nD - nD: Multidimensional dynamical systems, multi-linear numerical algorithms and tensor data
From 01-10-2015 to 30-09-2022
Description
Summary
Twenty years ago, one of the research tracks we started was the identification of dynamical models from observed data, using concepts and algorithms from numerical linear algebra. This endeavor has proven to be very rewarding, not only scientifically, but also from the point of view of engineering applications. Indeed, the last 10 years we have been diversifying into the biomedical field (signal processing, health decision support, bioinformatics), the process industry (modeling and control, data-assimilation, data-mining) and even quantum information theory. This has led to fruitful and inspiring interactions with industrial partners, and the creation of 6 spin-off companies.
With this proposal, we want to return to the basic roots of that research track, however with a fundamental twist to each of the three ingredients: The time series of the 90’s have now turned into higher-order (nD) data, lots of them (‘big data’). The concepts and algorithms of numerical linear algebra are now maturing into exciting new developments of multi-linear algebra (e.g. tensor decompositions). The ‘1D’ dynamical models, with basically only time as an independent variable, are to be generalized into multi-dimensional dynamical models, which are calculated from the nD data, using multi-linear algebra tools.
All of the applications we envisage 1 are characterized by a tsunami of data. They have in common their high dimensionality, and are described in terms of several (instead of only 1) ‘independent’ variables (e.g. time, 3 space coordinates, a frequency axis, physical quantities such as temperature, pressure, concentrations, etc.). The 2nd ingredient of this proposal concerns mathematical models of dynamical systems. These are used to simulate in silico, to design control strategies, to monitor the behavior and to predict. Increasingly, models are used to compress the tsunami of data in order to deal with the so-called ‘curse-of-dimensionality’. Indeed, nD data points tend to be correlated with neighbors in the nD data space, and by modeling this and deeper correlations by means of nD state space models, one can achieve a dramatic compression. The 3rd ingredient of the proposal describes how we develop new numerical multi-linear algebra algorithms to obtain nD models from nD data.
The proposal is partitioned in three work packages, corresponding to the three relevant Research Challenges we have identified:
Research Challenge I: Back to the roots, or a new numerical linear algebra theory to calculate all or some of the roots of a set of multivariable polynomials. This is an important ingredient for RC II and III;
Research Challenge II: Tensor decompositions and applications in signal processing, 1D system modeling and big data analysis;
Research Challenge III: nD subspace identification for nD systems.
Team
- Lieven De Lathauwer, Co-promoter
- Bart De Moor, Promoter
- Katrien De Cock, Team member
Financing
Funding: KU Leuven - Internal Funding KU Leuven
Program/Grant Type: C1 - KU Leuven Category 1 Funding
Events
2/09/2024:
PhD defense - Martijn Oldenhof
Machine Learning for Advanced Chemical Analysis and Structure Recognition in Drug Discovery
3/09/2024:
Meet the Jury Igor Tetko on Advanced Machine Learning in Drug Discovery
12/09/2024:
Multimodal analysis of cell-free DNA for sensitive cancer detection in low-coverage and low-sample settings
Seminar by Antoine Passemiers
News
STADIUS Alumni Herman Verrelst – new CEO of Biocartis
08 June 2017
Herman Verrelst, the founder of KU Leuven spin-off Cartagenia, who has been working in Silicon Valley, US for the last few years will be returning to Belgium to follow the steps of Rudi Pauwels as CEO of the Belgian diagnostic company, Biocartis.
Supporting healthcare policymaking via machine learning – batteries included!
29 May 2017
STADIUS takes the lead in the data analytics efforts in an ambitious European Project MIDAS.
Marc Claesen gives an interview about his PhD for the magazine of the Faculty of Engineering Sciences "Geniaal"
10 February 2017
Did you know that in Belgium approximately one third of type 2 diabetes patients are unaware of their condition?
Joos Vandewalle is nieuwe voorzitter KVAB
09 October 2016
Op 5 oktober 2016 heeft de Algemene Vergadering van de Academie KVAB Joos Vandewalle verkozen tot voorzitter van de KVAB.