BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Sabre//Sabre VObject 4.5.8//EN CALSCALE:GREGORIAN BEGIN:VTIMEZONE TZID:Europe/Zurich X-LIC-LOCATION:Europe/Zurich TZURL:http://tzurl.org/zoneinfo/Europe/Zurich BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19810329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19961027T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:news393@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20181116T170413 DTSTART;TZID=Europe/Zurich:20181123T110000 SUMMARY:Seminar in Numerical Analysis: Assyr Abdulle (EPFL) DESCRIPTION:In this talk we discuss several challenges that arise in Bayesi an inference for ordinary and partial differential equations. The numeric al solvers used to compute the forward model of such problems induce a p ropagation of the discretization error into the posterior measure for the parameters of interest. This uncertainty originating from the numerical approximation error can be accounted for using probabilistic numerical me thods. New probabilistic numerical methods for ordinary differential equa tions that share geometric properties of the true solution will be presen ted in the first part of this talk.  In the second part of the talk\, w e will discuss a Bayesian approach for inverse problems involving ellipti c partial differential equations with multiple scales. Computing repeated forward problems in a multiscale context is computationnally too expensi ve and we propose a new strategy  based on the use of  "effective" forw ard models originating from homogenization theory. Convergence of the tru e posterior distribution for the parameters of interest towards the homo genized posterior is established via G-convergence for the Hellinger metr ic. A computational approach based on numerical homogenization and reduce d basis methods is proposed for an efficient evaluation of the forward mo del in a Markov Chain Monte-Carlo procedure.  References: A. Abdulle\ , G. Garegnani\, Random time step probabilistic methods for uncertainty q uantification in chaotic and geometric numerical integration\, Preprint ( 2018)\, submitted for publication. A. Abdulle\, A. Di Blasio\, Numerical homogenization and model order reduction for multiscale inverse problems\ , to appear in SIAM MMS. A. Abdulle\, A. Di Blasio\, A Bayesian numerical homogenization method for elliptic multiscale inverse problems\, Preprin t (2018)\, submitted for publication. For further information about the s eminar\, please visit this webpage. X-ALT-DESC: In this talk we discuss several challenges that arise in Bayesi an inference for ordinary and partial differential equations. The numeric al solvers used to compute the forward model of such problems induce a p ropagation of the discretization error into the posterior measure for the parameters of interest. This uncertainty originating from the numerical approximation error can be accounted for using probabilistic numerical me thods. New probabilistic numerical methods for ordinary differential equa tions that share geometric properties of the true solution will be presen ted in the first part of this talk. \;
In the second part of t he talk\, we will discuss a Bayesian approach for inverse problems involv ing elliptic partial differential equations with multiple scales. Computi ng repeated forward problems in a multiscale context is computationnally too expensive and we propose a new strategy  \;based on the use of&nb sp\; "\;effective"\; forward models originating from homogenizati on theory. Convergence of the true posterior distribution for the paramet ers of interest towards the homogenized posterior is established via G-co nvergence for the Hellinger metric. A computational approach based on num erical homogenization and reduced basis methods is proposed for an effici ent evaluation of the forward model in a Markov Chain Monte-Carlo proced ure. \;

References:
A. Abdulle\, G. Garegnani\, R andom time step probabilistic methods for uncertainty quantification in c haotic and geometric numerical integration\, Preprint (2018)\, submitted for publication.
A. Abdulle\, A. Di Blasio\, Numerical homogenizati on and model order reduction for multiscale inverse problems\, to appear in SIAM MMS.
A. Abdulle\, A. Di Blasio\, A Bayesian numerical homog enization method for elliptic multiscale inverse problems\, Preprint (201 8)\, submitted for publication.

For further information about the seminar\, please visit this webpage. DTEND;TZID=Europe/Zurich:20181123T120000 END:VEVENT END:VCALENDAR