Speaker: Peter Benner
Affiliation: Max Planck Institute for Dynamics of Complex Technical Systems
Time: Thursday, 04 April 2019, h. 15:00
Place: Sala Seminari Ovest, Dipartimento di Informatica
Title: Low-rank tensor methods for PDE-constrained optimization under
uncertainty
We discuss optimization and control of unsteady partial differential
equations (PDEs), where some coefficient of the PDE as well as the
control may be uncertain. This may be due to the lack of knowledge about
the …
[View More]exact physical parameters, like material properties describing a
real-world problem (''epistemic uncertainty'') or the inability to apply
a computed optimal control exactly in practice. Using a stochastic
Galerkin space-time discretization of the optimality system resulting
from such PDE-constrained optimization problems under uncertainty leads
to large-scale linear or nonlinear systems of equations in saddle point
form. Nonlinearity is treated with a Picard-type iteration in which
linear saddle point systems have to be solved in each iteration step.
Using data compression based on separation of variables and the tensor
train (TT) format, we show how these large-scale indefinite and
(non)symmetric systems that typically have 10⁸ to 10¹⁵ unknowns can be
solved without the use of HPC technology. The key observation is that
the unknown and the data can be well approximated in a new block TT
format that reduces complexity by several orders of magnitude. As
examples, we consider control and optimization problems for the linear
heat equation, the unsteady Stokes and Stokes-Brinkman equations, as
well as the incompressible unsteady Navier-Stokes equations. The talk
surveys the results published in [1,2] and provides new results for the
Navier-Stokes case.
[1] P. Benner, A. Onwunta, M. Stoll, Block-diagonal preconditioning for
optimal control problems constrained by PDEs with uncertain inputs, SIAM
Journal on Matrix Analysis and Applications, 37(2):491--518, 2016.
[2] P. Benner, S. Dolgov, A. Onwunta, M. Stoll, Low-rank solvers for
unsteady Stokes-Brinkman optimal control problem with random data,
Computer Methods in Applied Mechanics and Engineering, 304:26--54, 2016.
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Dear all,
I would like to advertise the following seminar, that might be of
interest to some of you.
Best, -- Leonardo.
-------- Messaggio originale --------
Oggetto: [Dipartimento.di] Seminar: Machine Learning & Optimization: A
Fruitful Interplay - M. Sanguineti
Data: 06-03-2019 16:28
Mittente: Alessio Micheli <micheli(a)di.unipi.it>
Destinatario: dipartimento(a)di.unipi.it
Cari tutti,
con piacere annuncio il seguente seminario di Marcello Sanguineti in
dipartimento.
DATE/…
[View More]HOUR: Thursday, March 28, 2019 – 3 P.M.
ROOM: Sala seminari ovest - Dip. di Informatica – Pisa
TITLE: Machine Learning & Optimization: A Fruitful Interplay
SPEAKER: Marcello Sanguineti, Department of Computer Science,
Bioengineering,Robotics, and Systems Engineering (DIBRIS), University of
Genova
ABSTRACT: Since the very beginning, there has been a fruitful exchange
between machine learning and optimization. While machine learning
exploits optimization models and algorithms, it simultaneously poses
problems which often constitute optimization challenges. This
cross-fertilization is particularly evident nowadays. Many applications
produce data that have to be processed and many other applications are
based on data that have already been processed. In society,
data-producers and data-consumers continuously exchange their roles. At
the same time, scientists generate and collect huge amounts of data and
need to develop methodologies for data analysis. This requires the use
of ever more powerful approaches and techniques. Among these
improvements, those coming from the field of optimization surely play a
basic role. Not only classical optimization frameworks, such as
stochastic approximation, first-order methods, and convex relaxation,
are exploited in machine learning, but also more sophisticated models
and techniques, such as regularized optimization, robust optimization,
and functional optimization. In this talk, I provide a non-technical
review of some optimization paradigms and techniques used in machine
learning and I emphasize some aspects at the confluence of these two
disciplines. The interplay between machine learning and optimization
continues to develop, and its benefits are there for all to see.
Riferimento: Alessio Micheli.
--
Saluti, Alessio.
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Dear all,
next Monday we will have a seminar by Vanni Noferini; starting from the
following week, we will try to go back to the original schedule of
having seminars on Thursday afternoon.
You are all welcome!
Best wishes, -- Leonardo.
Speaker: Vanni Noferini
Affiliation: University of Essex / Aalto University
Time: Monday, 25 March 2019, h. 10:00
Place: Sala Seminari, Dipartimento di Matematica
Title: Matrices in companion rings and their Smith forms, with
applications to group theory …
[View More]and algebraic topology
In group theory, various properties of the abelianization of a
cyclically presented group can be deduced by the Smith normal form of an
integer circulant matrix. Motivated by this fact, we present a number of
results on the Smith form of matrices that are polynomials in the
companion matrix of a polynomial with coefficients in a generic
elementary divisor domain. Our tools are of purely matrix theoretical
nature and I will present them from the point of view of a matrix
theorist. However, they enable significant advances in pure algebra. In
particular, I plan to discuss how our results provide a tool to study
the homology of 3-dimensional Brieskorn manifolds, which are objects of
(apparently) interest for topologists. If time permits, I will mention
other possible applications to group theory.
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Dear all,
there will be two seminars next week: in addition to the one by Carla
Hernando on Monday, Vladimir Druskin will give a talk on Thursday at
SNS. You find more details in the abstract below.
You are all welcome to attend.
Best wishes, -- Leonardo.
Speaker: Vladimir Druskin
Affiliation: Worcester Polytechnic Institute
Time: Monday, 21 March 2019, h. 15:00
Place: Aula Mancini, SNS
Title: Embedding properties of network realizations of reduced order
models with applications to …
[View More]inverse scattering and data science
Continued fractions are known since antiquity as the most compact
representations of numbers. At the end of the 19th century Stieltjes
connected them with physics. This connection gave rise to network
syntheses in the first half of the 20th century that was at the base of
modern electronics design and consecutively to model order reduction
(MOR) that tremendously impacted many areas of engineering by enabling
efficient compression of the underlining dynamical systems. In his
seminal 1950s works Krein realized that in addition to their compressing
properties, Stieltjes continuous fractions can be used to embed the data
back into the state space of the underlying dynamical system via special
mechanical networks known as Stieltjes strings. Such networks can learn
the underlying PDE system from the data (transfer function) via
rigorously chosen hyper-parameters. Among many application of this
powerful approach we discuss the following two.
1. Imaging in strongly scattering media with waves (e.g.,seismic
exploration) via data-driven MOR.
2. Reduced order graph-Laplacians and efficient cluster analysis of big
data sets.
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Dear all,
on Monday next week Carla Hernando, a PhD student visiting the
department of Computer Science for three months, will give a seminar on
her research.
You are all welcome to attend, the abstract is attached below.
Best wishes, -- Leonardo.
Speaker: Carla Hernando
Affiliation: UC3M, Madrid
Time: Monday, 18 March 2019, h. 14:00
Place: Sala Seminari, Dipartimento di Matematica
Title: Sparse linearizations and (sparse) structured ell-ifications
The talk is divided in two main parts. …
[View More]The first one is focused on
(generalized) companion pencils, which are strong linearizations and
they present a template involving no arithmetic operations at all. In
addition, we are mainly interested in sparse (generalized) companion
pencils and then, we determine the smallest number of nonzero entries of
a particular class of companion pencils. In the case of generalized
companion pencils, we should impose natural conditions on its entries.
In the second one, a family of structured block Kronecker ell-ifications
will be introduced. This family has the particular structure of a
strong block minimal bases polynomial, introduced in [1]. Furthermore,
we have introduced two new subfamilies of structured block Kronecker
ell-ifications where not only there is no duplication of the
coefficients of the polynomial, but also the degree-ell polynomial is
sparse.
This is joint work with Fernando de Terán (UC3M, Spain), my thesis
director.
[1] F.M.Dopico, J.Pérez, P.Van Dooren. Block minimal bases
ell-ifications of matrix polynomials. Linear Algebra Appl., 562 (2019),
163-204
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Dear all,
the next seminar will be the next week on Thursday (so _not_ tomorrow),
and will be hosted at SNS. You find the abstract below.
See you there,
Best, -- Leonardo.
Speaker: Michiel Hochstenbach
Affiliation: TU Eindhoven
Time: Thursday, 14 March 2019, h. 15:00
Place: Aula Tonelli, SNS
Title: Solving polynomial systems by determinantal representations
Zeros of a polynomial, p(x)=0, are often determined by computing the
eigenvalues of a companion matrix: a matrix A which satisfies
…
[View More]det(A-xI)=p(x).
In this talk we consider polynomial systems, in particular in 2
variables: p(x,y)=0, q(x,y)=0.
We look for a determinantal representation for such a bivariate
polynomial: matrices A, B, C such that det(A-xB-yC)=p(x,y).
This means that we can compute the zeros of the system by solving a
2-parameter eigenvalue problem.
This approach, which already goes back to a theorem by Dixon in 1902,
leads to fast solution methods, as well as a multitude of interesting
open research questions.
This is mainly joint work with Bor Plestenjak (Ljubljana), and
additionally several colleagues in algebra, among which Ada Boralevi
(Torino).
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Speaker: Fabio Durastante
Affiliation: University of Pisa
Time: Thursday, 28 February 2019, h. 14:00
Place: Sala Seminari Est, Dipartimento di Informatica
Title: The Krylov--Jacobi method: functions of matrices for fractional
partial differential equations
In this talk I discuss briefly some computational issues concerning
a Krylov method of rational type for the computation of certain
matrix functions occurring in the solution of fractional partial
differential equations. Specifically, a …
[View More]new set of poles for
the computation of the following functions of symmetric positive
definite matrices is introduced:
- fractional power, $f(z) = z^{-\alpha/2}$,
- resolvent of fractional power, $f(z) = (1+\nu z^{\alpha/2})^{-1}$.
The underlying approach permits to efficiently semidiscretize the
fractional Laplacian operator on non Cartesian/regular grids
exploiting either Finite Differences, Finite Elements, or Finite
Volumes schemes, and to employ any appropriate linear multistep
method for marching in time.
Numerical experiments on some fractional partial differential
equation model problems and comparisons with other methods,
including other popular rational Krylov methods, confirm that the
proposed approach is promising.
This is a joint work with: L. Aceto, D. Bertaccini, and P. Novati.
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Cari tutti,
durante il secondo semestre ci saranno altri seminari nel ciclo di
analisi numerica, in continuazione con quelli del primo semestre.
Come per l'ultima volta, chiederei a chi è interessato a partecipare di
compilare il Doodle [1], per permetterci di scegliere un orario durante
la settimana che accontenti il maggior numero di persone.
Nei prossimi giorni cominceremo a stendere il calendario, e dai primi di
marzo dovrebbero cominciare con i seminari.
Grazie a tutti!
[1] https://…
[View More]doodle.com/poll/k4z8py3hwp3gen74
A presto, -- Leonardo.
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Inoltro questo annuncio di seminario a informatica.
*Data*: Martedì 5 Febbraio, 11-30-12:30, Sala Gerace, Dipartimento di
Informatica
*
*
*Speaker*: Prof. Francesco Rinaldi, Università di Padova
*Title*: Advances on first order algorithms for constrained optimization
problems in Machine Learning
*Abstract*: Thanks to the advent of the "Big Data era", simple iterative
first-order optimization approaches for constrained optimization have
re-gained popularity in the last few years. In the talk, …
[View More]we first review
a few classic methods (i.e., conditional and projected gradient method)
in the context
of Big Data applications. Then, we discuss both theoretical and
computational aspects of some variants of those classic methods.
Finally, we examine current challenges and future research perspectives.
*Ambito*: Progetto PRA 2017
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Speaker: Daniel Kressner
Affiliation: EPFL
Time: Wednesday, 9 January 2019, h. 11:00
Place: Aula Seminari, Dipartimento di Matematica
Title: Tensorized Krylov subspace methods: Algorithms, analysis, and
applications
Tensorized Krylov subspace methods are a versatile tool in numerical
linear algebra for addressing large-scale applications that involve
tensor product structure. This includes the discretization of
high-dimensional PDEs, the solution of linear matrix equations, as well
as …
[View More]low-rank updates and Frechet derivatives for matrix functions. This
talk gives an overview of such methods, discusses their theoretical
properties, and highlights applications.
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