Related papers: Radiation Transport for Explosive Outflows: Opacit…
Quantitative photoacoustic tomography aims at estimating optical parameters from photoacoustic images that are formed utilizing the photoacoustic effect caused by the absorption of an externally introduced light pulse. This optical…
Radiative transfer simulation is an important tool that allows us to generate synthetic images of various astrophysical objects. In the case of complex three-dimensional geometries, a Monte Carlo-based method that simulates photon packages…
Photon transport through a diffusing slab can be described by the radiative transfer equation (RTE). When the slab is highly scattering and weakly absorbing, the RTE simplifies to the diffusion equation. In this paper, an inverse diffusion…
Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different…
In this paper, we proposed a new Monte Carlo radiative transport (MCRT) scheme, which is based completely on the Neumann series solution of Fredholm integral equation. This scheme indicates that the essence of MCRT is the calculation of…
Bayesian inference in the physical sciences faces a fundamental challenge: the imperative for high-fidelity physical modeling often clashes with the intrinsic limitations of stochastic sampling algorithms. Complex, high-dimensional…
In this paper, we introduce \texttt{SuperLite}, an open-source Monte Carlo radiation transport code designed to produce synthetic spectra for astrophysical transient phenomena affected by circumstellar interaction. \texttt{SuperLite}…
We present density response estimators for Monte Carlo simulations that are based on a reweighting procedure, where the samples of an unperturbed system are used to estimate the properties of a system perturbed by an external harmonic…
This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…
The theory of radiative transfer provides the link between the physical conditions in an astrophysical object and the observable radiation which it emits. Thus accurately modelling radiative transfer is often a necessary part of testing…
This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…
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,…
The possibility of different interpretations of the stochastic term (or calculi) in the overdamped Langevin equation for the motion of a particle in an inhomogeneous medium is often referred to as the "Ito--Stratonovich dilemma," although…
We study Markov Chain Monte Carlo (MCMC) methods operating in primary sample space and their interactions with multiple sampling techniques. We observe that incorporating the sampling technique into the state of the Markov Chain, as done in…
We propose a novel sequential Monte Carlo (SMC) method for sampling from unnormalized target distributions based on a reverse denoising diffusion process. While recent diffusion-based samplers simulate the reverse diffusion using…
In this paper, we propose and analyze a new stochastic homogenization method for diffusion equations with random and fast oscillatory coefficients. In the proposed method, the homogenized solutions are sought through a two-stage procedure.…
Hamiltonian Monte Carlo is a powerful algorithm for sampling from difficult-to-normalize posterior distributions. However, when the geometry of the posterior is unfavorable, it may take many expensive evaluations of the target distribution…
Diffusion models have been successful in learning complex data distributions. This capability has driven their application to high-dimensional multi-objective black-box optimization problem. Existing approaches often employ an external…
Divide-and-conquer MCMC is a strategy for parallelising Markov Chain Monte Carlo sampling by running independent samplers on disjoint subsets of a dataset and merging their output. An ongoing challenge in the literature is to efficiently…
The Kinetic Monte Carlo (KMC) method has become an important tool for examination of phenomena like surface diffusion and thin film growth because of its ability to carry out simulations for time scales that are relevant to experiments. But…