Related papers: Non-Canonical Hamiltonian Monte Carlo
Stoquastic Hamiltonians are characterized by the property that their off-diagonal matrix elements in the standard product basis are real and non-positive. Many interesting quantum models fall into this class including the Transverse field…
Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part…
Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…
We introduce a variant of the Hybrid Monte Carlo (HMC) algorithm to address large-deviation statistics in stochastic hydrodynamics. Based on the path-integral approach to stochastic (partial) differential equations, our HMC algorithm…
Hamiltonian Monte Carlo (HMC) is a state-of-the-art Markov chain Monte Carlo sampling algorithm for drawing samples from smooth probability densities over continuous spaces. We study the variant most widely used in practice, Metropolized…
We propose a modification of the Hybrid Monte Carlo (HMC) algorithm that overcomes the topological freezing of a two-dimensional $U(1)$ gauge theory with and without fermion content. This algorithm includes reversible jumps between…
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…
In this work, a nonlinear momentum method is introduced to enhance the convergence performance of momentum-based gradient optimization algorithms. Classical momentum methods, such as the Heavy Ball method, can be viewed as a dynamical…
Stochastic sampling algorithms such as Langevin Monte Carlo are inspired by physical systems in a heat bath. Their equilibrium distribution is the canonical ensemble given by a prescribed target distribution, so they must balance…
An implicit mass-matrix penalization (IMMP) of Hamiltonian dynamics is proposed, and associated dynamical integrators, as well as sampling Monte-Carlo schemes, are analyzed for systems with multiple time scales. The penalization is based on…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
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…
Modified Hamiltonians are used in the field of geometric numerical integration to show that symplectic schemes for Hamiltonian systems are accurate over long times. For nonlinear systems the series defining the modified Hamiltonian usually…
We present the symplectic algorithm in the Lagrangian formalism for the Hamiltonian systems by virtue of the noncommutative differential calculus with respect to the discrete time and the Euler--Lagrange cohomological concepts. We also show…
We present a practical strategy to optimize a set of Hybrid Monte Carlo parameters in simulations of QCD and QCD-like theories. We specialize to the case of mass-preconditioning, with multiple time-step Omelyan integrators. Starting from…
Symplectic integrators constructed from Hamiltonian and Lie formalisms are obtained as symplectic maps whose flow follows the exact solution of a "sourrounded" Hamiltonian K = H + h^k H_1. Those modified Hamiltonians depends virtually on…
The problem of sampling constrained continuous distributions has frequently appeared in many machine/statistical learning models. Many Monte Carlo Markov Chain (MCMC) sampling methods have been adapted to handle different types of…
We explore a particular approach to the analysis of dynamical and geometrical properties of autonomous, Pfaffian non-holonomic systems in classical mechanics. The method is based on the construction of a certain auxiliary constrained…
Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space time by means of a generalized Hamiltonian dynamics in an extra time variable $\tau$ which, at…