Andersen Dynamics的联轴器
Couplings for Andersen Dynamics
摘要：
安德森动力学是分子模拟的标准方法，也是MCMC推理中使用的哈密顿蒙特卡罗算法的前身。对应于安德森动力学的随机过程是分段确定性马尔可夫过程，它在随机选择的粒子的哈密顿流和速度随机化之间迭代。从分子动力学和MCMC推论的观点来看，一个基本的问题是理解这个粒子的收敛性，特别是在高维情况下。在这里，我们提出了耦合，以获得尖锐的收敛界的Wasserstein意义上，不需要全局凸的潜在的势能。
英文摘要：
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.
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