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

Description

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.

Steps to reproduce

Open readme.pdf and follow the instructions in "Using the tables" section.

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