The Experts below are selected from a list of 3900 Experts worldwide ranked by ideXlab platform
Kenneth D. Jordan - One of the best experts on this subject based on the ideXlab platform.
-
Parallel Tempering monte carlo simulations of the water heptamer anion
Chemical Physics Letters, 2008Co-Authors: Albert Defusco, Thomas Sommerfeld, Kenneth D. JordanAbstract:Abstract Parallel Tempering Monte Carlo simulations of the water heptamer anion have been performed for temperatures ranging from 42 to 200 K. At low temperatures, a single peak near 250 meV in the electron binding energy distribution is obtained, while at high temperatures a second, weak peak near 450 meV is observed, in good agreement with those observed experimentally. It is further confirmed that the high electron binding energies are due to hydrogen bonding networks with large net dipole moments and, in most cases, also containing a single double-acceptor monomer, while weak electron binding arises from configurations with smaller dipoles.
-
On the convergence of Parallel Tempering Monte Carlo simulations of LJ38.
The journal of physical chemistry. A, 2005Co-Authors: Hanbin Liu, Kenneth D. JordanAbstract:The convergence of Parallel Tempering Monte Carlo simulations of the 38-atom Lennard-Jones cluster starting from the Oh global minimum and from the C5v second-lowest-energy minimum is investigated. It is found that achieving convergence is appreciably more difficult, particularly at temperatures in the vicinity of the Oh → C5v transformation when starting from the C5v structure. A strategy combining the Tsallis generalized ensemble and the Parallel Tempering algorithm is implemented and used to improve the convergence of the simulations in the vicinity of the Oh → C5v transformation.
-
Parallel-Tempering Monte Carlo simulations of the finite temperature behavior of (H2O)6−
The Journal of Chemical Physics, 2003Co-Authors: Feng Wang, Kenneth D. JordanAbstract:The Parallel-Tempering Monte Carlo method is used in combination with a Drude model to characterize the (H2O)6− cluster over the 50–190 K temperature range. Chainlike structures are found to account for about 50% of the population at 190 K, whereas they are unimportant at the temperatures below about 130 K. At the lowest temperature considered, prismlike structures are dominant. Two new low-energy forms of (H2O)6− are identified.
-
Parallel Tempering monte carlo simulations of the finite temperature behavior of h2o 6
Journal of Chemical Physics, 2003Co-Authors: Feng Wang, Kenneth D. JordanAbstract:The Parallel-Tempering Monte Carlo method is used in combination with a Drude model to characterize the (H2O)6− cluster over the 50–190 K temperature range. Chainlike structures are found to account for about 50% of the population at 190 K, whereas they are unimportant at the temperatures below about 130 K. At the lowest temperature considered, prismlike structures are dominant. Two new low-energy forms of (H2O)6− are identified.
-
Parallel Tempering monte carlo study of h2o n 6 9
Journal of Physical Chemistry A, 2003Co-Authors: Arnold N. Tharrington, Kenneth D. JordanAbstract:Parallel-Tempering Monte Carlo simulations are used to characterize the finite temperature behavior of the (H2O)n = 6-9 clusters. The heat capacities, quenched energy distributions, and Landau free energies are calculated and used to address the nature of the structural transformations that occur with increasing temperature.
J. Machta - One of the best experts on this subject based on the ideXlab platform.
-
Comparing Monte Carlo methods for finding ground states of Ising spin glasses: Population annealing, simulated annealing, and Parallel Tempering.
Physical review. E Statistical nonlinear and soft matter physics, 2015Co-Authors: Wenlong Wang, J. Machta, Helmut G. KatzgraberAbstract:Population annealing is a Monte Carlo algorithm that marries features from simulated-annealing and Parallel-Tempering Monte Carlo. As such, it is ideal to overcome large energy barriers in the free-energy landscape while minimizing a Hamiltonian. Thus, population-annealing Monte Carlo can be used as a heuristic to solve combinatorial optimization problems. We illustrate the capabilities of population-annealing Monte Carlo by computing ground states of the three-dimensional Ising spin glass with Gaussian disorder, while comparing to simulated-annealing and Parallel-Tempering Monte Carlo. Our results suggest that population annealing Monte Carlo is significantly more efficient than simulated annealing but comparable to Parallel-Tempering Monte Carlo for finding spin-glass ground states.
-
Correlations between the dynamics of Parallel Tempering and the free-energy landscape in spin glasses.
Physical review. E Statistical nonlinear and soft matter physics, 2013Co-Authors: Burcu Yucesoy, J. Machta, Helmut G. KatzgraberAbstract:We present the results of a large-scale numerical study of the equilibrium three-dimensional Edwards-Anderson Ising spin glass with Gaussian disorder. Using Parallel Tempering (replica exchange) Monte Carlo we measure various static, as well as dynamical quantities, such as the autocorrelation times and round-trip times for the Parallel Tempering Monte Carlo method. The correlation between static and dynamic observables for 5000 disorder realizations and up to 1000 spins down to temperatures at 20$%$ of the critical temperature is examined. Our results show that autocorrelation times are directly correlated with the roughness of the free-energy landscape.
-
Monte Carlo Methods for Rough Free Energy Landscapes: Population Annealing and Parallel Tempering
Journal of Statistical Physics, 2011Co-Authors: J. Machta, R. S. EllisAbstract:Parallel Tempering and population annealing are both effective methods for simulating equilibrium systems with rough free energy landscapes. Parallel Tempering, also known as replica exchange Monte Carlo, is a Markov chain Monte Carlo method while population annealing is a sequential Monte Carlo method. Both methods overcome the exponential slowing associated with high free energy barriers. The convergence properties and efficiencies of the two methods are compared. For large systems, population annealing is closer to equilibrium than Parallel Tempering for short simulations. However, with respect to the amount of computation, Parallel Tempering converges exponentially while population annealing converges only inversely. As a result, for sufficiently long simulations Parallel Tempering approaches equilibrium more quickly than population annealing.
-
monte carlo methods for rough free energy landscapes population annealing and Parallel Tempering
arXiv: Statistical Mechanics, 2011Co-Authors: J. Machta, R. S. EllisAbstract:Parallel Tempering and population annealing are both effective methods for simulating equilibrium systems with rough free energy landscapes. Parallel Tempering, also known as replica exchange Monte Carlo, is a Markov chain Monte Carlo method while population annealing is a sequential Monte Carlo method. Both methods overcome the exponential slowing associated with high free energy barriers. The convergence properties and efficiency of the two methods are compared. For large systems, population annealing initially converges to equilibrium more rapidly than Parallel Tempering for the same amount of computational work. However, Parallel Tempering converges exponentially and population annealing inversely in the computational work so that ultimately Parallel Tempering approaches equilibrium more rapidly than population annealing.
-
Strengths and weaknesses of Parallel Tempering.
Physical Review E, 2009Co-Authors: J. MachtaAbstract:Parallel Tempering, also known as replica exchange Monte Carlo, is studied in the context of two simple free-energy landscapes. The first is a double-well potential defined by two macrostates separated by a barrier. The second is a "golf course" potential defined by microstates having two possible energies with exponentially more high-energy states than low-energy states. The equilibration time for replica exchange is analyzed for both systems. For the double-well system, Parallel Tempering with a number of replicas that scales as the square root of the barrier height yields exponential speedup of the equilibration time. On the other hand, replica exchange yields only marginal speedup for the golf course system. For the double-well system, the free-energy difference between the two wells has a large effect on the equilibration time. Nearly degenerate wells equilibrate much more slowly than strongly asymmetric wells. It is proposed that this difference in equilibration time may lead to a bias in measuring overlaps in spin glasses. These examples illustrate the strengths and weaknesses of replica exchange and may serve as a guide for understanding and improving the method in various applications.
Helmut G. Katzgraber - One of the best experts on this subject based on the ideXlab platform.
-
Comparing Monte Carlo methods for finding ground states of Ising spin glasses: Population annealing, simulated annealing, and Parallel Tempering.
Physical review. E Statistical nonlinear and soft matter physics, 2015Co-Authors: Wenlong Wang, J. Machta, Helmut G. KatzgraberAbstract:Population annealing is a Monte Carlo algorithm that marries features from simulated-annealing and Parallel-Tempering Monte Carlo. As such, it is ideal to overcome large energy barriers in the free-energy landscape while minimizing a Hamiltonian. Thus, population-annealing Monte Carlo can be used as a heuristic to solve combinatorial optimization problems. We illustrate the capabilities of population-annealing Monte Carlo by computing ground states of the three-dimensional Ising spin glass with Gaussian disorder, while comparing to simulated-annealing and Parallel-Tempering Monte Carlo. Our results suggest that population annealing Monte Carlo is significantly more efficient than simulated annealing but comparable to Parallel-Tempering Monte Carlo for finding spin-glass ground states.
-
Correlations between the dynamics of Parallel Tempering and the free-energy landscape in spin glasses.
Physical review. E Statistical nonlinear and soft matter physics, 2013Co-Authors: Burcu Yucesoy, J. Machta, Helmut G. KatzgraberAbstract:We present the results of a large-scale numerical study of the equilibrium three-dimensional Edwards-Anderson Ising spin glass with Gaussian disorder. Using Parallel Tempering (replica exchange) Monte Carlo we measure various static, as well as dynamical quantities, such as the autocorrelation times and round-trip times for the Parallel Tempering Monte Carlo method. The correlation between static and dynamic observables for 5000 disorder realizations and up to 1000 spins down to temperatures at 20$%$ of the critical temperature is examined. Our results show that autocorrelation times are directly correlated with the roughness of the free-energy landscape.
-
Feedback-optimized Parallel Tempering Monte Carlo
Journal of Statistical Mechanics: Theory and Experiment, 2006Co-Authors: Helmut G. Katzgraber, Simon Trebst, David A. Huse, Matthias TroyerAbstract:We introduce an algorithm to systematically improve the efficiency of Parallel Tempering Monte Carlo simulations by optimizing the simulated temperature set. Our approach is closely related to a recently introduced adaptive algorithm that optimizes the simulated statistical ensemble in generalized broad-histogram Monte Carlo simulations. Conventionally, a temperature set is chosen in such a way that the acceptance rates for replica swaps between adjacent temperatures are independent of the temperature and large enough to ensure frequent swaps. In this paper, we show that by choosing the temperatures with a modified version of the optimized ensemble feedback method we can minimize the round-trip times between the lowest and highest temperatures which effectively increases the efficiency of the Parallel Tempering algorithm. In particular, the density of temperatures in the optimized temperature set increases at the "bottlenecks'' of the simulation, such as phase transitions. In turn, the acceptance rates are now temperature dependent in the optimized temperature ensemble. We illustrate the feedback-optimized Parallel Tempering algorithm by studying the two-dimensional Ising ferromagnet and the two-dimensional fully-frustrated Ising model, and briefly discuss possible feedback schemes for systems that require configurational averages, such as spin glasses.
-
feedback optimized Parallel Tempering monte carlo
Journal of Statistical Mechanics: Theory and Experiment, 2006Co-Authors: Helmut G. Katzgraber, Simon Trebst, David A. Huse, Matthias TroyerAbstract:We introduce an algorithm for systematically improving the efficiency of Parallel Tempering Monte Carlo simulations by optimizing the simulated temperature set. Our approach is closely related to a recently introduced adaptive algorithm that optimizes the simulated statistical ensemble in generalized broad-histogram Monte Carlo simulations. Conventionally, a temperature set is chosen in such a way that the acceptance rates for replica swaps between adjacent temperatures are independent of the temperature and large enough to ensure frequent swaps. In this paper, we show that by choosing the temperatures with a modified version of the optimized ensemble feedback method we can minimize the round-trip times between the lowest and highest temperatures which effectively increases the efficiency of the Parallel Tempering algorithm. In particular, the density of temperatures in the optimized temperature set increases at the 'bottlenecks' of the simulation, such as phase transitions. In turn, the acceptance rates are now temperature dependent in the optimized temperature ensemble. We illustrate the feedback-optimized Parallel Tempering algorithm by studying the two-dimensional Ising ferromagnet and the two-dimensional fully frustrated Ising model, and briefly discuss possible feedback schemes for systems that require configurational averages, such as spin glasses.
-
Feedback-optimized Parallel Tempering
2006Co-Authors: Helmut G. Katzgraber, Matthias TroyerAbstract:We intro duce an algorithm for systematically improving the efficiency of Parallel Tempering Monte Carlo simulations by optimizing the simulated temperature set. Our approach is closely related to a recently introduced adaptive algorithm that optimizes the simulated statistical ensemble in generalized broad-histogram Monte Carlo simulations. Conventionally, a temperature set is chosen in such a way that the acceptance rates for replica swaps between adjacent temperatures are independent of the temperature and large enough to ensure frequent swaps. In this paper, we show that by choosing the temperatures with a modified version of the optimized ensemble feedback method we can minimize the round-trip times between the lowest and highest temperatures which effectively increases the efficiency of the Parallel Tempering algorithm. In particular, the density of temperatures in the optimized temperature set increases at the 'bottlenecks' of the simulation, such as phase transitions. In turn, the acceptance rates are now temperature dependent in the optimized temperature ensemble. We illustrate the feedback-optimized Parallel Tempering algorithm by studying the two-dimensional Ising ferromagnet and the two-dimensional fully frustrated Ising model, and briefly discuss possible feedback schemes for systems that require configurational averages, such as spin glasses.
Gareth O. Roberts - One of the best experts on this subject based on the ideXlab platform.
-
Accelerating Parallel Tempering: Quantile Tempering Algorithm (QuanTA)
Advances in Applied Probability, 2019Co-Authors: Nicholas G. Tawn, Gareth O. RobertsAbstract:It is well known that traditional Markov chain Monte Carlo (MCMC) methods can fail to effectively explore the state space for multimodal problems. Parallel Tempering is a well-established population approach for such target distributions involving a collection of particles indexed by temperature. However, this method can suffer dramatically from the curse of dimensionality. In this paper we introduce an improvement on Parallel Tempering called QuanTA. A comprehensive theoretical analysis quantifying the improved efficiency and scalability of the approach is given. Under weak regularity conditions, QuanTA gives accelerated mixing through the temperature space. Empirical evidence of the effectiveness of this new algorithm is illustrated on canonical examples.
-
accelerating Parallel Tempering quantile Tempering algorithm quanta
arXiv: Methodology, 2018Co-Authors: Nicholas G. Tawn, Gareth O. RobertsAbstract:Using MCMC to sample from a target distribution, $\pi(x)$ on a $d$-dimensional state space can be a difficult and computationally expensive problem. Particularly when the target exhibits multimodality, then the traditional methods can fail to explore the entire state space and this results in a bias sample output. Methods to overcome this issue include the Parallel Tempering algorithm which utilises an augmented state space approach to help the Markov chain traverse regions of low probability density and reach other modes. This method suffers from the curse of dimensionality which dramatically slows the transfer of mixing information from the auxiliary targets to the target of interest as $d \rightarrow \infty$. This paper introduces a novel prototype algorithm, QuanTA, that uses a Gaussian motivated transformation in an attempt to accelerate the mixing through the temperature schedule of a Parallel Tempering algorithm. This new algorithm is accompanied by a comprehensive theoretical analysis quantifying the improved efficiency and scalability of the approach; concluding that under weak regularity conditions the new approach gives accelerated mixing through the temperature schedule. Empirical evidence of the effectiveness of this new algorithm is illustrated on canonical examples.
Wenlong Wang - One of the best experts on this subject based on the ideXlab platform.
-
simulating thermal boundary conditions of spin lattice models using Parallel Tempering monte carlo
arXiv: Disordered Systems and Neural Networks, 2015Co-Authors: Wenlong WangAbstract:Thermal boundary conditions has played an increasingly important role in recent spin glass research and is likely to be also relevant for other disordered systems. Simulating thermal boundary conditions efficiently using population annealing is straightforward and well studied, but much less is known for Parallel Tempering. Two methods to simulate thermal boundary conditions using Parallel Tempering are proposed and their performance are studied, the diffusion method and the weighted average method. Numerical results are compared with those of population annealing using the three-dimensional Edwards-Anderson Ising spin glass model as benchmark tests showing the efficiency of the two methods. The relative strengths and weaknesses of all methods are also discussed.
-
Comparing Monte Carlo methods for finding ground states of Ising spin glasses: Population annealing, simulated annealing, and Parallel Tempering.
Physical review. E Statistical nonlinear and soft matter physics, 2015Co-Authors: Wenlong Wang, J. Machta, Helmut G. KatzgraberAbstract:Population annealing is a Monte Carlo algorithm that marries features from simulated-annealing and Parallel-Tempering Monte Carlo. As such, it is ideal to overcome large energy barriers in the free-energy landscape while minimizing a Hamiltonian. Thus, population-annealing Monte Carlo can be used as a heuristic to solve combinatorial optimization problems. We illustrate the capabilities of population-annealing Monte Carlo by computing ground states of the three-dimensional Ising spin glass with Gaussian disorder, while comparing to simulated-annealing and Parallel-Tempering Monte Carlo. Our results suggest that population annealing Monte Carlo is significantly more efficient than simulated annealing but comparable to Parallel-Tempering Monte Carlo for finding spin-glass ground states.
-
Measuring free energy in spin-lattice models using Parallel Tempering Monte Carlo
Physical review. E Statistical nonlinear and soft matter physics, 2015Co-Authors: Wenlong WangAbstract:An efficient and simple approach of measuring the absolute free energy as a function of temperature for spin lattice models using a two-stage Parallel Tempering Monte Carlo and the free energy perturbation method is discussed and the results are compared with those of population annealing Monte Carlo using the three-dimensional Edwards-Anderson Ising spin glass model as benchmark tests. This approach requires little modification of regular Parallel Tempering Monte Carlo codes with also little overhead. Numerical results show that Parallel Tempering, even though using a much less number of temperatures than population annealing, can nevertheless equally efficiently measure the absolute free energy by simulating each temperature for longer times.
