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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…
In this paper we present two efficient implementations of the diffusion approximation to be employed in Monte Carlo computations of radiative transfer in dusty media of massive circumstellar disks. The aim is to improve the accuracy of the…
Monte Carlo dropout may effectively capture model uncertainty in deep learning, where a measure of uncertainty is obtained by using multiple instances of dropout at test time. However, Monte Carlo dropout is applied across the whole network…
We study the multi-dimensional radiative transfer phenomena using the ISMC scheme, in both gray and multi-frequency problems. Implicit Monte-Carlo (IMC) schemes have been in use for five decades. The basic algorithm yields teleportation…
In a typical finite temperature quantum Monte Carlo (QMC) simulation, estimators for simple static observables such as specific heat and magnetization are known. With a great deal of system-specific manual labor, one can sometimes also…
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…
This work generalizes the discrete implicit Monte-Carlo (DIMC) method for modeling the radiative transfer equation from a gray treatment to an frequency-dependent one. The classic implicit Monte-Carlo (IMC) algorithm, that has been used for…
This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as…
This study investigates numerical methods to solve nonlinear transport problems characterized by various sorption isotherms with a focus on the Freundlich type of isotherms. We describe and compare second order accurate numerical schemes,…
Radiative transfer describes the propagation of electromagnetic radiation through an interacting medium. This process is often simulated by the use of the Monte Carlo method, which involves the probabilistic determination and tracking of…
Quasi-Monte Carlo methods have become the industry standard in computer graphics. For that purpose, efficient algorithms for low discrepancy sequences are discussed. In addition, numerical pitfalls encountered in practice are revealed. We…
An open source software package for simulating thermal neutron propagation in geometry is presented. In this system, neutron propagation can be treated by either the particle transport method or the ray-tracing method. Supported by an…
We obtain an expansion of the implicit weak discretization error for the target of stochastic approximation algorithms introduced and studied in [Frikha2013]. This allows us to extend and develop the Richardson-Romberg extrapolation method…
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…
Many problems require to approximate an expected value by some kind of Monte Carlo (MC) sampling, e.g. molecular dynamics (MD) or simulation of stochastic reaction models (also termed kinetic Monte Carlo (kMC)). Often, we are furthermore…
We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…
In this paper, we propose and analyze a new semi-implicit stochastic multiscale method for the radiative heat transfer problem with additive noise fluctuation in composite materials. In the proposed method, the strong nonlinearity term…
In this paper, we use reduced precision checking (RPC) to detect errors in floating point arithmetic. Prior work explored RPC for addition and multiplication. In this work, we extend RPC to a complete floating point unit (FPU), including…
We present a Multi-Index Quasi-Monte Carlo method for the solution of elliptic partial differential equations with random coefficients. By combining the multi-index sampling idea with randomly shifted rank-1 lattice rules, the algorithm…
We develop a new numerical scheme which allows precise solution of coherent tunneling problems, i.e., problems with exponentially small transition amplitudes between quasidegenerate states. We explain how this method works for the…