Direttore Vicario: Prof. Gabriele Grillo
Responsabile Gestionale: Dr.ssa Franca Di Censo



Le storie delle tre vincitrici tutte diverse tra loro, ma accomunate da una naturale passione per le materie scientifiche.....




Holistic Impact Assessment: i risultati italiani


June 17 - June 20


Educazione in contesti svantaggiati
Presentazione dei risultati del progetto TEEN e lancio dell'app #StreetMath


La matematica come strumento per arginare per il Covid


di Alfio Quarteroni


Seminari di Cultura Matematica
2020 - XIX ciclo


Civil Week Milano
Edufin@polimi - 6 marzo 2020


Modelling the Cardiac Function - Convegno iHEART




Il cielo sopra Giza - Giulio Magli e Maria Eugenia D'Aquino
Civico Planetario di Milano - venerdì 31 gennaio 2020 - ore 21.00


PIday 2020 e Giornata Internazionale della Matematica
13 marzo 2020


 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
    logo matematica
    MOX Numeth

    • 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:
    • 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
      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

Didattica Innovativa


Corso di studi
Ingegneria Matematica

Dottorato di Ricerca
Modelli e Metodi Matematici
per l'Ingegneria

Dottorato di Ricerca
DADS (Data Analytics and Decision Sciences)

AIM Associazione degli Ingegneri Matematici
Associazione degli
Ingegneri Matematici