Efficient Numerical Algorithms for the Generalized Langevin Equation
Efficient Numerical Algorithms for the Generalized Langevin Equation
复制标题
广义朗之万方程的高效数值算法
DOI：
10.1137/20m138497x
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Matthias Sachs
中科院分区：
文献类型：
--
作者：
B. Leimkuhler;Matthias Sachs
研究了求解广义朗之万方程（GLE）的数值方法的设计与实现，重点研究了数值积分器的正则抽样特性。为此，我们将GLE转化为扩展的相空间形式，并推导出一组分裂方法，这些方法推广了现有的朗格万动力学积分方法。我们证明了通过这些积分方法得到的马尔可夫链的指数收敛规律和中心极限定理的有效性，并且我们证明了所建议的积分方案的动力学与精确动力学的渐近极限一致，并且可以（在短记忆极限下）再现下阻尼朗格万动力学的类似分裂的超收敛性质。然后，我们将我们提出的集成方法应用于几个模型系统，包括一个贝叶斯推理问题。我们在数值实验中证明了我们的方法在采样精度方面优于其他提出的GLE积分方案。此外，使用Ceriotti等人提出的GLE中内存内核的参数化，我们的实验表明，所获得的基于GLE的采样方案在鲁棒性和效率方面优于基于下阻尼朗格万动态的最新采样方案。
We study the design and implementation of numerical methods to solve the generalized Langevin equation (GLE) focusing on canonical sampling properties of numerical integrators. For this purpose, we cast the GLE in an extended phase space formulation and derive a family of splitting methods which generalize existing Langevin dynamics integration methods. We show exponential convergence in law and the validity of a central limit theorem for the Markov chains obtained via these integration methods, and we show that the dynamics of a suggested integration scheme is consistent with asymptotic limits of the exact dynamics and can reproduce (in the short memory limit) a superconvergence property for the analogous splitting of underdamped Langevin dynamics. We then apply our proposed integration method to several model systems, including a Bayesian inference problem. We demonstrate in numerical experiments that our method outperforms other proposed GLE integration schemes in terms of the accuracy of sampling. Moreover, using a parameterization of the memory kernel in the GLE as proposed by Ceriotti et al [9], our experiments indicate that the obtained GLE-based sampling scheme outperforms state-of-the-art sampling schemes based on underdamped Langevin dynamics in terms of robustness and efficiency.
DOI：
10.1063/1.4981816
发表时间：
2016-12
期刊：
The Journal of chemical physics
影响因子：
--
作者：
H. Ness;L. Stella;C. Lorenz;L. Kantorovich
通讯作者：
H. Ness;L. Stella;C. Lorenz;L. Kantorovich
DOI：
--
发表时间：
2019-08
期刊：
ArXiv
影响因子：
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作者：
Wenlong Mou;Yian Ma;Yi-An Ma;M. Wainwright;P. Bartlett;Michael I. Jordan
通讯作者：
Wenlong Mou;Yian Ma;Yi-An Ma;M. Wainwright;P. Bartlett;Michael I. Jordan