Finding the optimal integration coefficient for a palindromic multi-stage splitting integrator in HMC applications to Bayesian inference

We present the tables of integration coefficients for the 2- and 3-stage adaptive splitting integrators derived for Hamiltonian Monte Carlo (HMC) using the Adaptive Integration Approach s-AIA introduced in

- Nagar, L., Fernández-Pendás, M., Sanz-Serna, J. M., Akhmatskaya, E. (2023). Adaptive multi-stage integration schemes for Hamiltonian Monte Carlo. arXiv:2307.02096. doi:10.48550/arXiv.2307.02096 .

The tables provide the maps that assign the optimal (in terms of the best conservation of energy for harmonic forces) integration coefficient for a k-stage palindromic splitting integrator to a nondimensional simulation step size in the stability interval (0, 2 k).

The repository includes the two tables for 2- and 3-stage s-AIA, a Python script that provides the optimal integration coefficient for a user-chosen dimensional step size, two .txt files containing the values of the optimal integration coefficients for 2- and 3-stage s-AIA used by the Python script, and a readme.pdf file describing the s-AIA methodology and the usage guidelines for the tables.

本报告呈现了为哈密顿蒙特卡洛（Hamiltonian Monte Carlo，简称 HMC）方法所推导的，基于自适应积分方法 s-AIA（Adaptive Integration Approach s-AIA）的二维与三维自适应分裂积分器（adaptive splitting integrators）的积分系数表。s-AIA 方法由 Nagar 等（2023）在论文《Adaptive multi-stage integration schemes for Hamiltonian Monte Carlo》中提出，该论文发表于 arXiv:2307.02096，并拥有 doi:10.48550/arXiv.2307.02096。该积分系数表提供了将最优（就谐力能量守恒而言）的积分系数分配给 k 阶回文分裂积分器与无量纲模拟步长在稳定性区间（0, 2k）内的对应映射。存储库中包含了 2 阶与 3 阶 s-AIA 的两个表格，一个 Python 脚本，该脚本能够为用户所选的维度步长提供最优积分系数，以及两个包含 2 阶与 3 阶 s-AIA 所用最优积分系数的 .txt 文件，此外还包含一个 readme.pdf 文件，该文件描述了 s-AIA 方法及其表格使用指南。