Publications related to Multi-index Monte Carlo: when sparsity meets sampling

Compressibility of Symmetric-α-Stable Processes

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

Within a deterministic framework, it is well known that n-term wavelet approximation rates of functions can be deduced from their Besov regularity. We use this principle to determine approximation rates for symmetric-α-stable (SαS) stochastic processes. Fi ...

IEEE2015

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

Fabio Nobile, Erik Gustaf Bogislaw Von Schwerin

We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The CMLMC algorithm so ...

MATHICSE2014

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

Fabio Nobile, Erik Gustaf Bogislaw Von Schwerin

We perform a general optimization of the parameters in the Multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation orders and computational costs. Moreover, we discuss extensions to non-unif ...

MATHICSE2014

MATHICSE Technical Report : Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Fabio Nobile, Daniel Kressner, Christine Tobler, Rajesh Kumar

Gaussian random fields are widely used as building blocks for modeling stochastic processes. This paper is concerned with the efficient representation of d-point correlations for such fields, which in turn enables the representation of more general stochas ...

MATHICSE2014

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

Simultaneous estimation of phase and phase derivative using a difference equation representation of the interference field

Pramod Rastogi, Rishikesh Dilip Kulkarni

A computationally efficient technique for fringe analysis in digital holographic interferometry using a difference equation representation of the interference field is presented. The spatially varying coefficient of the difference equation is estimated acc ...

Optical Soc Amer2014

Thumbnail galleries for procedural models

Mark Pauly, Pablo Federico Mueller, Boris Neubert, Stefan Lienhard

Procedural modeling allows for the generation of innumerable variations of models from a parameterized, conditional or stochastic rule set. Due to the abstractness, complexity and stochastic nature of rule sets, it is often very difficult to have an unders ...

Wiley-Blackwell2014

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

Incremental Model Identification of Fluid-Fluid Reaction Systems – Dynamic Accumulation and Reactions in the Diffusion Layer

Dominique Bonvin, Julien Léo Billeter, Sriniketh Srinivasan

The identification of kinetic models is an important step for the monitoring, control and optimization of industrial processes. This is particularly the case for highly competitive business sectors such as chemical and pharmaceutical industries, where the ...

2013

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

Multi-index Monte Carlo: when sparsity meets sampling

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Compressibility of Symmetric-α-Stable Processes

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

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

MATHICSE Technical Report : Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

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

Simultaneous estimation of phase and phase derivative using a difference equation representation of the interference field

Thumbnail galleries for procedural models

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

Incremental Model Identification of Fluid-Fluid Reaction Systems – Dynamic Accumulation and Reactions in the Diffusion Layer

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

Simultaneous estimation of phase and phase derivative using a difference equation representation of the interference field

Thumbnail galleries for procedural models

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

Incremental Model Identification of Fluid-Fluid Reaction Systems – Dynamic Accumulation and Reactions in the Diffusion Layer

MATHICSE Technical Report : Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

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

Compressibility of Symmetric-α-Stable Processes

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

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

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