Veranstaltungen

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Dienstag, 22.11.2022, 15:00 Uhr (WIAS-405-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. Pavel Dvurechensky, WIAS Berlin:
Generalized self-concordant analysis of Frank-Wolfe algorithms (hybrid talk)
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Abstrakt
We propose several variants of the Frank-Wolfe method for minimizing generalized self-concordant (GSC) functions over compact sets. Such problems are ill-conditioned and are motivated by machine learning applications such as inverse covariance estimation or distance-weighted discrimination problems in support vector machines. We obtain O(1/k) convergence rate guarantees in the general situation and linear convergence under strong convexity and additional assumptions.

Weitere Informationen
Dieser Vortrag findet bei Zoom statt: https://zoom.us/j/492088715

Veranstalter
WIAS Berlin
Mittwoch, 23.11.2022, 10:00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Alexei Kroshnin, WIAS Berlin:
Robust k-means clustering in Hilbert and metric spaces (hybrid talk)
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
In this talk, we consider the robust algorithms for the k-means clustering (quantization) problem where a quantizer is constructed based on N independent observations. While the well-known asymptotic result by Pollard shows that the existence of two moments is sufficient for strong consistency of an empirically optimal quantizer in Rd, non-asymptotic bounds are usually obtained under the assumption of bounded support. We discuss a robust k-means in Hilbert and metric spaces based on trimming, and prove non-asymptotic bounds on the excess distortion, which depend on the probability mass of the lightest cluster and the second moment of the distribution.

Weitere Informationen
Der Vortrag findet bei Zoom statt: https://zoom.us/j/159082384

Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Mittwoch, 23.11.2022, 15:15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Richard Schubert, Universität Bonn:
A variational approach to data-driven problems in fluid mechanics (hybrid talk)
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
In this talk, we discuss a data-driven approach to viscous fluid mechanics. Typically, in order to describe the behaviour of fluids, two different kinds of modelling assumptions are used. On the one hand, there are first principles like the balance of forces or the incompressibility condition. On the other hand there are material specific constitutive laws that describe the relation between the strain and the viscous stress of the fluid. Combining both, one obtains the partial differential equations of fluid mechanics like the Stokes or Navier--Stokes equations. The constitutive laws are obtained by fitting a law from a certain class (for example linear, power law, etc.) to experimental data. This leads to modelling errors. Instead of using a constitutive relation, we introduce a data-driven formulation that has previously been examined in the context of solid mechanics and directly draws on material data. This leads to a variational solution concept, that incorporates differential constraints coming from first principles and produces fields that are optimal in terms of closeness to the data. In order to derive this formulation we recast the differential constraints of fluid mechanics in the language of constant-rank differential operators. We will see that the data-driven solutions are consistent with PDE solutions if the data are given by a constitutive law. Furthermore we show a Gamma-convergence result for the functionals arising in the data-driven fluid mechanical problem which implies that the method is well-adapted to the convergence of experimental data through increasing experimental accuracy. This is based on joint work with Christina Lienstromberg (Stuttgart) and Stefan Schiffer (Leipzig).

Weitere Informationen
Hybridveranstaltung - Teilnahme vor Ort bitte bei Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) anmelden.
Hybrid event - please give Dr. A. Glitzky (annegret.glitzky@wias-berlin.de) notice of your on-site participation.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Freitag, 25.11.2022, 13:00 Uhr (WIAS-Library)
E-Coffee-Lecture
Dr. Renita Danabalan, WIAS:
From Interviewee to Interviewer: Perspectives of both sides
mehr ... Veranstaltungsort
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, Library (4. Etage)

Veranstalter
WIAS Berlin