Publications related to MATHICSE Technical Report : Optimization of mesh hierarchies in multilevel Monte Carlo samplers

MATHICSE Technical Report : Multi-index stochastic collocation for random PDEs

In this work we introduce the Multi-Index Stochastic Collocation method (MISC) for computing statistics of the solution of a PDE with random data. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the ...

MATHICSE2015

Fabrication-Aware Design with Performative Criteria

Yuliy Gennadievich Schwartzburg

Artists and architects often need to handle multiple constraints during design of physical constructions. We define a performative constraint as any constraint on design that is tied to the performance of the model--either during fabrication, construction, ...

EPFL2015

On Handling Cost Gradient Uncertainty in Real-Time Optimization

Dominique Bonvin, Timm Faulwasser, Martand Singhal

This paper deals with the real-time optimization of uncertain plants and proposes an approach based on surrogate models to reach the plant optimum when the plant cost gradient is imperfectly known. It is shown that, for processes with only box constraints, ...

2015

On the Design of Economic NMPC Based on an Exact Turnpike Property

Dominique Bonvin, Timm Faulwasser

We discuss the design of sampled-data economic nonlinear model predictive control schemes for continuous-time systems. We present novel sufficient convergence conditions that do not require any kind of terminal constraints nor terminal penalties. Instead, ...

IFAC2015

Manipulating the Optical Bistability in a Nonlinear Plasmonic Nanoantenna Array with a Reflecting Surface

Olivier Martin, Jérémy Butet

The influence of a reflecting surface on the optical bistability in a nanoantenna array is investigated theoretically. The optical response of the array is modeled using a surface integral equation method developed for periodic structures, and the descript ...

Springer Verlag2015

MATHICSE Technical Report : On the dynamically orthogonal approximation of time dependent random PDEs

Fabio Nobile, Eleonora Musharbash

In this work we discuss the Dynamically Orthogonal (DO) approximation of time dependent partial differential equations with random data. The approximate solution is expanded at each time instant on a time dependent orthonormal basis in the physical domain ...

MATHICSE2014

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

Fabio Nobile, Lorenzo Tamellini

In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number

N

of random inputs and an analytic dependence of the s ...

2014

On the Use of Second-Order Modifiers for Real-Time Optimization

Dominique Bonvin, Timm Faulwasser

We consider the real-time optimization of static plants and propose a generalized version of the modifier-adaptation strategy that relies on second-order adaptation of the cost and constraint functions. We show that second-order adaptation allows checking ...

2014

Accurate and efficient evaluation of failure probability for partial different equations with random input data

Alfio Quarteroni, Peng Chen

Several computational challenges arise when evaluating the failure probability of a given system in the context of risk prediction or reliability analysis. When the dimension of the uncertainties becomes high, well established direct numerical methods can ...

Elsevier Science Sa2013

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of p ...

Siam Publications2013

MATHICSE Technical Report : Optimization of mesh hierarchies in multilevel Monte Carlo samplers

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MATHICSE Technical Report : Multi-index stochastic collocation for random PDEs

Fabrication-Aware Design with Performative Criteria

On Handling Cost Gradient Uncertainty in Real-Time Optimization

On the Design of Economic NMPC Based on an Exact Turnpike Property

Manipulating the Optical Bistability in a Nonlinear Plasmonic Nanoantenna Array with a Reflecting Surface

MATHICSE Technical Report : On the dynamically orthogonal approximation of time dependent random PDEs

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

On the Use of Second-Order Modifiers for Real-Time Optimization

Accurate and efficient evaluation of failure probability for partial different equations with random input data

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

MATHICSE Technical Report : Multi-index stochastic collocation for random PDEs

Fabrication-Aware Design with Performative Criteria

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

Accurate and efficient evaluation of failure probability for partial different equations with random input data

On Handling Cost Gradient Uncertainty in Real-Time Optimization

Manipulating the Optical Bistability in a Nonlinear Plasmonic Nanoantenna Array with a Reflecting Surface

MATHICSE Technical Report : On the dynamically orthogonal approximation of time dependent random PDEs

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

On the Design of Economic NMPC Based on an Exact Turnpike Property

On the Use of Second-Order Modifiers for Real-Time Optimization