PDMP Characterisation of Event-Chain Monte Carlo Algorithms for Particle Systems
PDMP Characterisation of Event-Chain Monte Carlo Algorithms for Particle Systems
复制标题
粒子系统事件链蒙特卡罗算法的 PDMP 表征
DOI：
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复制
发表时间：
2022
影响因子：
1.6
通讯作者：
Manon Michel
中科院分区：
文献类型：
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作者：
Athina Monemvassitis;A. Guillin;Manon Michel
Monte Carlo模拟的粒子系统，如硬球或软球奇异内核可以显示周围的相变时，使用传统的黑斯廷斯-大都会可逆计划的收敛时间长得惊人。然后开发了称为事件链蒙特卡罗（ECMC）的有效算法以达到必要的加速度。它们基于不可逆的连续时间马尔可夫过程。证明这种计划的不变性和遍历性不能做离散时间计划和理论框架，这样做是缺乏的，阻碍了ECMC算法的推广到更复杂的系统或过程。在这项工作中，我们的特点是在ECMC中产生的马尔可夫过程分段确定的马尔可夫过程。它首先允许我们提出更一般的方案，例如关于方向刷新。然后，我们证明了正确的平稳分布的不变性。最后，我们展示了软球和硬球系统中的过程的遍历性，后者的密度条件。
Monte Carlo simulations of systems of particles such as hard spheres or soft spheres with singular kernels can display around a phase transition prohibitively long convergence times when using traditional Hasting–Metropolis reversible schemes. Efficient algorithms known as event-chain Monte Carlo (ECMC) were then developed to reach necessary accelerations. They are based on non-reversible continuous-time Markov processes. Proving invariance and ergodicity for such schemes cannot be done as for discrete-time schemes and a theoretical framework to do so was lacking, impeding the generalisation of ECMC algorithms to more sophisticated systems or processes. In this work, we characterize the Markov processes generated in ECMC as piecewise deterministic Markov processes. It first allows us to propose more general schemes, for instance regarding the direction refreshment. We then prove the invariance of the correct stationary distribution. Finally, we show the ergodicity of the processes in soft- and hard-sphere systems, with a density condition for the latter.