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Computational Science Seminar

When: Tuesday, March 24, 2015
3:30 PM - 4:30 PM
Where: Textiles Building 105
Description: The Center for Scientific Computing and Visualization Research announces the following seminar.

Speaker: Daniele Venturi (Brown University)
Title: "Coarse-graining high-dimensional random systems: the probability density function approach"
Time: Tuesday, March 24, 2015, 3:30pm-4:30pm
Location: Textiles 105

Abstract: In this talk, I will present different methods to develop reduced-order equations for the probability density function (PDF) of quantities of interest (phase space functions) in high-dimensional stochastic dynamical systems.

In principle, this allows us to avoid computing high-dimensional stochastic flows and reduce a great mass of information to a more tractable and more interesting form (the PDF evolution of a low-dimensional quantity of interest). I will discuss two different classes of methods to achieve this goal: the first one is based on separated series expansions such as proper generalized decomposition (PGD) or high-dimensional model representations (HDMR).

When applied to high-dimensional systems, these methods yield a hierarchy of low-dimensional PDF equations that resembles the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of kinetic gas theory. The second approach stems from techniques of irreversible statistical mechanics, in particular the Mori-Zwanzig (MZ) formulation, and it yields directly formally exact equations for the PDF of quantities of interest. I will address the question of approximation of MZ-PDF equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Throughout the presentation I will provide numerical examples and applications of the proposed methods to prototype stochastic problems, such as the Lorenz-96 system, stochastic advection-reaction and stochastic Burgers equations.

For additional information, see the CSCVR webpage http://cscvr.umassd.edu/seminars.html, or contact Akil Narayan at akil.narayan@umassd.edu or 508-999-8318.
Contact: Center for Scientific Computing and Visualization Research
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