Related papers: A Particle Method for Solving Fredholm Equations o…
Objective: The subtraction approach is known for being a theoretically-rigorous and accurate technique for solving the forward problem in electroencephalography by means of the finite element method. One key aspect of this approach consists…
Particle smoothers are widely used algorithms allowing to approximate the smoothing distribution in hidden Markov models. Existing algorithms often suffer from slow computational time or degeneracy. We propose in this paper a way to improve…
A physical model based on a Monte-Carlo approach is proposed to calculate the ionization dynam- ics of warm dense matters (WDM) within particle-in-cell simulations, and where the impact (col- lision) ionization (CI), electron-ion…
Particle-in-cell (PIC) simulations are essential for studying kinetic plasma processes, but they often suffer from statistical noise, especially in plasmas with fast flows. We have also found that the typical central difference scheme used…
We construct deterministic particle solutions for linear and fast diffusion equations using a nonlocal approximation. We exploit the $2$-Wasserstein gradient flow structure of the equations in order to obtain the nonlocal approximating PDEs…
Using diffusion models to solve inverse problems is a growing field of research. Current methods assume the degradation to be known and provide impressive results in terms of restoration quality and diversity. In this work, we leverage the…
We present a novel sequential Monte Carlo approach to online smoothing of additive functionals in a very general class of path-space models. Hitherto, the solutions proposed in the literature suffer from either long-term numerical…
Previously, the authors derived an analog of the Euler-Maru\-yama method (fEMM) for free stochastic differential equations (fSDEs) and proved strong convergence of order $\gamma=0.5$ in $L_1(\varphi)$-norm under certain assumptions. In this…
We propose two new Bayesian smoothing methods for general state-space models with unknown parameters. The first approach is based on the particle learning and smoothing algorithm, but with an adjustment in the backward resampling weights.…
This paper presents a class of boundary integral equations for the solution of problems of electromagnetic and acoustic scattering by two dimensional homogeneous penetrable scatterers with smooth boundaries. The new integral equations,…
The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the…
A major challenge facing existing sequential Monte-Carlo methods for parameter estimation in physics stems from the inability of existing approaches to robustly deal with experiments that have different mechanisms that yield the results…
Traditional Monte Carlo integration using uniform random sampling exhibits degraded efficiency in low-regularity or high-dimensional problems. We propose a novel deep learning framework based on deterministic number-theoretic sampling…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
The discretization of surface intrinsic elliptic partial differential equations (PDEs) poses interesting challenges not seen in flat space. The discretization of these PDEs typically proceeds by either parametrizing the surface,…
In this article we design a novel quasi-regression Monte Carlo algorithm in order to approximate the solution of discrete time backward stochastic differential equations (BSDEs), and we analyze the convergence of the proposed method. The…
Many applications in science and engineering require the solution of large linear discrete ill-posed problems that are obtained by the discretization of a Fredholm integral equation of the first kind in several space-dimensions. The matrix…
The purpose of this paper is to give a convergence analysis of the iterative scheme: \bee u_n^\dl=qu_{n-1}^\dl+(1-q)T_{a_n}^{-1}K^*f_\dl,\quad u_0^\dl=0,\eee where $T:=K^*K,\quad T_a:=T+aI,\quad q\in(0,1),\quad a_n:=\alpha_0q^n,…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
This paper presents a novel formulation and consequently a new solution for two dimensional TM electromagnetic integral equations by the method of moments in polar coordination. The main idea is the reformulation of the 2-D problem…