All Years Seminars
[INMA] 2012-02-14 (14.00) : Model reduction of conservation laws
At Euler building
Speaker :
Samuel MELCHIOR (UCL)
Abstract :
In continuum mechanics, the unknown fields must satisfy a system of
conservation and constitution laws everywhere in space and time. This can
be reformulated equivalently as weak formulations that can be discretized
using the Finite Element Method (FEM). Usually, the shape and test
functions are piecewise low-order polynomial defined on a compact support.
However, considering totally discrete prolongation and restrictions spaces
can be quite more optimal. This is especially true when the motivation for
using such models is not necessarily to estimate the value of the
quantities everywhere in the domain. For instance, it might be important
to approximate only the relation between several inputs and outputs of the
systems. In this case, the order of the model can be reduced to a much
lower value without losing much accuracy. In this talk, we investigate the
connections between Model Order Reduction (MOR) and multimesh schemes on
Linear Time-Invariant (LTI), Linear Time-Varying (LTV) and nonlinear
dynamical systems.
[INMA] 2012-02-07 (14.00) : A centuries-old problem: how to compute the roots of a polynomial
At Euler building
Speaker :
Raf VANDEBRIL (K.U.Leuven)
Abstract :
Asking a pure mathematician how he would determine the eigenvalues of a matrix, odds are
fifty-fifty he'll just reply: ``retrieve them as roots from the characteristic
polynomial''. Confronting a computer scientist with the problem of computing roots of a
polynomial he'll likely answer: ``put the polynomial in a matrix and then compute the
eigenvalues of that matrix''. A confrontation could end in an absurd chicken-and-egg discussion.
Theoretically, the mathematician's idea is as valuable as
the computer scientist's. From a computational point of view, however, it is too time
consuming to compute the characteristic polynomial, and moreover, numerically it is no
good idea either.
Computing eigenvalues is done nowadays with one of the top 10 algorithms of the 20th
century: the QR-algorithm [B.A. Cipra, Siam News 33, 2000]. Root solving is done, in practice, by placing the polynomial
coefficients in a matrix, the so-called companion matrix. The roots are then retrieved by
simply applying the QR-algorithm on the companion matrix; all eigenvalues pop up one after
the other until eventually all eigenvalues/roots are found. Cleve Moler, pointed out,
however, in the Mathworks Newsletter in 1991 that this approach may not yet be optimal: `` it uses n^2
storage and order n^3 time. An algorithm designed specifically for polynomial roots might
use order n storage and n^2 time. ''
The goal of this talk is to elaborate on contemporary root solvers effectively using n
storage and achieving a computational complexity of n^2 operations. Roughly a
decade ago it emerged from exploiting rank structures in matrices, that the companion
matrix exhibited quite some useful, so far unexploited, properties. By splitting the
matrix in two parts a whole variety of algorithms was developed. About the same time that
the first successful fast solvers were developed, Fiedler proved that the companion matrix
is just an instance of a whole family of matrices, suitable for computing roots of a
polynomial. We will show that one can also, cheaply, and fastly compute eigenvalues based
on such Fiedler factorizations of companion matrices. The algorithm is simple in nature and numerical
evidence shows that this approach supersedes --in terms of speed-- the fastest currently
available root solvers.
This is joint work with
David Watkins and Jared Aurentz
[INMA] 2012-01-31 (14.00) : Control design and reverse engineering using observer-based structures: Application to the control of flexible aerospace vehicles
At Euler building
Speaker :
Daniel ALAZARD (Supaero Toulouse)
Abstract :
This seminar aims to present convenient tools, based on the observer-based realization
of a given arbitrary controller, to solve robust, multi-objective and gain-scheduling con-
trol problems. These tools are applied on practical examples in the field of aerospace
engineering (launcher, aircraft flight control, ...).
Observer based compensators are useful for different practical
reasons. The key advantage of these controller structures no doubt
lies in the fact that the controller states are meaningful variables
as estimates of the physical plant states: thus, the interpolation of
controllers or the initialization of switched controllers becomes
easier using observer based realization.
Based on the observer based realization of a given controller, the
Cross Standard Form (CSF) is also introduced as a reverse engineering
tool: i.e. a solution to the generalized inverse optimal control
problem. The CSF is a canonical augmented standard plant whose H_\infty or
H2 optimal controller is a given controller. From the multi-objective
point of view, the general idea is to apply the CSF to a first
controller satisfying nominal performances in order to initialize an
H_\infty design procedure to handle frequency-domain constraints or
robustness specifications.
[INMA] 2012-01-24 (14.00) : Statistical Methods for Developing Reliable Fundamental Models
At Euler building
Speaker :
Kim McAuley (Department of Chemical Engineering, Queen's University, Canada)
Abstract : Fundamental models are used to design, debottleneck, optimize and control chemical processes. Obtaining reliable model predictions requires an appropriate balance between simplicity and complexity of model equations, as well as appropriate values for model parameters. This talk will focus on statistical tools that can assist modellers when they develop model equations, estimate parameters and select conditions for new experiments. One common problem that arises when modeling chemical processes is the large number of parameters that appear in equations describing rates of chemical reactions and transport of species between phases. A modeller with a large and informative data set will be able to reliably estimate a large number of model parameters. When there is insufficient information in the data to reliably estimate all of the model parameters, only a subset of the parameters should be estimated. This talk will introduce easy-to-use parameter ranking and selection techniques (based on mean-squared error) that can help modellers to decide which parameters to estimate to get the best possible model predictions. Use of models to select operating conditions for new dynamic and steady-state experiments will also be discussed. These methods will be illustrated using models and data from a steam-methane reformer, bioreactors, and industrial polymerization processes.
[INMA] 2011-12-20 (14.00) : A Geometric Approach for Sparse Signal Processing: Algorithms and Performance Guarantees
At Euler building
Speaker :
Wei Dai (Imperial College London)
Abstract : Sparse signal processing is a technology for acquiring and
analyzing sparse signals efficiently. Many signals, including
biomedical signals, sensor network measurements, and social network
data are sparse in the sense that the signal can be well approximated
by only a small number of linear principal components. Sparse signal
processing allows us to work on the intrinsic information directly
without worrying about the details of the signal, hence results in a
large saving in data collection or a huge improvement on data
analysis.
In this talk we discuss a geometric view of sparse signal
processing. More specifically, we look at low-rank matrix completion
and dictionary learning problems in sparse signal processing, show how
these topics can be formulated as optimization problems on Grassmann
manifolds, and discuss what kind of performance guarantees can be
obtained based on the geometric approach. Various applications of
sparse signal processing are also briefly discussed.
Seminars
Subscribe (ICS)
INMA Contact Info
Mathematical Engineering (INMA)
L4.05.01
Avenue Georges Lemaître, 4
+32 10 47 80 36
secretaire-inma@uclouvain.be
Mon – Fri 9:00A.M. – 5:00P.M.
JOIN US