Dipartimento di Matematica

Ricerca - Laboratori - Formazione

DIPARTIMENTO DI

MATEMATICA

Direttore: Prof. Giulio Magli

Direttore Vicario: Prof. Gabriele Grillo

Responsabile Gestionale: Dr.ssa Franca Di Censo

PRIVACY E SICUREZZA

Normativa di Ateneo

Piano d'Emergenza Locale

P.E.L. – Piano di Emergenza locale Edifici 14, 14A, 14B

Per comunicazioni o chiarimenti contattare: Salute e Sicurezza dip. Matematica

IN CASO DI EMERGENZA

in presenza di una situazione di pericolo valutare sommariamente la natura e le dimensioni dell'evento, intervenire per ripristinare la normalità solo nel caso di situazioni controllabili, e se in possesso di una adeguata formazione;
in presenza di una situazione di pericolo che possa rapidamente degenerare (principio di incendio, rischio di crollo o allagamento, rischio elettrico o altro), contattare immediatamente il numero esposto nelle planimetrie di emergenza e procedere come indicato in seguito;
nel caso la comunicazione con il numero di emergenza richiedesse troppo tempo, azionare immediatamente il sistema dall’allarme agendo sul pulsante di emergenza

IN CASO DI EVACUAZIONE

a seguito del segnale di evacuazione (sirena) oppure nei casi gravi, al verificarsi dell’emergenza, senza, cioè, attendere segnale alcuno, bisogna
- interrompere l’attività in corso (lezione, esercitazione, esame, colloquio, ricerca) e uscire dal locale in cui ci si trova invitando ad uscire anche gli altri eventuali soggetti presenti nonché chi occupa locali vicini e/o adiacenti;
- seguire i percorsi e raggiungere le uscite di emergenza coerentemente con la cartellonistica esposta;
- informare gli addetti presenti al punto di raccolta, individuabili dal giubbino di emergenza, dell’avvenuta evacuazione, di eventuali criticità verificatesi e rimanere a loro disposizione;
si ricorda che durante l’evacuazione i piani superiori hanno la precedenza, quindi, giunti alle scale (gli ascensori non possono essere utilizzati), si dovrà attendere fino a che queste non risulteranno sgombre;
in ogni caso, sia durante l’evacuazione sia dopo avere raggiunto il punto di raccolta, seguire le indicazioni degli addetti.

Dicono di noi...

Prossimi Eventi

lug 16 gio 2020

MOX Colloquia
Gitta Kutyniok, Deep learning meets parametric partial differential equations, 16-07-2020, ore 14:00

MOX Colloquia
Gitta Kutyniok
Institute of Mathematics, Technische Universität Berlin (DE)
Deep learning meets parametric partial differential equations
Giovedì 16 luglio 2020 alle ore 14:00
Online seminar: https://mox.polimi.it/elenco-seminari/?id_evento=1977&t=763724
Abstract

High-dimensional parametric partial differential equations (PDEs) appear in various contexts including control and optimization problems, inverse problems, risk assessment, and uncertainty quantification. In most such scenarios the set of all admissible solutions associated with the parameter space is inherently low dimensional. This fact forms the foundation for the reduced basis method.
Recently, numerical experiments demonstrated the remarkable efficiency of using deep neural networks to solve parametric problems. In this talk, after an introduction into deep learning, we will present a theoretical justification for this class of approaches. More precisely, we will derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric PDEs. In fact, without any knowledge of its concrete shape, we use the inherent low-dimensionality of the solution manifold to obtain approximation rates which are significantly superior to those provided by classical approximation results. We use this low-dimensionality to guarantee the existence of a reduced basis. Then, for a large variety of parametric PDEs, we construct neural networks that yield approximations of the parametric maps not suffering from a curse of dimensionality and essentially only depending on the size of the reduced basis.
Finally, we present a comprehensive numerical study of the effect of approximation-theoretical results for neural networks on practical learning problems in the context of parametric partial differential equations. These experiments strongly support the hypothesis that approximation-theoretical effects heavily influence the practical behavior of learning problems in numerical analysis.
Gitta Kutyniok currently holds an Einstein Chair in the Institute of Mathematics at the Technische Universität Berlin, a courtesy appointment in the Department of Computer Science and Engineering, an Adjunct Professorship in Machine Learning at the University of Tromso, and is also the head of the Applied Functional Analysis Group. She received her Diploma in Mathematics and Computer Science as well as her Ph.D. degree from the Universität Paderborn in Germany, and her Habilitation in Mathematics in 2006 at the Justus-Liebig Universität Gießen. From 2001 to 2008 she held visiting positions at several US institutions, including Princeton University, Stanford University, Yale University, Georgia Institute of Technology, and Washington University in St. Louis. In 2008, she became a full professor of mathematics at the Universität Osnabrück, and moved to Berlin three years later.
She received various awards for her research such as an award from the Universität Paderborn in 2003, the Research Prize of Gießen and a Heisenberg-Fellowship in 2006, the von Kaven Prize by the DFG in 2007, and an Einstein Chair in 2008. She gave the Noether Lecture at the ÖMG-DMV Congress in 2013 and the Hans Schneider ILAS Lecture at IWOTA in 2016. She also became a member of the Berlin-Brandenburg Academy of Sciences and Humanities in 2017, a SIAM Fellow in 2019, and an IEEE Senior Member in the same year.
She was Chair of the SIAM Activity Group on Imaging Sciences from 2018-2019 and is Co-Chair of the first SIAM conference on Mathematics of Data Science taking place this year. She is also, for instance, Scientific Director of the graduate school BIMoS at TU Berlin and Chair of the GAMM Activity Groups on Mathematical Signal- and Image Processing and Computational and Mathematical Methods in Data Science, as well as of the MATH+ Activity Group on Mathematics of Data Science. Her main research interests are in the areas of applied harmonic analysis, compressed sensing, high-dimensional data analysis, imaging science, inverse problems, machine learning, numerical mathematics, partial differential equations, and applications to life sciences and telecommunication.

Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568