Publications related to Stochastic approximation methods for PDE constrained optimal control problems with uncertain parameters

MATHICSE Technical Report : A posteriori error estimations for elliptic partial differential equations with small uncertainties

Fabio Nobile, Marco Picasso, Diane Sylvie Guignard

In this paper, a finite element error analysis is performed on a class of linear and nonlinear elliptic problems with small uncertain input. Using a perturbation approach, the exact (random) solution is expanded up to a certain order with respect to a para ...

MATHICSE2014

Perturbation analysis for the Darcy problem with log-normal permeability

Fabio Nobile, Francesca Bonizzoni

We study the single-phase flow in a saturated, bounded heterogeneous porous medium. We model the permeability as a log-normal random field. We perform a perturbation analysis, expanding the solution in Taylor series. The series is directly computable in th ...

2014

MATHICSE Technical Report : Analytic regularity and collocation approximation for PDEs with random domain deformations

Fabio Nobile

In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem is remap ...

MATHICSE2013

MATHICSE Technical Report : Perturbation analysis for the Darcy problem with log-normal permeability

Fabio Nobile, Francesca Bonizzoni

We study the single-phase flow in a saturated, bounded heterogeneous porous medium. We model the permeability as a log-normal random field. We perform a perturbation analysis, expanding the solution in Taylor series. The series is directly computable in th ...

MATHICSE2013

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

In this work we consider the random discrete

L^2

projection on polynomial spaces (hereafter RDP) for the approximation of scalar quantities of interest (QOIs) related to the solution of a partial differential equation model with random input parameters. ...

Siam Publications2013

Multistable randomly switching oscillators: The odds of meeting a ghost

Martin Hasler, Igor Belykh

We consider oscillators whose parameters randomly switch between two values at equal time intervals. If random switching is fast compared to the oscillator's intrinsic time scale, one expects the switching system to follow the averaged system, obtained by ...

Springer Verlag2013

Stochastic Optimal Robin Boundary Control Problems of Advection-Dominated Elliptic Equations

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

In this work we deal with a stochastic optimal Robin boundary control problem constrained by an advection-diffusion-reaction elliptic equation with advection-dominated term. We assume that the uncertainty comes from the advection led and consider a stochas ...

Society for Industrial and Applied Mathematics2013

Robust Capacity Assignment Solutions for Telecommunications Networks with Uncertain Demands

Frédéric Louis François Babonneau

We consider the capacity planning of telecommunications networks with linear investment costs and uncertain future traffic demands. Transmission capacities must be large enough to meet, with a high quality of service (QoS), the range of possible demands, a ...

Wiley-Blackwell2013

Risk-averse shortest path problems

Daniel Kuhn, Grani Adiwena Hanasusanto

We investigate routing policies for shortest path problems with uncertain arc lengths. The objective is to minimize a risk measure of the total travel time. We use the conditional value-at-risk (CVaR) for when the arc lengths (durations) have known distrib ...

IEEE2012

Methodology to account for uncertainties and tradeoffs in pharmaceutical environmental hazard assessment

David Andrew Barry, Luca Rossi, Sylvain Coutu

Many pharmaceutical products find their way into receiving waters, giving rise to concerns regarding their environmental impact. A procedure was proposed that enables ranking of the hazard to aquatic species and human health due to such products. In the pr ...

Elsevier2012

Stochastic approximation methods for PDE constrained optimal control problems with uncertain parameters

Graph Chatbot

Chat with Graph Search

MATHICSE Technical Report : A posteriori error estimations for elliptic partial differential equations with small uncertainties

Perturbation analysis for the Darcy problem with log-normal permeability

MATHICSE Technical Report : Analytic regularity and collocation approximation for PDEs with random domain deformations

MATHICSE Technical Report : Perturbation analysis for the Darcy problem with log-normal permeability

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Multistable randomly switching oscillators: The odds of meeting a ghost

Stochastic Optimal Robin Boundary Control Problems of Advection-Dominated Elliptic Equations

Robust Capacity Assignment Solutions for Telecommunications Networks with Uncertain Demands

Risk-averse shortest path problems

Methodology to account for uncertainties and tradeoffs in pharmaceutical environmental hazard assessment

MATHICSE Technical Report : A posteriori error estimations for elliptic partial differential equations with small uncertainties

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Robust Capacity Assignment Solutions for Telecommunications Networks with Uncertain Demands

Multistable randomly switching oscillators: The odds of meeting a ghost

MATHICSE Technical Report : Analytic regularity and collocation approximation for PDEs with random domain deformations

Methodology to account for uncertainties and tradeoffs in pharmaceutical environmental hazard assessment

MATHICSE Technical Report : Perturbation analysis for the Darcy problem with log-normal permeability

Perturbation analysis for the Darcy problem with log-normal permeability

Risk-averse shortest path problems

Stochastic Optimal Robin Boundary Control Problems of Advection-Dominated Elliptic Equations