### Abstract

Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel simulations. From the perspective of large deviations it is optimal to let the swap rate tend to infinity and it is possible to construct a corresponding simulation scheme, known as infinite swapping. In this paper we propose a novel use of large deviations for empirical measures for a more detailed analysis of the infinite swapping limit in the setting of continuous time jump Markov processes. Using the large deviations rate function and associated stochastic control problems we consider a diagnostic based on temperature assignments, which can be easily computed during a simulation. We show that the convergence of this diagnostic to its a priori known limit is a necessary condition for the convergence of infinite swapping. The rate function is also used to investigate the impact of asymmetries in the underlying potential landscape, and where in the state space poor sampling is most likely to occur.

Original language | English |
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Pages (from-to) | 103-144 |

Journal | Applied Mathematics and Optimization |

Volume | 78 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Aug 2018 |

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*Applied Mathematics and Optimization*, vol. 78, no. 1, pp. 103-144. https://doi.org/10.1007/s00245-017-9401-9

**A large deviations analysis of certain qualitative properties of parallel tempering and infinite swapping algorithms.** / Doll, J.; Dupuis, P.; Nyquist, P.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - A large deviations analysis of certain qualitative properties of parallel tempering and infinite swapping algorithms

AU - Doll, J.

AU - Dupuis, P.

AU - Nyquist, P.

PY - 2018/8/1

Y1 - 2018/8/1

N2 - Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel simulations. From the perspective of large deviations it is optimal to let the swap rate tend to infinity and it is possible to construct a corresponding simulation scheme, known as infinite swapping. In this paper we propose a novel use of large deviations for empirical measures for a more detailed analysis of the infinite swapping limit in the setting of continuous time jump Markov processes. Using the large deviations rate function and associated stochastic control problems we consider a diagnostic based on temperature assignments, which can be easily computed during a simulation. We show that the convergence of this diagnostic to its a priori known limit is a necessary condition for the convergence of infinite swapping. The rate function is also used to investigate the impact of asymmetries in the underlying potential landscape, and where in the state space poor sampling is most likely to occur.

AB - Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel simulations. From the perspective of large deviations it is optimal to let the swap rate tend to infinity and it is possible to construct a corresponding simulation scheme, known as infinite swapping. In this paper we propose a novel use of large deviations for empirical measures for a more detailed analysis of the infinite swapping limit in the setting of continuous time jump Markov processes. Using the large deviations rate function and associated stochastic control problems we consider a diagnostic based on temperature assignments, which can be easily computed during a simulation. We show that the convergence of this diagnostic to its a priori known limit is a necessary condition for the convergence of infinite swapping. The rate function is also used to investigate the impact of asymmetries in the underlying potential landscape, and where in the state space poor sampling is most likely to occur.

UR - http://www.scopus.com/inward/record.url?scp=85011844953&partnerID=8YFLogxK

U2 - 10.1007/s00245-017-9401-9

DO - 10.1007/s00245-017-9401-9

M3 - Article

AN - SCOPUS:85011844953

VL - 78

SP - 103

EP - 144

JO - Applied Mathematics and Optimization

JF - Applied Mathematics and Optimization

SN - 0095-4616

IS - 1

ER -