Accession Number : AD1001410

Title :   Goal-Oriented Probability Density Function Methods for Uncertainty Quantification

Descriptive Note : Technical Report,01 Aug 2014,01 Sep 2015

Corporate Author : Brown University Providence United States

Personal Author(s) : Venturi,Daniele

Full Text :

Report Date : 11 Dec 2015

Pagination or Media Count : 14

Abstract : During the performance period of the grant we developed the proposed goal-oriented probability density function method based on the Mori-Zwanzig formulation and applied it to stochastic partial differential equations (SPDEs) such as advection-reaction and Burgers equations. We also developed new algorithms to solve high-dimensional probability density function (PDF) equations and stochastic domain decomposition techniques to propagate uncertainty across heterogeneous domains. The main findings can be summarized as follows: The Mori-Zwanzig approach has the potential to overcome well-known limitations encountered in stochastic simulations of high-dimensional random systems, in particular the curse of dimensionality and the lack of regularity of the solution. This comes at the price of solving complex integro-differential PDEs whose computability relies on either analytical approximations or data-driven approaches. The new methods we developed for high-dimensional PDF equations can be used in many different disciplines, ranging from optimal control under uncertainty of nonlinear dynamical systems to plasma dynamics (numerical solution to the full Bolzmann equation).

Descriptors :   probability density functions , algorithms , boltzmann equation , STOCHASTIC PROCESSES , uncertainty

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE