Dieuwertje Alblas - MIA
Riccardo Bardin - MACS
Vincent Bosboom - MACS
Nicoló Botteghi - MIA
Xiaoyu Cheng - MACS
Giacomo Cristinelli - MIA
Sven Dummer - MIA
Sagy Ephrati - MMS
Arnout Franken - MMS
Elena Giamatteo - MACS
Leonardo del Grande - MIA
source: http://www.malinc.se/math/trigonometry/geocentrismen.php - Heeringa - MIA
Lucas Jansen Klomp - MIA
Muhammad Hamza Khalid - MACS
Nishant Kumar - MACS
Kaifang Liu - MACS
Xiangyi Meng - MACS
Nida Mir - MIA / MDI-TNW
Hongliang Mu - MAST
Kevin Redosado - 3MS
Julian Suk - MIA
Hannah van Susteren - MIA
Elina Thibeua-Sutre - MIA
Alexander Wierzba - MAST
Jens de Vries - MAST
Fengna Yan - MACS
Weihao Yan - MIA

Discovery of equations, model sparsity and uncertainty, deep machine learning for PDEs

It is a major challenge to turn raw data into models that are not just predictive (data assimilation), but also provide insight into the nature of the underlying dynamical system that generated the data. Model order reduction via reduced basis methods will be of great interest in this context.

Assimilation as well as in partial differential equations, is important for many of our research areas (inverse problems, model order reduction). Deep recurrent artificial neural networks share a lot of structural and numerical similarities with nonlinear dynamical systems and are able to represent complex nonlinear, multiscale maps in a compressible linearizable fashion. Whereas, nearly all past approximation algorithms for PDEs suffered from the well-known curse of dimensionality, deep learning networks are able to tackle this dimensionality reduction efficiently via automatically learned emerging multiscale patterns (wavelet scattering, low-rank methods).

People working on this subject within SACS are:


Post Doc / PhD