Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methods

Modified Hamiltonian Monte Carlo (MHMC) methods combine the ideas behind two popular sampling approaches: Hamiltonian Monte Carlo (HMC) and importance sampling. As in the HMC case, the bulk of the computational cost of MHMC algorithms lies in the numerical integration of a Hamiltonian system of diff...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational physics 2018-11, Vol.373, p.900-916
Main Authors: Radivojević, Tijana, Fernández-Pendás, Mario, Sanz-Serna, Jesús María, Akhmatskaya, Elena
Format: Article
Language:English
Subjects:
Algorithms
Computational physics
Differential equations
Enhanced sampling
Hamiltonian functions
Hamiltonian Monte Carlo
Importance sampling
Integrators
Modified Hamiltonian
Molecular dynamics
Monte Carlo simulation
Multi-stage integrators
Numerical integration
Splitting
Statistical methods
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Modified Hamiltonian Monte Carlo (MHMC) methods combine the ideas behind two popular sampling approaches: Hamiltonian Monte Carlo (HMC) and importance sampling. As in the HMC case, the bulk of the computational cost of MHMC algorithms lies in the numerical integration of a Hamiltonian system of differential equations. We suggest novel integrators designed to enhance accuracy and sampling performance of MHMC methods. The novel integrators belong to families of splitting algorithms and are therefore easily implemented. We identify optimal integrators within the families by minimizing the energy error or the average energy error. We derive and discuss in detail the modified Hamiltonians of the new integrators, as the evaluation of those Hamiltonians is key to the efficiency of the overall algorithms. Numerical experiments show that the use of the new integrators may improve very significantly the sampling performance of MHMC methods, in both statistical and molecular dynamics problems. •We introduce new multi-stage splitting integrators for enhanced sampling with modified Hamiltonian Monte Carlo methods.•The integrators are obtained from the minimization of the (expected) modified energy error introduced by integration.•We propose computationally efficient expressions for modified Hamiltonians of order 4 and 6 for the multi-stage integrators.•An outstanding improvement over Verlet observed for problems in which the potential function is (approximately) quadratic.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2018.07.023