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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:373

Article

Radivojevic, Tijana¹  Fernandez-Pendas, Mario¹  Maria Sanz-Serna, Jesus³  Akhmatskaya, Elena^1,2 

[1] BCAM, Alameda Mazarredo 14, E-48009 Bilbao, Spain

[2] Basque Fdn Sci, Ikerbasque, Maria Diaz de Haro 3, E-48013 Bilbao, Spain

[3] Univ Carlos III Madrid, Dept Matemat, Ave Univ 30, E-28911 Leganes, Madrid, Spain

关键词: Hamiltonian Monte Carlo;    Modified Hamiltonian;    Multi-stage integrators;    Enhanced sampling;   

DOI  :  10.1016/j.jcp.2018.07.023

来源: Elsevier

【 摘 要 】

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. Published by Elsevier Inc.

【 授权许可】

Free