Related papers: Non-Boltzmann Ensembles and Monte Carlo Simulation
Quantum Boltzmann machines are natural quantum generalizations of Boltzmann machines that are expected to be more expressive than their classical counterparts, as evidenced both numerically for small systems and asymptotically under various…
We present a novel framework for performing statistical sampling, expectation estimation, and partition function approximation using \emph{arbitrary} heuristic stochastic processes defined over discrete state spaces. Using a highly parallel…
We consider the Ensemble Kalman Inversion which has been recently introduced as an efficient, gradient-free optimisation method to estimate unknown parameters in an inverse setting. In the case of large data sets, the Ensemble Kalman…
We develop a formulation for molecular dynamics, Langevin, and hybrid Monte Carlo algorithms in the recently proposed generalized ensemble that is based on a physically motivated realisation of Tsallis weights. The effectiveness of the…
Umbrella sampling is an efficient method for the calculation of free energy changes of a system along well-defined reaction coordinates. However, when multiple parallel channels along the reaction coordinate or hidden barriers in directions…
We present a new Monte Carlo algorithm that produces results of high accuracy with reduced simulational effort. Independent random walks are performed (concurrently or serially) in different, restricted ranges of energy, and the resultant…
Entropy is a quantity for counting physical degrees of freedom in a system. At a finite temperature, one can use thermal entropy to study thermodynamical properties. At zero temperature, entanglement entropy is expected to provide a…
We demonstrate the use of a new algorithm called the Flat Histogram sampling algorithm for the simulation of lattice polymer systems. Thermodynamics properties, such as average energy or entropy and other physical quantities such as…
The postulates of thermodynamics were originally formulated for macroscopic systems. They lead to the definition of the entropy, which, for a homogeneous system, is a homogeneous function of order one in the extensive variables and is…
Quantum Monte Carlo methods are powerful tools for studying quantum many-body systems but face difficulties in accessing excited states and in treating sign problems. We present a continuous-time path-integral Monte Carlo method for…
We consider generalizations of the classical inverse problem to Bayesien type estimators, where the result is not one optimal parameter but an optimal probability distribution in parameter space. The practical computational tool to compute…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…
Continuous-time quantum Monte Carlo refers to a class of algorithms designed to sample the thermal distribution of a quantum Hamiltonian through exact expansions of the Boltzmann exponential in terms of stochastic trajectories which are…
I generalize the well-known classical Metropolis-Hastings algorithm into a quantum algorithm that can equilibrate, measure, and mix a quantum thermal state on a quantum computer. It performs non-symmetric transitions on labels of state…
The combinatorial basis of entropy by Boltzmann can be written $H= {N}^{-1} \ln \mathbb{W}$, where $H$ is the dimensionless entropy of a system, per unit entity, $N$ is the number of entities and $\mathbb{W}$ is the number of ways in which…
In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model…
To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…
Local Shannon entropy lies at the heart of modern thermodynamics, with much discussion of trajectory-dependent entropy production. When taken at both boundaries of a process in phase space, it reproduces the second law of thermodynamics…
A generic algorithm for the extraction of probabilistic (Bayesian) information about model parameters from data is presented. The algorithm propagates an ensemble of particles in the product space of model parameters and outputs. Each…