[图书][B] Uncertainty quantification in variational inequalities: theory, numerics, and applications
Uncertainty Quantification (UQ) is an emerging and extremely active research discipline
which aims to quantitatively treat any uncertainty in applied models. The primary objective of …
which aims to quantitatively treat any uncertainty in applied models. The primary objective of …
Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration
We study the application of a tailored quasi-Monte Carlo (QMC) method to a class of optimal
control problems subject to parabolic partial differential equation (PDE) constraints under …
control problems subject to parabolic partial differential equation (PDE) constraints under …
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 …
(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 …
optimization problem subject to a convection–diffusion equation with uncertain terms. Our …
A relaxation-based probabilistic approach for PDE-constrained optimization under uncertainty with pointwise state constraints
We consider a class of convex risk-neutral PDE-constrained optimization problems subject
to pointwise control and state constraints. Due to the many challenges associated with …
to pointwise control and state constraints. Due to the many challenges associated with …
A new regularized stochastic approximation framework for stochastic inverse problems
We study the nonlinear inverse problem of estimating stochastic parameters in the fourth-
order partial differential equation with random data. The primary focus is on developing a …
order partial differential equation with random data. The primary focus is on developing a …
A stochastic regularized second-order iterative scheme for optimal control and inverse problems in stochastic partial differential equations
Numerous applied models used in the study of optimal control problems, inverse problems,
shape optimization, machine learning, fractional programming, neural networks, image …
shape optimization, machine learning, fractional programming, neural networks, image …
Multilevel optimization for inverse problems
Inverse problems occur in a variety of parameter identification tasks in engineering. Such
problems are challenging in practice, as they require repeated evaluation of computationally …
problems are challenging in practice, as they require repeated evaluation of computationally …
Consistency of Monte Carlo estimators for risk-neutral PDE-constrained optimization
J Milz - Applied Mathematics & Optimization, 2023 - Springer
We apply the sample average approximation (SAA) method to risk-neutral optimization
problems governed by nonlinear partial differential equations (PDEs) with random inputs …
problems governed by nonlinear partial differential equations (PDEs) with random inputs …
Reliable error estimates for optimal control of linear elliptic PDEs with random inputs
J Milz - SIAM/ASA Journal on Uncertainty Quantification, 2023 - SIAM
We discretize a risk-neutral optimal control problem governed by a linear elliptic partial
differential equation with random inputs using a Monte Carlo sample-based approximation …
differential equation with random inputs using a Monte Carlo sample-based approximation …