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Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standard uncertainty quantification (UQ) tools for a wide class of…
A continuous-time path integral Quantum Monte Carlo method using the directed-loop algorithm is developed to simulate the Anderson single-impurity model in the occupation number basis. Although the method suffers from a sign problem at low…
In this article, we study the application of Multi-Level Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some functionals of the homogenized coefficients, or of the…
It is almost 80 years since Hans Bethe described the level density as a non-interacting gas of protons and neutrons. In all these years, experimental data were interpreted within this picture of a fermionic gas. However, the renewed…
The nuclear shell model is known to describe the properties of various nuclei extremely well. However, the auxiliary-field quantum Monte Carlo calculations cannot be applied to it with general interactions due to the sign problem. The model…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
We present a novel multilevel Monte Carlo approach for estimating quantities of interest for stochastic partial differential equations (SPDEs). Drawing inspiration from [Giles and Szpruch: Antithetic multilevel Monte Carlo estimation for…
We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element…
This work introduces two Monte Carlo (MC)-based sampling methods, known as line sampling and subset simulation, to improve the performance of standard MC analyses in the context of asteroid impact risk assessment. Both techniques sample the…
The nuclear shell model assumes an effective mean-field plus interaction Hamiltonian in a specific configuration space. We want to understand how various interaction matrix elements affect the observables, the collectivity in nuclei and the…
Reaction and elastic differential cross sections are calculated for light nuclei in the framework of the Glauber theory. The optical phase-shift function is evaluated by Monte Carlo integration. This enables us to use the most accurate wave…
The efficient approximation of quantity of interest derived from PDEs with lognormal diffusivity is a central challenge in uncertainty quantification. In this study, we propose a multilevel quasi-Monte Carlo framework to approximate…
Nuclei will play a prominent role in searches for physics beyond the Standard Model as the active material in experiments. In order to reliably interpret new physics signals, one needs an accurate model of the underlying nuclear dynamics.…
The following electromagnetism (EM) inverse problem is addressed. It consists in estimating local radioelectric properties of materials recovering an object from global EM scattering measurements, at various incidences and wave frequencies.…
We describe a general radiative equilibrium and temperature correction procedure for use in Monte Carlo radiation transfer codes with sources of temperature-independent opacity, such as astrophysical dust. The technique utilizes the fact…
Techniques for evaluating the normalization integral of the target density for Markov Chain Monte Carlo algorithms are described and tested numerically. It is assumed that the Markov Chain algorithm has converged to the target distribution…
We introduce a multiscale Monte Carlo algorithm to simulate dense simple fluids. The probability of an update follows a power law distribution in its length scale. The collective motion of clusters of particles requires generalization of…
An approach has been devised and tested for preserving the molecular geometry and taking into account energetic considerations during Reverse Monte Carlo modeling. Instead of the commonly used fixed neighbour constraints, where molecules…
A many-flavor electron gas (MFEG) in a semiconductor with a valley degeneracy ranging between 6 and 24 was analyzed using diffusion Monte Carlo (DMC) calculations. The DMC results compare well with an analytic expression derived by one of…
Monte Carlo methods are used to study the phase transition in ammonium chloride from the orientationally ordered $\delta$ phase to the orientationally disordered $\gamma$ phase. An effective pair potential is used to model the interaction…