BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Sabre//Sabre VObject 4.5.7//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:news1550@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20231204T091610 DTSTART;TZID=Europe/Zurich:20231215T110000 SUMMARY:Seminar in Numerical Analysis: Caroline Geiersbach (WIAS Berlin) DESCRIPTION:Many problems in shape optimization involve constraints in the form of one or more partial differential equations. In practice\, the mate rial properties of the underlying shape on which a PDE is defined are not known exactly\; it is natural to use a probability distribution based on e mpirical measurements and incorporate this information when designing an o ptimal shape. Additionally\, one might wish to obtain a shape that is robu st in its response to certain external inputs\, such as forces. It is help ful to view shape optimization problems subject to uncertainty through the lens of stochastic optimization\, where a wealth of theory and algorithms already exist for finite-dimensional problems. The focus will be on the a lgorithmic handling of these problems in the case of a high stochastic dim ension. Stochastic approximation\, which dynamically samples from the stoc hastic space over the course of iterations\, is favored in this case\, and we show how these methods can be applied to shape optimization. We study the classical stochastic gradient method\, which was introduced in 1951 by Robbins and Monro and is widely used in machine learning. In particular\, we investigate its application to infinite-dimensional shape manifolds. F urther\, we present numerical examples showing the performance of the meth od\, also in combination with the augmented Lagrangian method for problems with geometric constraints. \\r\\nJoint work with: Kathrin Welker\, Este fania Loayza-Romero\, Tim Suchan\\r\\n\\r\\nFor further information about the seminar\, please visit this webpage [t3://page?uid=1115]. X-ALT-DESC:

Many problems in shape optimization involve constraints in th e form of one or more partial differential equations. In practice\, the ma terial properties of the underlying shape on which a PDE is defined are no t known exactly\; it is natural to use a probability distribution based on empirical measurements and incorporate this information when designing an optimal shape. Additionally\, one might wish to obtain a shape that is ro bust in its response to certain external inputs\, such as forces. It is he lpful to view shape optimization problems subject to uncertainty through t he lens of stochastic optimization\, where a wealth of theory and algorith ms already exist for finite-dimensional problems. The focus will be on the algorithmic handling of these problems in the case of a high stochastic d imension. Stochastic approximation\, which dynamically samples from the st ochastic space over the course of iterations\, is favored in this case\, a nd we show how these methods can be applied to shape optimization. We stud y the classical stochastic gradient method\, which was introduced in 1951 by Robbins and Monro and is widely used in machine learning. In particular \, we investigate its application to infinite-dimensional shape manifolds. Further\, we present numerical examples showing the performance of the me thod\, also in combination with the augmented Lagrangian method for proble ms with geometric constraints. \;

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Joint work with: Kathrin Wel ker\, Estefania Loayza-Romero\, Tim Suchan

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For further informati on about the seminar\, please visit this webpage.

DTEND;TZID=Europe/Zurich:20231215T120000 END:VEVENT END:VCALENDAR