Related papers: Computing active subspaces with Monte Carlo
The Auxiliary Field Diffusion Monte Carlo method has been applied to simulate droplets of 7 and 8 neutrons. Results for realistic nucleon-nucleon interactions, which include tensor, spin--orbit and three--body forces, plus a standard…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…
The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…
Microscopic processes on surfaces such as adsorption, desorption, diffusion and reaction of interacting particles can be simulated using kinetic Monte Carlo (kMC) algorithms. Even though kMC methods are accurate, they are computationally…
The advances in materials and biological sciences have necessitated the use of molecular simulations to study polymers. The Markov chain Monte Carlo simulations enable the sampling of relevant microstates of polymeric systems by traversing…
Eigenmaps are important in analysis, geometry, and machine learning, especially in nonlinear dimension reduction. Approximation of the eigenmaps of a Laplace operator depends crucially on the scaling parameter $\epsilon$. If $\epsilon$ is…
Active subspace (AS) methods are a valuable tool for understanding the relationship between the inputs and outputs of a Physics simulation. In this paper, an elegant generalization of the traditional ASM is developed to assess the…
Lower-dimensional subspaces that impact estimates of uncertainty are often described by Linear combinations of input variables, leading to active variables. This paper extends the derivative-based active subspace methods and…
This paper concerns the use of sequential Monte Carlo methods (SMC) for smoothing in general state space models. A well-known problem when applying the standard SMC technique in the smoothing mode is that the resampling mechanism introduces…
An efficient Path Integral Monte Carlo procedure is proposed to simulate the behavior of quantum many-body dissipative systems described within the framework of the influence functional. Thermodynamic observables are obtained by Monte Carlo…
This paper introduces a subspace method for the estimation of an array covariance matrix. It is shown that when the received signals are uncorrelated, the true array covariance matrices lie in a specific subspace whose dimension is…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
In the context of principal components analysis (PCA), the bootstrap is commonly applied to solve a variety of inference problems, such as constructing confidence intervals for the eigenvalues of the population covariance matrix $\Sigma$.…
We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…
Monte Carlo (MC) is generally considered as the most accurate dose calculation tool for particle therapy. However, a proper description of the beam particles kinematics is a necessary input for a realistic simulation. Such a description can…
This paper investigates a novel a-posteriori variance reduction approach in Monte Carlo image synthesis. Unlike most established methods based on lateral filtering in the image space, our proposition is to produce the best possible estimate…
We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated (we consider…
The properties of ideal tri-functional dendrimers with forty-five, ninety-three and one hundred and eighty-nine branches are investigated. Three methods are employed to calculate the mean-square radius of gyration, $g$-ratios, asphericity,…
Stochastic PDE eigenvalue problems often arise in the field of uncertainty quantification, whereby one seeks to quantify the uncertainty in an eigenvalue, or its eigenfunction. In this paper we present an efficient multilevel quasi-Monte…