Publications related to An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data

A stochastic collocation method for the second order wave equation with a discontinuous random speed

In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and ...

Springer Verlag2013

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 : 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

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

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

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

Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

Gilles Brunner

In this project, we study and compare two methods to solve stochastic ordinary differential equations. The first is the Monte Carlo method and the second uses Polynomial Chaos. In the first part, we will solve a stochastic ordinary differential equation by ...

2013

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

What are the Odds? Probabilistic programming in Scala

Tiark Rompf, Nada Amin, Sandro Stucki, Manohar Jonnalagedda

Probabilistic programming is a powerful high-level paradigm for probabilistic modeling and inference. We present Odds, a small domain-specific language (DSL) for probabilistic programming, embedded in Scala. Odds provides first-class support for random var ...

ACM2013

Lyapunov Exponents of Random Walks in Small Random Potential: The Lower Bound

Thomas Mountford, Jean-Christophe Mourrat

We consider the simple random walk on , d > 3, evolving in a potential of the form beta V, where are i.i.d. random variables taking values in [0, + a), and beta > 0. When the potential is integrable, the asymptotic behaviours as beta tends to 0 of the asso ...

Springer Berlin Heidelberg2013

An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data

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A stochastic collocation method for the second order wave equation with a discontinuous random speed

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

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

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

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

Multistable randomly switching oscillators: The odds of meeting a ghost

Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

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

What are the Odds? Probabilistic programming in Scala

Lyapunov Exponents of Random Walks in Small Random Potential: The Lower Bound

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

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

Multistable randomly switching oscillators: The odds of meeting a ghost

A stochastic collocation method for the second order wave equation with a discontinuous random speed

What are the Odds? Probabilistic programming in Scala

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

Lyapunov Exponents of Random Walks in Small Random Potential: The Lower Bound

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

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

Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos