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Hamiltonian Monte Carlo (HMC) is a powerful tool for Bayesian statistical inference due to its potential to rapidly explore high dimensional state space, avoiding the random walk behavior typical of many Markov Chain Monte Carlo samplers.…
This is the write-up of three lectures on algorithms for dynamical fermions that were given at the ILFTN workshop 'Perspectives in Lattice QCD' in Nara during November 2005. The first lecture is on the fundamentals of Markov Chain Monte…
Symplectic integration algorithms are well-suited for long-term integrations of Hamiltonian systems because they preserve the geometric structure of the Hamiltonian flow. However, this desirable property is generally lost when adaptive…
We investigate the properties of the Hybrid Monte-Carlo algorithm (HMC) in high dimensions. HMC develops a Markov chain reversible w.r.t. a given target distribution $\Pi$ by using separable Hamiltonian dynamics with potential $-\log\Pi$.…
Monte Carlo simulations are a powerful tool to investigate the thermodynamic properties of atomic systems. In practice however, sampling of the complete configuration space is often hindered by high energy barriers between different regions…
Monte Carlo simulation using a combination of Wang Landau (WL) and Transition Matrix (TM) Monte Carlo algorithms to simulate two lattice spin models with continuous energy is described. One of the models, the one dimensional Lebwohl-Lasher…
This paper considers the challenging computational task of estimating nested expectations. Existing algorithms, such as nested Monte Carlo or multilevel Monte Carlo, are known to be consistent but require a large number of samples at both…
A possible solution of the notorious sign problem preventing direct Monte Carlo calculations for systems with non-zero chemical potential is to deform the integration region in the complex plane to a Lefschetz thimble. We investigate this…
A general algorithm toward the solution of the fermion sign problem in finite-temperature quantum Monte Carlo simulations has been formulated for discretized fermion path integrals with nearest-neighbor interactions in the Trotter…
By leveraging the natural geometry of a smooth probabilistic system, Hamiltonian Monte Carlo yields computationally efficient Markov Chain Monte Carlo estimation. At least provided that the algorithm is sufficiently well-tuned. In this…
Numerically exact continuous-time Quantum Monte Carlo algorithm for finite fermionic systems with non-local interactions is proposed. The scheme is particularly applicable for general multi-band time-dependent correlations since it does not…
We report the results of simulations of the Lebwohl-Lasher model of the nematic-isotropic transition using a new cluster Monte Carlo algorithm. The algorithm is a modification of the Wolff algorithm for spin systems, and greatly reduces…
Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian…
We present numerically exact continuous-time Quantum Monte Carlo algorithm for fermions with a general non-local in space-time interaction. The new determinantal grand-canonical scheme is based on a stochastic series expansion for the…
We offer a new proposal for the Monte Carlo treatment of many-fermion systems in continuous space. It is based upon Diffusion Monte Carlo with significant modifications: correlated pairs of random walkers that carry opposite signs;…
The purely numerical evaluation of multi-loop integrals and amplitudes can be a viable alternative to analytic approaches, in particular in the presence of several mass scales, provided sufficient accuracy can be achieved in an acceptable…
We apply the Hybrid Monte Carlo method to the simulation of overlap fermions. We give the fermionic force for the molecular dynamics update. We present early results on a small dynamical chiral ensemble.
Hamiltonian Monte Carlo is a popular sampling technique for smooth target densities. The scale lengths of the target have long been known to influence integration error and sampling efficiency. However, quantitative measures intrinsic to…
Applications that require substantial computational resources today cannot avoid the use of heavily parallel machines. Embracing the opportunities of parallel computing and especially the possibilities provided by a new generation of…
In the stochastic gradient descent (SGD) for sequential simulations such as the neural stochastic differential equations, the Multilevel Monte Carlo (MLMC) method is known to offer better theoretical computational complexity compared to the…