论文标题
安徒生动力的耦合
Couplings for Andersen Dynamics
论文作者
论文摘要
Andersen Dynamics是一种用于分子模拟的标准方法，也是MCMC推断中使用的Hamiltonian Monte Carlo算法的前体。与Andersen Dynamics相对应的随机过程是PDMP（分段确定性马尔可夫过程），该过程在汉密尔顿流量和随机选择粒子的速度随机化之间进行迭代。从分子动力学的角度和MCMC推断的角度来看，一个基本问题是了解与该PDMP平衡的融合，尤其是在高维度下。在这里，我们提出耦合，以在瓦斯恒星意义上获得尖锐的收敛范围，而这种界限不需要基础势能的全局凸度。
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.
