相关论文: Kinetic energy choice in Hamiltonian/hybrid Monte …

Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…

In Hamiltonian Monte Carlo sampling, the shape of the potential and the choice of the momentum distribution jointly give rise to the Hamiltonian dynamics of the sampler. An efficient sampler propagates quickly in all regions of the…

We show how the Hamiltonian Monte Carlo algorithm can sometimes be speeded up by "splitting" the Hamiltonian in a way that allows much of the movement around the state space to be done at low computational cost. One context where this is…

We investigate instability and reversibility within Hybrid Monte Carlo simulations using a non-perturbatively improved Wilson action. We demonstrate the onset of instability as tolerance parameters and molecular dynamics step sizes are…

The HMC algorithm, combining the advantages of molecular dynamics and Monte-Carlo methods, is the most efficient algorithm to simulate QCD including the effects of sea quarks. In the standard approach momentum fields are generated with a…

Hamiltonian Monte Carlo (HMC) improves the computational efficiency of the Metropolis algorithm by reducing its random walk behavior. Riemannian Manifold HMC (RMHMC) further improves HMC's performance by exploiting the geometric properties…

Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of simple random-walk proposals. Though…

We develop Microcanonical Hamiltonian Monte Carlo (MCHMC), a class of models which follow a fixed energy Hamiltonian dynamics, in contrast to Hamiltonian Monte Carlo (HMC), which follows canonical distribution with different energy levels.…

Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also…

Hamiltonian Monte Carlo (HMC) samples efficiently from high-dimensional posterior distributions with proposed parameter draws obtained by iterating on a discretized version of the Hamiltonian dynamics. The iterations make HMC…

Existing rigorous convergence guarantees for the Hamiltonian Monte Carlo (HMC) algorithm use Gaussian auxiliary momentum variables, which are crucially symmetrically distributed. We present a novel convergence analysis for HMC utilizing new…

Multiple pendulums are investigated numerically and analytically to clarify the nonuniformity of average kinetic energies of particles. The nonuniformity is attributed to the system having constraints and it is consistent with the…

When properly tuned, Hamiltonian Monte Carlo scales to some of the most challenging high-dimensional problems at the frontiers of applied statistics, but when that tuning is suboptimal the performance leaves much to be desired. In this…

Estimating the eigenvalue or energy gap of a Hamiltonian H is vital for studying quantum many-body systems. Particularly, many of the problems in quantum chemistry, condensed matter physics, and nuclear physics investigate the energy gap…

The energy variance optimization algorithm over a fixed ensemble of configurations in variational Monte Carlo is formally identical to a problem of fitting data: we reexamine it from a statistical maximum-likelihood point of view. We detect…

We consider several multiscale-in-time kinetic Monte Carlo models, in which some variables evolve on a fast time scale, while the others evolve on a slow time scale. In the first two models we consider, a particle evolves in a…

We establish a physically meaningful representation of a quantum energy density for use in Quantum Monte Carlo calculations. The energy density operator, defined in terms of Hamiltonian components and density operators, returns the correct…

Sampling from an unnormalized probability distribution is a fundamental problem in machine learning with applications including Bayesian modeling, latent factor inference, and energy-based model training. After decades of research,…

Properties of the turbulent cascade of kinetic energy are studied using direct numerical simulations of three-dimensional hydrodynamic decaying turbulence with a moderate Reynolds number and the initial Mach number $M=1$. Compressible and…

For quantum systems with competing potentials, the conventional perturbation theory often yields an asymptotic series and the subsequent numerical outcome becomes uncertain. To tackle such kind of problems, we develop a general solution…