Related papers: Monte Carlo Dynamically Weighted Importance Sampli…

Recent papers in the field of Finite Element Model (FEM) updating have highlighted the benefits of Bayesian techniques. The Bayesian approaches are designed to deal with the uncertainties associated with complex systems, which is the main…

The Finite Element Method (FEM) is a well-established procedure for computing approximate solutions to deterministic engineering problems described by partial differential equations. FEM produces discrete approximations of the solution with…

Finite element model updating is challenging because 1) the problem is oftentimes underdetermined while the measurements are limited and/or incomplete; 2) many combinations of parameters may yield responses that are similar with respect to…

Malliavin weight sampling (MWS) is a stochastic calculus technique for computing the derivatives of averaged system properties with respect to parameters in stochastic simulations, without perturbing the system's dynamics. It applies to…

In this paper, a non-probabilistic method based on fuzzy logic is used to update finite element models (FEMs). Model updating techniques use the measured data to improve the accuracy of numerical models of structures. However, the measured…

It is common practice in Markov chain Monte Carlo to update the simulation one variable (or sub-block of variables) at a time, rather than conduct a single full-dimensional update. When it is possible to draw from each full-conditional…

Adaptive importance sampling is a widely spread Monte Carlo technique that uses a re-weighting strategy to iteratively estimate the so-called target distribution. A major drawback of adaptive importance sampling is the large variance of the…

In the study of complex systems, evaluating physical observables often requires sampling representative configurations via Monte Carlo techniques. These methods rely on repeated evaluations of the system's energy and force fields, which can…

Full-Waveform Inversion (FWI) has now become a widely accepted tool to obtain high-resolution velocity models from seismic data. Typically, the velocity model in its discrete form is represented on a rectangular grid, and we solve for the…

This paper is dedicated to the rigorous numerical analysis of a Multiscale Finite Element Method (MsFEM) for the Stokes system, when dealing with highly heterogeneous media, as proposed in [B.P.~Muljadi et al., arXiv:1404.2837]. The method…

The importance sampling (IS) method lies at the core of many Monte Carlo-based techniques. IS allows the approximation of a target probability distribution by drawing samples from a proposal (or importance) distribution, different from the…

For adaptive mixed finite element methods (AMFEM), we first introduce the data oscillation to analyze, without the restriction that the inverse of the coefficient matrix of the partial differential equations (PDEs) is a piecewise polynomial…

Various Markov chain Monte Carlo (MCMC) methods are studied to improve upon random walk Metropolis sampling, for simulation from complex distributions. Examples include Metropolis-adjusted Langevin algorithms, Hamiltonian Monte Carlo, and…

Equilibrium systems evolve according to Detailed Balance (DB). This principe guided development of the Monte-Carlo sampling techniques, of which Metropolis-Hastings (MH) algorithm is the famous representative. It is also known that DB is…

The Adaptive Multiple Importance Sampling (AMIS) algorithm is aimed at an optimal recycling of past simulations in an iterated importance sampling scheme. The difference with earlier adaptive importance sampling implementations like…

When solving stochastic partial differential equations (SPDEs) driven by additive spatial white noise, the efficient sampling of white noise realizations can be challenging. Here, we present a new sampling technique that can be used to…

The Metropolis Hastings algorithm and its multi-proposal extensions are aimed at the computation of the expectation $<\pi,f>$ of a function $f$ under a probability measure $\pi$ difficult to simulate. They consist in constructing by an…

In general, there is a mismatch between a finite element model {(FEM)} of a structure and its real behaviour. In aeronautics, this mismatch must be small because {FEM}s are a fundamental part of the development of an aircraft and of…

Importance weighting is a general way to adjust Monte Carlo integration to account for draws from the wrong distribution, but the resulting estimate can be highly variable when the importance ratios have a heavy right tail. This routinely…

Recent years have seen a rise in the application of machine learning techniques to aid the simulation of hard-to-sample systems that cannot be studied using traditional methods. Despite the introduction of many different architectures and…