Couplings for Andersen dynamics
Couplings for Andersen dynamics
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DOI：
10.1214/21-aihp1197
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发表时间：
2020-09
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影响因子：
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通讯作者：
Nawaf Bou-Rabee;A. Eberle
中科院分区：
文献类型：
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作者：
Nawaf Bou-Rabee;A. Eberle
Andersen动力学是分子模拟的标准方法，也是用于MCMC推理的哈密顿蒙特卡罗算法的前身。对应于Andersen动力学的随机过程是在随机选择的粒子的哈密顿流和速度随机化之间迭代的PDMP(分段确定马尔可夫过程)。无论是从分子动力学的角度，还是从MCMC推论的角度，一个基本的问题都是理解这个PDMP的收敛到平衡，特别是在高维。在这里，我们提出了耦合，以获得在沃瑟斯坦意义下不需要潜在势能的全局凸性的尖锐收敛界。
Andersen dynamics is a standard method for molecular simulations, and a precursor of the Hamiltonian Monte Carlo algorithm used in MCMC inference. The stochastic process corresponding to Andersen dynamics is a PDMP (piecewise deterministic Markov process) that iterates between Hamiltonian flows and velocity randomizations of randomly selected particles. Both from the viewpoint of molecular dynamics and MCMC inference, a basic question is to understand the convergence to equilibrium of this PDMP particularly in high dimension. Here we present couplings to obtain sharp convergence bounds in the Wasserstein sense that do not require global convexity of the underlying potential energy.