Related papers: Computing active subspaces with Monte Carlo
In recent years dynamical systems (of deterministic and stochastic nature), describing many models in mathematics, physics, engineering and finances, become more and more complex. Numerical analysis narrowed only to deterministic algorithms…
Consider a central problem in randomized approximation schemes that use a Monte Carlo approach. Given a sequence of independent, identically distributed random variables $X_1,X_2,\ldots$ with mean $\mu$ and standard deviation at most $c…
Correlated fermions are of high interest in condensed matter (Fermi liquids, Wigner molecules), cold atomic gases and dense plasmas. Here we propose a novel approach to path integral Monte Carlo (PIMC) simulations of strongly degenerate…
This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a…
Probability Theory and Statistics are two of the most useful mathematical fields, and also two of the most difficult to learn. In other science fields, as Physics, experimentation is an useful tool to develop students intuition, but the…
In this paper, we propose a type of tensor-neural-network-based machine learning method to compute multi-eigenpairs of high dimensional eigenvalue problems without Monte-Carlo procedure. Solving multi-eigenvalues and their corresponding…
Artificial Neural Networks were recently shown to be an efficient representation of highly-entangled many-body quantum states. In practical applications, neural-network states inherit numerical schemes used in Variational Monte Carlo, most…
An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as…
We propose a novel Monte-Carlo based ab-initio algorithm for directly computing the statistics for quantities of interest in an immiscible two-phase compressible flow. Our algorithm samples the underlying probability space and evolves these…
In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the…
We introduce a novel variance-reducing Monte Carlo algorithm for accurate determination of autocorrelation times. We apply this method to two-dimensional Ising systems with sizes up to $15 \times 15$, using single-spin flip dynamics, random…
We propose that a combination of the semiclassical approximation with Monte Carlo simulations can be an efficient and reliable impurity solver for dynamical mean field theory equations and their cluster extensions with large cluster sizes.…
One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…
Accurate free energy representations are crucial for understanding phase dynamics in materials. We employ a scale-bridging approach to incorporate atomistic information into our free energy model by training a neural network on DFT-informed…
The behaviour of the one--dimensional random--forced Burgers equation is investigated in the path integral formalism, using a discrete space--time lattice. We show that by means of Monte Carlo methods one may evaluate observables, such as…
Pixel-space full spectrum fitting exploiting non-linear $\chi^2$ minimization became a \emph{de facto} standard way of deriving internal kinematics from absorption line spectra of galaxies and star clusters. However, reliable estimation of…
Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…
A one-dimensional model of electrons locally coupled to spin-1/2 degrees of freedom is studied by numerical techniques. The model is one in the class of $dynamic$ $Hubbard$ $models$ that describe the relaxation of an atomic orbital upon…
The trace of a matrix function f(A), most notably of the matrix inverse, can be estimated stochastically using samples< x,f(A)x> if the components of the random vectors x obey an appropriate probability distribution. However such a…
We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…