight into a specific physical problem strenuous. Our primary aim in this review is to focus on unsupervised machine learning methods that can be used on simulation data to find a low-dimensional manifold providing a collective and informative characterization of the studied process. Such manifolds can be used for sampling long-timescale processes and free-energy estimation. We describe methods that can work on datasets from standard and enhanced sampling atomistic simulations. Unlike recent reviews on manifold learning for atomistic simulations, we consider only methods that construct low-dimensional manifolds based on Markov transition probabilities between high-dimensional samples. We discuss these techniques from a conceptual point of view, including their underlying theoretical frameworks and possible limitations.
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