15 citations · 26 across the 15 of their papers we have counts for
16 papers
Dynamic output-feedback stabilization of uncertain linear dynamics via digital twins
Philipp A. Guth, Karl Kunisch, Sergio S. Rodrigues +1
This work presents a digital twin framework for output-feedback stabilization and parameter identification in uncertain dynamical systems. A virtual model evolves in parallel with…
Multilevel Stochastic Gradient Descent for Risk-Averse PDE-Constrained Optimization
Niklas Baumgarten, Philipp A. Guth, David Schneiderhan +1
We present recent advances in applying and analyzing multilevel stochastic gradient descent algorithms to risk-averse, three-dimensional PDE-constrained optimization problems. The…
On the optimality of dimension truncation error rates for a class of parametric partial differential equations
Philipp A. Guth, Vesa Kaarnioja
In uncertainty quantification for parametric partial differential equations (PDEs), it is common to model uncertain random field inputs using countably infinite sequences of indepe…
Approximation of risk-averse optimal feedback control
Philipp A. Guth, Karl Kunisch
The challenge of constructing feedback control laws for risk-averse optimal control of partial differential equations (PDEs) with random coefficients is addressed. The control obje…
Quasi-Monte Carlo for partial differential equations with generalized Gaussian input uncertainty
Philipp A. Guth, Vesa Kaarnioja
There has been a surge of interest in uncertainty quantification for parametric partial differential equations (PDEs) with Gevrey regular inputs. The Gevrey class contains function…
Quasi-Monte Carlo integration for feedback control under uncertainty
Philipp A. Guth, Peter Kritzer, Karl Kunisch
A control in feedback form is derived for linear quadratic, time-invariant optimal control problems subject to parabolic partial differential equations with coefficients depending…
Tracking optimal feedback control under uncertain parameters
Philipp A. Guth, Karl Kunisch, Sergio S. Rodrigues
Optimal control problems of tracking type for a class of linear systems with uncertain parameters in the dynamics are investigated. An affine tracking feedback control input is obt…
Stabilization of uncertain linear dynamics: an offline-online strategy
Philipp A. Guth, Karl Kunisch, Sérgio S. Rodrigues
A strategy is proposed for adaptive stabilization of linear systems, depending on an uncertain parameter. Offline, the Riccati stabilizing feedback input control operators, corresp…
Ensemble Feedback Stabilization of Linear Systems
Philipp A. Guth, Karl Kunisch, Sergio S. Rodrigues
Stabilization of linear control systems with parameter-dependent system matrices is investigated. A Riccati based feedback mechanism is proposed and analyzed. It is constructed by…
Application of dimension truncation error analysis to high-dimensional function approximation in uncertainty quantification
Philipp A. Guth, Vesa Kaarnioja
Parametric mathematical models such as parameterizations of partial differential equations with random coefficients have received a lot of attention within the field of uncertainty…
Generalized dimension truncation error analysis for high-dimensional numerical integration: lognormal setting and beyond
Philipp A. Guth, Vesa Kaarnioja
Partial differential equations (PDEs) with uncertain or random inputs have been considered in many studies of uncertainty quantification. In forward uncertainty quantification, one…
Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration
Philipp A. Guth, Vesa Kaarnioja, Frances Y. Kuo +2
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 un…
One-shot Learning of Surrogates in PDE-constrained Optimization Under Uncertainty
Philipp A. Guth, Claudia Schillings, Simon Weissmann
We propose a general framework for machine learning based optimization under uncertainty. Our approach replaces the complex forward model by a surrogate, which is learned simultane…
Multilevel Quasi-Monte Carlo for Optimization under Uncertainty
Philipp A. Guth, Andreas Van Barel
This paper considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In partic…
Ensemble Kalman filter for neural network based one-shot inversion
Philipp A. Guth, Claudia Schillings, Simon Weissmann
We study the use of novel techniques arising in machine learning for inverse problems. Our approach replaces the complex forward model by a neural network, which is trained simulta…
A quasi-Monte Carlo Method for an Optimal Control Problem Under Uncertainty
Philipp A. Guth, Vesa Kaarnioja, Frances Y. Kuo +2
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…