Tuning HMC using Poisson Brackets
Tuning HMC using Poisson Brackets
复制标题
使用泊松括号调整 HMC
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Paulo J. Silva
中科院分区：
文献类型：
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作者：
A. D. Kennedy;Michael Clark;Paulo J. Silva
我们讨论了混合蒙特卡罗（HMC）算法中使用的积分器如何不仅近似地保持某些哈密顿量H，而且精确地保持附近的阴影哈密顿量H，以及如何将差值H H −H表示为泊松括号中的展开式。通过测量这些泊松括号在HMC生成的平衡分布ε e−H上的平均值，我们可以从单个模拟中找到最佳积分器参数。我们表明，在实践中这样做的一个很好的方法是最小化的方差，而不是它的大小，如前所述。如何计算泊松括号规范和费米子场，嵌套和力梯度积分的一些细节也提出。
We discuss how the integrators used for the Hybrid Monte Carlo (HMC) algorithm not only approximately conserve some Hamiltonian H but exactly conserve a nearby shadow Hamiltonian H, and how the difference ∆H ≡ H −H may be expressed as an expansion in Poisson brackets. By measuring average values of these Poisson brackets over the equilibrium distribution ∝ e−H generated by HMC we can find the optimal integrator parameters from a single simulation. We show that a good way of doing this in practice is to minimize the variance of ∆H rather than its magnitude, as has been previously suggested. Some details of how to compute Poisson brackets for gauge and fermion fields, and for nested and force gradient integrators are also presented.