Related papers: Surrogate-based multilevel Monte Carlo methods for…

Bayesian inverse problems arise in various scientific and engineering domains, and solving them can be computationally demanding. This is especially the case for problems governed by partial differential equations, where the repeated…

The multilevel Monte Carlo method is applied to an academic example in the field of electromagnetism. The method exhibits a reduced variance by assigning the samples to multiple models with a varying spatial resolution. For the given…

Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…

In this paper, we consider the implementation of multi-level Monte Carlo method to a stochastic optimal control problem with log-normal coefficients and its surrogate model problem. From the perspective of two optimization problems, i.e.,…

Quantification and minimization of uncertainty is an important task in the design of electromagnetic devices, which comes with high computational effort. We propose a hybrid approach combining the reliability and accuracy of a Monte Carlo…

The embedded ensemble propagation approach introduced in [49] has been demonstrated to be a powerful means of reducing the computational cost of sampling-based uncertainty quantification methods, particularly on emerging computational…

The paper addresses Bayesian inferences in inverse problems with uncertainty quantification involving a computationally expensive forward map associated with solving a partial differential equations. To mitigate the computational cost, the…

Numerical simulations in climate, chemistry, or astrophysics are computationally too expensive for uncertainty quantification or parameter-exploration at high-resolution. Reduced-order or surrogate models are multiple orders of magnitude…

This article proposes a weighted-variational model as an approximated surrogate model to lessen numerical complexity and lower the execution times of brittle fracture simulations. Consequently, Monte Carlo studies of brittle fractures…

Predictive estimation, which comprises model calibration, model prediction, and validation, is a common objective when performing inverse uncertainty quantification (UQ) in diverse scientific applications. These techniques typically require…

Hybrid methods for simulating rarefied gas flows reduce computational cost by coupling a particle-based model, typically the direct simulation Monte Carlo (DSMC) method, to a continuum-based solver, i.e. a computational fluid dynamics (CFD)…

Vertical equilibrium (VE) models have been introduced as computationally efficient alternatives to traditional mass and momentum balance equations for fluid flow in porous media. Since VE models are only accurate in regions where phase…

Monte Carlo simulations of quantum field theories on a lattice become increasingly expensive as the continuum limit is approached since the cost per independent sample grows with a high power of the inverse lattice spacing. Simulations on…

We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational…

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…

In this paper we present an algorithm for yield estimation and optimization exploiting Hessian based optimization methods, an adaptive Monte Carlo (MC) strategy, polynomial surrogates and several error indicators. Yield estimation is used…

Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models for variance reduction to make tractable uncertainty quantification even when numerically simulating the physical systems of interest with high-fidelity models is…

We propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modelling magnetic plasma equilibrium in axisymmetric confinement devices. In the fixed boundary case, the equation is posed on curved…

In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large--scale applications with high dimensional parameter spaces, e.g. in uncertainty quantification in…

Estimation of patient-specific model parameters is important for personalized modeling, although sparse and noisy clinical data can introduce significant uncertainty in the estimated parameter values. This importance source of uncertainty,…