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.

本研究针对哈密顿蒙特卡洛（Hamiltonian Monte Carlo, HMC），采用Nagar等人于2023年提出的自适应积分方法s-AIA（Adaptive Integration Approach），推导得到二阶段与三阶段自适应分裂积分器的积分系数表，相关引用文献如下：
Nagar, L., Fernández-Pendás, M., Sanz-Serna, J. M., Akhmatskaya, E. (2023). 哈密顿蒙特卡洛的自适应多阶段积分格式. arXiv:2307.02096. DOI:10.48550/arXiv.2307.02096.
该系数表集构建了映射关系，可将k阶回文分裂积分器的最优积分系数（以简谐作用力下的最优能量守恒性为评价标准），匹配至稳定区间(0, 2k)内的无量纲仿真步长。本数据集仓库包含二阶段与三阶段s-AIA对应的两张积分系数表、一款可根据用户指定的有量纲步长计算最优积分系数的Python脚本、两个存储该Python脚本所需的二阶段与三阶段s-AIA最优积分系数值的.txt文件，以及一份阐述s-AIA方法原理与表格使用指南的readme.pdf文档。