Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey

J Zhang - Wiley Interdisciplinary Reviews: Computational …, 2021 - Wiley Online Library
Uncertainty quantification (UQ) includes the characterization, integration, and propagation of
uncertainties that result from stochastic variations and a lack of knowledge or data in the …

Optimal design of acoustic metamaterial cloaks under uncertainty

P Chen, MR Haberman, O Ghattas - Journal of Computational Physics, 2021 - Elsevier
In this work, we consider the problem of optimal design of an acoustic cloak under
uncertainty and develop scalable approximation and optimization methods to solve this …

A quasi-Monte Carlo method for optimal control under uncertainty

PA Guth, V Kaarnioja, FY Kuo, C Schillings… - SIAM/ASA Journal on …, 2021 - SIAM
We study an optimal control problem under uncertainty, where the target function is the
solution of an elliptic partial differential equation with random coefficients, steered by a …

Existence and optimality conditions for risk-averse PDE-constrained optimization

DP Kouri, TM Surowiec - SIAM/ASA Journal on Uncertainty Quantification, 2018 - SIAM
Uncertainty is ubiquitous in virtually all engineering applications, and, for such problems, it is
inadequate to simulate the underlying physics without quantifying the uncertainty in …

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

M Martin, S Krumscheid, F Nobile - ESAIM: Mathematical Modelling …, 2021 - esaim-m2an.org
We consider the numerical approximation of an optimal control problem for an elliptic Partial
Differential Equation (PDE) with random coefficients. Specifically, the control function is a …

Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty

P Chen, U Villa, O Ghattas - Journal of Computational Physics, 2019 - Elsevier
In this work we develop a scalable computational framework for the solution of PDE-
constrained optimal control problems under high-dimensional uncertainty. Specifically, we …

On multilevel best linear unbiased estimators

D Schaden, E Ullmann - SIAM/ASA Journal on Uncertainty Quantification, 2020 - SIAM
We present a general variance reduction technique for the estimation of the expectation of a
scalar-valued quantity of interest associated with a family of model evaluations. The key idea …

A stochastic gradient method with mesh refinement for PDE-constrained optimization under uncertainty

C Geiersbach, W Wollner - SIAM Journal on Scientific Computing, 2020 - SIAM
Models incorporating uncertain inputs, such as random forces or material parameters, have
been of increasing interest in PDE-constrained optimization. In this paper, we focus on the …

An efficient ADAM-type algorithm with finite elements discretization technique for random elliptic optimal control problems

H Song, H Wang, J Wu, J Yang - Journal of Computational and Applied …, 2025 - Elsevier
We consider an optimal control problem governed by an elliptic partial differential equation
(PDE) with random coefficient, and introduce an efficient numerical method for the problem …

A stochastic gradient algorithm with momentum terms for optimal control problems governed by a convection–diffusion equation with random diffusivity

SC Toraman, H Yücel - Journal of Computational and Applied Mathematics, 2023 - Elsevier
In this paper, we focus on a numerical investigation of a strongly convex and smooth
optimization problem subject to a convection–diffusion equation with uncertain terms. Our …