Noisy Monte Carlo Algorithm

We present an exact Monte Carlo algorithm designed to sample theories where the energy is a sum of many couplings of decreasing strength. The algorithm avoids the computation of almost all non-leading terms. Its use is illustrated by simulating SU(2) lattice gauge theory with a 5-loop improved action. A new approach for dynamical fermion simulations is proposed.Comment: Lattice 2000 (Algorithms), latex, espcrc2.sty, 4 page

Odd-flavor Simulations by the Hybrid Monte Carlo

The standard hybrid Monte Carlo algorithm is known to simulate even flavors QCD only. Simulations of odd flavors QCD, however, can be also performed in the framework of the hybrid Monte Carlo algorithm where the inverse of the fermion matrix is approximated by a polynomial. In this exploratory study we perform three flavors QCD simulations. We make a comparison of the hybrid Monte Carlo algorithm and the R-algorithm which also simulates odd flavors systems but has step-size errors. We find that results from our hybrid Monte Carlo algorithm are in agreement with those from the R-algorithm obtained at very small step-size.Comment: 9 pages, 8 figures, Proceedings of the International Workshop on Nonperturbative Methods and Lattice QCD, Guangzhou, Chin

A Noisy Monte Carlo Algorithm

We propose a Monte Carlo algorithm to promote Kennedy and Kuti's linear accept/reject algorithm which accommodates unbiased stochastic estimates of the probability to an exact one. This is achieved by adopting the Metropolis accept/reject steps for both the dynamical and noise configurations. We test it on the five state model and obtain desirable results even for the case with large noise. We also discuss its application to lattice QCD with stochastically estimated fermion determinants.Comment: 10 pages, 1 tabl

Simulation of n_f =3 QCD by Hybrid Monte Carlo

Simulations of odd flavors QCD can be performed in the framework of the hybrid Monte Carlo algorithm where the inverse of the fermion matrix is approximated by a polynomial. In this exploratory study we perform three flavors QCD simulations. We make a comparison of the hybrid Monte Carlo algorithm and the R-algorithm which also simulates odd flavors systems but has step-size errors. We find that results from our hybrid Monte Carlo algorithm are in agreement with those from the R-algorithm obtained at very small step-size.Comment: Lattice 2000 (Algorithms), 5 pages, 8 figures, LaTe

The Tunneling Hybrid Monte-Carlo algorithm

The hermitian Wilson kernel used in the construction of the domain-wall and overlap Dirac operators has exceptionally small eigenvalues that make it expensive to reach high-quality chiral symmetry for domain-wall fermions, or high precision in the case of the overlap operator. An efficient way of suppressing such eigenmodes consists of including a positive power of the determinant of the Wilson kernel in the Boltzmann weight, but doing this also suppresses tunneling between topological sectors. Here we propose a modification of the Hybrid Monte-Carlo algorithm which aims to restore tunneling between topological sectors by excluding the lowest eigenmodes of the Wilson kernel from the molecular-dynamics evolution, and correcting for this at the accept/reject step. We discuss the implications of this modification for the acceptance rate.Comment: improved discussion in appendix B, RevTeX, 19 page

A Continuation Multilevel Monte Carlo algorithm

We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error tolerance is satisfied. CMLMC assumes discretization hierarchies that are defined a priori for each level and are geometrically refined across levels. The actual choice of computational work across levels is based on parametric models for the average cost per sample and the corresponding weak and strong errors. These parameters are calibrated using Bayesian estimation, taking particular notice of the deepest levels of the discretization hierarchy, where only few realizations are available to produce the estimates. The resulting CMLMC estimator exhibits a non-trivial splitting between bias and statistical contributions. We also show the asymptotic normality of the statistical error in the MLMC estimator and justify in this way our error estimate that allows prescribing both required accuracy and confidence in the final result. Numerical results substantiate the above results and illustrate the corresponding computational savings in examples that are described in terms of differential equations either driven by random measures or with random coefficients

Accelerating the Hybrid Monte Carlo algorithm

An algorithm for separating the high- and low-frequency molecular dynamics modes in Hybrid Monte Carlo simulations of gauge theories with dynamical fermions is presented. The separation is based on splitting the pseudo-fermion action into two parts, as was initially proposed by Hasenbusch. We propose to introduce different evolution time-scales for each part. We test our proposal in realistic simulations of two-flavor O(a) improved Wilson fermions. A speed-up of more than a factor of three compared to the standard HMC algorithm is observed in a typical run.Comment: 6 pages, late

The Rational Hybrid Monte Carlo Algorithm

The past few years have seen considerable progress in algorithmic development for the generation of gauge fields including the effects of dynamical fermions. The Rational Hybrid Monte Carlo (RHMC) algorithm, where Hybrid Monte Carlo is performed using a rational approximation in place the usual inverse quark matrix kernel is one of these developments. This algorithm has been found to be extremely beneficial in many areas of lattice QCD (chiral fermions, finite temperature, Wilson fermions etc.). We review the algorithm and some of these benefits, and we compare against other recent algorithm developements. We conclude with an update of the Berlin wall plot comparing costs of all popular fermion formulations.Comment: 15 pages. Proceedings from Lattice 200

A Polynomial Hybrid Monte Carlo Algorithm

We present a simulation algorithm for dynamical fermions that combines the multiboson technique with the Hybrid Monte Carlo algorithm. We find that the algorithm gives a substantial gain over the standard methods in practical simulations. We point out the ability of the algorithm to treat fermion zeromodes in a clean and controllable manner.Comment: Latex, 1 figure, 12 page