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GOAL-ORIENTED ERROR ESTIMATION FOR PARAMETER-DEPENDENT NONLINEAR PROBLEMS, APPLICATION TO SENSITIVITY ANALYSIS

Presented by: 
Clémentine Prieur Université de Grenoble, INRIA Grenoble - Rhône-Alpes
Date: 
Wednesday 20th June 2018 - 10:30 to 13:00
Venue: 
INI Seminar Room 2
Abstract: 
During this talk, we will present a numerically efficient method to bound the error that is made when approximating the output of a nonlinear problem depending on an unknown parameter (described by a probability distribution). The class of nonlinear problems under consideration includes high-dimensional nonlinear problems with a nonlinear output function. A goal-oriented probabilistic bound is computed by considering two phases. An offline phase dedicated to the computation of a reduced model during which the full nonlinear problem needs to be solved only a small number of times. The second phase is an online phase which approximates the output. This approach is applied to a toy model and to a nonlinear partial differential equation, more precisely the Burgers equation with unknown initial condition given by two probabilistic parameters. The savings in computational cost are evaluated and presented.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons