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

Published: 4 December 2023| Version 1 | DOI: 10.17632/5mmh4wcdd6.1
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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.

Files

Steps to reproduce

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

Institutions

Donostia International Physics Center, Universidad Carlos III de Madrid Departamento de Matematicas, Centro Vasco de Matematicas Aplicadas, Ikerbasque

Categories

Numerical Algorithm, Hybrid Monte Carlo

Funding

Ministerio de Ciencia e Innovación

CEX2021-001142-S

Ministerio de Ciencia e Innovación

PID2019-104927GB-C22

Ministerio de Ciencia e Innovación

PID2019-104927GB-C21

Ministerio de Ciencia e Innovación

MCIN/AEI/10.13039/501100011033

Ministerio de Ciencia e Innovación

ERDF (“A way of making Europe”)

Eusko Jaurlaritza

BERC 2022-2025 Program

Eusko Jaurlaritza

Convenio IKUR 21-HPC-IA

Eusko Jaurlaritza

ELKARTEK KK-2022/00006

Eusko Jaurlaritza

ELKARTEK KK-2021/00022

Eusko Jaurlaritza

ELKARTEK KK-2021/00064

'la Caixa' Foundation

LCF/BQ/DI20/11780022

Licence