06

Jun

2024
Seminars

BILEVEL LEARNING FOR INVERSE PROBLEMS AND VARIATIONAL DATA ASSIMILATION

Time
16h00
Place
Praia de Botafogo, 190 - sala 537 ou Via Zoom

About Event

In recent years, novel ideas have been applied to several inverse problems in combination with machine learning approaches, to improve the inversion by optimally choosing different parameters of interest and observation strategies. A fruitful approach in this sense is bilevel optimization, where the inverse problems are considered as lower-level constraints, while on the upper-level a loss function based on a training set is used. When confronted with inverse problems with sparsity-based regularizers or nonlinear dynamics, however, the bilevel optimization problem structure becomes quite involved, and classical nonlinear or bilevel programming results cannot be directly utilized. In this talk, I will present the general setting of bilevel inverse problems and discuss the main theoretical challenges, as well as the applicability to relevant practical instances. Particular attention will be paid to imaging problems with sparsity-based regularizers, for which a strategy to reformulate the bilevel problems as mathematical programs with complementarity constraints will be presented, and their theoretical and algorithmic consequences discussed. A strategy to derive optimality conditions for bilevel problems with nonlinear operators will be presented as well, with satellite variational data assimilation for numerical weather prediction in sight.

Texto informado pelo autor.

 

* Os participantes dos seminários não poderão acessar às dependências da FGV usando bermuda, chinelos, blusa modelo top ou cropped, minissaia ou camiseta regata. O uso da máscara é facultativo, porém é obrigatória a apresentação do comprovante de vacinação (físico ou digital).

Apoiadores / Parceiros / Patrocinadores

Speakers

Juan Carlos De Los Reyes

Juan Carlos De los Reyes is the Founding Director of the Ecuadorian Research Center for Mathematical Modeling (MODEMAT) in Ecuador and Professor of Mathematical Optimization at Escuela Politécnica Nacional. He obtained his PhD in 2003 at the University of Graz, Austria, and worked as postdoctoral researcher at the Technical University of Berlin (2005-2006). In 2009 he was awarded an Alexander von Humboldt Fellowship for Experienced Researchers to carry out research in Germany, and in 2010 he was awarded a J.T. Oden Faculty Fellowship at The University of Texas at Austin. He has held Visiting Professor positions at the Humboldt University of Berlin (2010), the University of Hamburg (2013), the Weierstrass Institute of Berlin (2021) and the Courant Institute of Mathematical Sciences in New York (2022). From 2019 to 2021 he was appointed Director of Research of Escuela Politécnica Nacional de Ecuador. He is former President of the Ecuadorian Mathematical Society (2012-2014), member of the Ecuadorian Academy of Sciences (since 2015), and Fellow of TWAS (since 2016). Dr. De los Reyes has served as member of organizing committees of various academic events, and has promoted the creation and strengthening of scientific networks in Latin-America.

Location

Fundação Getulio Vargas

a) Opção presencial *

Praia de Botafogo, 190

5o andar, Auditório 537

 

b) Opção remota (via Zoom)

Link: ID: 95348442773

 

Informações adicionais:

emap@fgv.br

Tel: 55 21 3799-5917

Endereço

a) Opção presencial *

Praia de Botafogo, 190

5o andar, Auditório 537

 

b) Opção remota (via Zoom)

Link: ID: 95348442773

 

Informações adicionais:

emap@fgv.br

Tel: 55 21 3799-5917

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