### Abstract

A variant of the parallel tempering method is proposed in terms of a stochastic switching process for the coupled dynamics of replica configuration and temperature permutation. This formulation is shown to facilitate the analysis of the convergence properties of parallel tempering by large deviation theory, which indicates that the method should be operated in the infinite swapping limit to maximize sampling efficiency. The effective equation for the replica alone that arises in this infinite swapping limit simply involves replacing the original potential by a mixture potential. The analysis of the geometric properties of this potential offers a new perspective on the issues of how to choose of temperature ladder, and why many temperatures should typically be introduced to boost the sampling efficiency. It is also shown how to simulate the effective equation in this many temperature regime using multiscale integrators. Finally, similar ideas are also used to discuss extensions of the infinite swapping limits to the technique of simulated tempering.

Original language | English (US) |
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Journal | Journal of Statistical Physics |

DOIs | |

State | Accepted/In press - Jan 1 2019 |

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### Keywords

- Infinite swapping limit
- Multiscale integrator
- Parallel tempering
- Sampling

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

**Methodological and Computational Aspects of Parallel Tempering Methods in the Infinite Swapping Limit.** / Lu, Jianfeng; Vanden Eijnden, Eric.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Methodological and Computational Aspects of Parallel Tempering Methods in the Infinite Swapping Limit

AU - Lu, Jianfeng

AU - Vanden Eijnden, Eric

PY - 2019/1/1

Y1 - 2019/1/1

N2 - A variant of the parallel tempering method is proposed in terms of a stochastic switching process for the coupled dynamics of replica configuration and temperature permutation. This formulation is shown to facilitate the analysis of the convergence properties of parallel tempering by large deviation theory, which indicates that the method should be operated in the infinite swapping limit to maximize sampling efficiency. The effective equation for the replica alone that arises in this infinite swapping limit simply involves replacing the original potential by a mixture potential. The analysis of the geometric properties of this potential offers a new perspective on the issues of how to choose of temperature ladder, and why many temperatures should typically be introduced to boost the sampling efficiency. It is also shown how to simulate the effective equation in this many temperature regime using multiscale integrators. Finally, similar ideas are also used to discuss extensions of the infinite swapping limits to the technique of simulated tempering.

AB - A variant of the parallel tempering method is proposed in terms of a stochastic switching process for the coupled dynamics of replica configuration and temperature permutation. This formulation is shown to facilitate the analysis of the convergence properties of parallel tempering by large deviation theory, which indicates that the method should be operated in the infinite swapping limit to maximize sampling efficiency. The effective equation for the replica alone that arises in this infinite swapping limit simply involves replacing the original potential by a mixture potential. The analysis of the geometric properties of this potential offers a new perspective on the issues of how to choose of temperature ladder, and why many temperatures should typically be introduced to boost the sampling efficiency. It is also shown how to simulate the effective equation in this many temperature regime using multiscale integrators. Finally, similar ideas are also used to discuss extensions of the infinite swapping limits to the technique of simulated tempering.

KW - Infinite swapping limit

KW - Multiscale integrator

KW - Parallel tempering

KW - Sampling

UR - http://www.scopus.com/inward/record.url?scp=85059443822&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85059443822&partnerID=8YFLogxK

U2 - 10.1007/s10955-018-2210-y

DO - 10.1007/s10955-018-2210-y

M3 - Article

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

ER -