Related papers: Event-driven Monte Carlo algorithm for general pot…
Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…
We consider the application of multilevel Monte Carlo methods to elliptic PDEs with random coefficients. We focus on models of the random coefficient that lack uniform ellipticity and boundedness with respect to the random parameter, and…
In this paper, we solve quantum many-body problem by propagating ensembles of trajectories and guiding waves in physical space. We introduce the 'effective potential' correction within the recently proposed time-dependent quantum Monte…
We present a Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix without the need to compute the inner product of two vectors or store all the components of any one vector.…
We discuss non-reversible Markov-chain Monte Carlo algorithms that, for particle systems, rigorously sample the positional Boltzmann distribution and that have faster than physical dynamics. These algorithms all feature a non-thermal…
Any search or sampling algorithm for solution of inverse problems needs guidance to be efficient. Many algorithms collect and apply information about the problem on the fly, and much improvement has been made in this way. However, as a…
In this paper a method based on a Markov chain Monte Carlo (MCMC) algorithm is proposed to compute the probability of a rare event. The conditional distribution of the underlying process given that the rare event occurs has the probability…
In this paper, I investigate more closely the recently proposed Free Energy Monte Carlo algorithm that is devised in particular for calculations where conventional Monte Carlo simulations struggle with ergodicity problems. The simplest…
We prove that for any Monte Carlo algorithm of Metropolis type, the autocorrelation time of a suitable ``energy''-like observable is bounded below by a multiple of the corresponding ``specific heat''. This bound does not depend on whether…
For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed…
Zero- and two-dimensional crystal defects form in open statistical ensembles, such as the grand canonical, that are usually inaccessible with conventional simulation techniques. This longstanding challenge is overcome with a new Hamiltonian…
Hamiltonian Monte Carlo (HMC) is a popular Markov chain Monte Carlo (MCMC) algorithm that generates proposals for a Metropolis-Hastings algorithm by simulating the dynamics of a Hamiltonian system. However, HMC is sensitive to large time…
Quantum computing was so far mainly concerned with discrete problems. Recently, E. Novak and the author studied quantum algorithms for high dimensional integration and dealt with the question, which advantages quantum computing can bring…
In this work, we developed an efficient approach to compute ensemble averages in systems with pairwise-additive energetic interactions between the entities. Methods involving full enumeration of the configuration space result in exponential…
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.…
In the framework of uncertainty quantification, we consider a quantity of interest which depends non-smoothly on the high-dimensional parameter representing the uncertainty. We show that, in this situation, the multilevel Monte Carlo…
We study a method, Extra Chance Generalized Hybrid Monte Carlo, to avoid rejections in the Hybrid Monte Carlo method and related algorithms. In the spirit of delayed rejection, whenever a rejection would occur, extra work is done to find a…
We analyze the convergence of the irreversible event-chain Monte Carlo algorithm for continuous spin models in the presence of topological excitations. In the two-dimensional XY model, we show that the local nature of the Markov-chain…