Publications related to Efficient Solution of Ordinary Differential Equations with High-Dimensional Parametrized Uncertainty

Upgrading of Roskrepp hydropower plant to a pumped storage plant: Necessary reconstruction of the surge tank

The scope of this thesis is to build a 1D numerical model of a hydraulic powerplant, transform it to simulate the upgrade of the powerplant into a pumped storage system, establish the issues that would emerge from it in the surge tanks and test several sol ...

2018

Stochastic Optimal Control of Epidemic Processes in Networks

Utkarsh Upadhyay, William Trouleau

We approach the development of models and control strategies of susceptible-infected-susceptible (SIS) epidemic processes from the perspective of marked temporal point processes and stochastic optimal control of stochastic differential equations (SDEs) wit ...

2018

Stochastic partial differential equations driven by Lévy white noises

Thomas Marie Jean-Baptiste Humeau

We study various aspects of stochastic partial differential equations driven by Lévy white noise. This driving noise, which is a generalization of Gaussian white noise, can be viewed either as a generalized random process or as an independently scattered r ...

EPFL2017

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of

2S

dynamica ...

2017

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash, Eva Vidlicková

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...

MATHICSE2017

Multi-index Monte Carlo: when sparsity meets sampling

Fabio Nobile

We propose and analyze a novel Multi Index Monte Carlo (MIMC) method for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The MIMC method is both a s ...

2016

MATHICSE Technical Report : Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition

Alfio Quarteroni, Andrea Manzoni, Federico Negri

The numerical solution of partial differential equations (PDEs) depending on para- metrized or random input data is computationally intensive. Reduced order modeling techniques, such as the reduced basis methods, have been developed to alleviate this compu ...

MATHICSE2016

Sampling and (Sparse) Stochastic Processes: A Tale of Splines and Innovation

Michaël Unser

The commonality between splines and Gaussian or sparse stochastic processes is that they are ruled by the same type of differential equations. Our purpose here is to demonstrate that this has profound implications for the three primary forms of sampling: u ...

IEEE2015

Stabilized Numerical Methods for Stochastic Differential Equations driven by Diffusion and Jump-Diffusion Processes

Adrian Blumenthal

Stochastic models that account for sudden, unforeseeable events play a crucial role in many different fields such as finance, economics, biology, chemistry, physics and so on. That kind of stochastic problems can be modeled by stochastic differential equat ...

EPFL2015

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

Efficient Solution of Ordinary Differential Equations with High-Dimensional Parametrized Uncertainty

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Upgrading of Roskrepp hydropower plant to a pumped storage plant: Necessary reconstruction of the surge tank

Stochastic Optimal Control of Epidemic Processes in Networks

Stochastic partial differential equations driven by Lévy white noises

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Multi-index Monte Carlo: when sparsity meets sampling

MATHICSE Technical Report : Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition

Sampling and (Sparse) Stochastic Processes: A Tale of Splines and Innovation

Stabilized Numerical Methods for Stochastic Differential Equations driven by Diffusion and Jump-Diffusion Processes

Compressibility of Symmetric-α-Stable Processes

Stochastic partial differential equations driven by Lévy white noises

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

MATHICSE Technical Report : Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition

Sampling and (Sparse) Stochastic Processes: A Tale of Splines and Innovation

Compressibility of Symmetric-α-Stable Processes

Upgrading of Roskrepp hydropower plant to a pumped storage plant: Necessary reconstruction of the surge tank

Stochastic Optimal Control of Epidemic Processes in Networks

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Multi-index Monte Carlo: when sparsity meets sampling

Stabilized Numerical Methods for Stochastic Differential Equations driven by Diffusion and Jump-Diffusion Processes