Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany.
J Chem Phys. 2013 May 28;138(20):204106. doi: 10.1063/1.4804302.
Based on a given time series, the data-driven Langevin equation proposed by Hegger and Stock [J. Chem. Phys. 130, 034106 (2009)] aims to construct a low-dimensional dynamical model of the system. Adopting various simple model problems of biomolecular dynamics, this work presents a systematic study of the theoretical virtues and limitations as well as of the practical applicability and performance of the method. As the method requires only local information, the input data need not to be Boltzmann weighted in order to warrant that the Langevin model yields correct Boltzmann-distributed results. Moreover, a delay embedding of the state vector allows for the treatment of memory effects. The robustness of the modeling with respect to wrongly chosen model parameters or low sampling is discussed, as well as the treatment of inertial effects. Given sufficiently sampled input data, the Langevin modeling is shown to successfully recover the correct statistics (such as the probability distribution) and the dynamics (such as the position autocorrelation function) of all considered problems.
基于给定的时间序列，Hegger 和 Stock 提出的数据驱动朗之万方程[J. Chem. Phys. 130, 034106 (2009)]旨在构建系统的低维动力学模型。采用生物分子动力学的各种简单模型问题，本工作对该方法的理论优点和局限性以及实际适用性和性能进行了系统研究。由于该方法仅需要局部信息，因此输入数据不必进行玻尔兹曼加权，以保证朗之万模型产生正确的玻尔兹曼分布结果。此外，状态向量的延迟嵌入允许处理记忆效应。讨论了模型参数选择错误或采样不足时建模的稳健性，以及惯性效应的处理。对于充分采样的输入数据，朗之万建模被证明可以成功地恢复所有考虑问题的正确统计数据（例如概率分布）和动力学（例如位置自相关函数）。
