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A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are…
This paper considers uncertainty quantification for an elliptic nonlocal equation. In particular, it is assumed that the parameters which define the kernel in the nonlocal operator are uncertain and a priori distributed according to a…
This paper considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In particular, the application of the multilevel quasi-Monte Carlo…
Numerical models of complex real-world phenomena often necessitate High Performance Computing (HPC). Uncertainties increase problem dimensionality further and pose even greater challenges. We present a parallelization strategy for…
We quantify uncertainties in the location and magnitude of extreme pressure spots revealed from large scale multi-phase flow simulations of cloud cavitation collapse. We examine clouds containing 500 cavities and quantify uncertainties…
In many models used in engineering and science, material properties are uncertain or spatially varying. For example, in geophysics, and porous media flow in particular, the uncertain permeability of the material is modelled as a random…
Efficient uncertainty quantification algorithms are key to understand the propagation of uncertainty -- from uncertain input parameters to uncertain output quantities -- in high resolution mathematical models of brain physiology. Advanced…
Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies.…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…
Mathematical models are essential for understanding and making predictions about systems arising in nature and engineering. Yet, mathematical models are a simplification of true phenomena, thus making predictions subject to uncertainty.…
We develop a multilevel Monte Carlo (MLMC) framework for uncertainty quantification with Monte Carlo dropout. Treating dropout masks as a source of epistemic randomness, we define a fidelity hierarchy by the number of stochastic forward…
We consider the application of multilevel Monte Carlo methods to steady state Darcy flow in a random porous medium, described mathematically by elliptic partial differential equations with random coefficients. The levels in the multilevel…
We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such…
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…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
We study time harmonic acoustic scattering on large deviation rough random scatterers. Therein, the roughness of the scatterers is caused by a low Sobolev regularity in the covariance function of their deformation field. The motivation for…
This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…
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…
We consider a class of high-dimensional spatial filtering problems, where the spatial locations of observations are unknown and driven by the partially observed hidden signal. This problem is exceptionally challenging as not only is…