Integrated VAC：一种识别动力学算子本征函数的鲁棒策略
Integrated VAC: A robust strategy for identifying eigenfunctions of dynamical operators
AI总结：
针对 VAC 对滞后时间敏感且神经网络参数化易过拟合的问题，本文提出 IVAC，通过在求解前积分多个滞后时间来更鲁棒、可复现地识别动力学算子本征函数。
摘要：
分析物理系统动力学的一种方法是在其运动中寻找长寿命模式。这种方法在分子动力学数据方面尤为成功，其中缓慢去相关的模式可以指示大尺度构象变化。检测此类模式是构象动力学变分方法（VAC）以及时间滞后独立成分分析和马尔可夫状态建模等相关方法的核心目标。在 VAC 中，对缓慢去相关模式的搜索被形式化为一个变分问题，该问题由系统转移算子的本征函数求解。VAC 通过利用时间序列数据优化本征函数的线性或非线性模型来计算该变分问题的解。在此，我们在 VAC 成功的基础上解决两个实际局限。第一，当滞后时间参数选择不当时，VAC 可能给出较差的本征函数估计。第二，当使用人工神经网络等灵活参数化且正则化不足时，VAC 可能过拟合。为解决这些问题，我们提出一种称为 integrated VAC（IVAC）的扩展。IVAC 在求解变分问题之前对多个滞后时间进行积分，使其结果比 VAC 更具鲁棒性和可复现性。
英文摘要：
One approach to analyzing the dynamics of a physical system is to search for long-lived patterns in its motions. This approach has been particularly successful for molecular dynamics data, where slowly decorrelating patterns can indicate large-scale conformational changes. Detecting such patterns is the central objective of the variational approach to conformational dynamics (VAC), as well as the related methods of time-lagged independent component analysis and Markov state modeling. In VAC, the search for slowly decorrelating patterns is formalized as a variational problem solved by the eigenfunctions of the system's transition operator. VAC computes solutions to this variational problem by optimizing a linear or nonlinear model of the eigenfunctions using time series data. Here, we build on VAC's success by addressing two practical limitations. First, VAC can give poor eigenfunction estimates when the lag time parameter is chosen poorly. Second, VAC can overfit when using flexible parameterizations such as artificial neural networks with insufficient regularization. To address these issues, we propose an extension that we call integrated VAC (IVAC). IVAC integrates over multiple lag times before solving the variational problem, making its results more robust and reproducible than VAC's.
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。
