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Colloquio De Giorgi - Volker Mehrmann, Dirac and Lagrange structures in energy-based mathematical modeling 24/02/23, 16:00
by Fabio Durastante 01 Feb '23

01 Feb '23

We apologize in advance for cross-posting. ******************************************************************************** CENTRO DI RICERCA MATEMATICA "ENNIO DE GIORGI" ******************************************************************************** COLLOQUIO DE GIORGI Centro De Giorgi, Pisa, 24th February 2023 Aula Dini: 4.00 pm The event will take place in person. Volker Mehrmann Technische Universität Berlin Title:“Dirac and Lagrange structures in energy-based mathematical modeling” Abstract: Most real world dynamical systems consist of subsystems from different physical domains, modelled by partial-differential equations, ordinary differential equations, and algebraic equations, combined with input and output connections. To deal with such complex system, in recent years the class of dissipative port-Hamiltonian (pH) descriptor systems has emerged as a very successful modeling methodology. The main reasons are that the network based interconnection of pH systems is again pH, Galerkin projection in PDE discretization and model reduction preserve the pH structure and the physical properties are encoded in the geometric properties of the flow as well as the algebraic properties of the equations. Furthermore, dissipative pH system form a very robust representation under structured perturbations and directly indicate Lyapunov functions for stability analysis. Using global geometric and algebraic points of view, via Dirac and Lagrange spaces or manifolds, translations between different representations are presented. Characterizations are also derived when a general differential-algebraic system can be transformed into one of these structured representations. Numerical approaches for computing the structural information and the described transformations are derived and the results are demonstrated with some real world examples. Web site: http://www.crm.sns.it/course/6529/ <https://es.sonicurlprotection-fra.com/click?PV=2&MSGID=20230131222506106602…> Please note that for organizational purposes, registration <https://es.sonicurlprotection-fra.com/click?PV=2&MSGID=20230131222506106602…>is mandatory. CRM Secretariat Scuola Normale Superiore Piazza dei Cavalieri, 3 56126 Pisa, Italy

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[Indico] Dr Gianluca Ceruti, Robust numerical integrators for dynamical low-rank approximation, 15/12/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 14 Dec '22

14 Dec '22

Title: Robust numerical integrators for dynamical low-rank approximation, Speaker(s): Dr Gianluca Ceruti, École Polytechnique Fédérale de Lausanne, Date and time: 15 Dec 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: room Aula Magna (Dipartimento di Matematica). You can access the full event here: https://events.dm.unipi.it/e/138 Abstract -------- The discretization of time-dependent high-dimensional PDEs suffers from an undesired effect, the so-called curse of dimensionality: The amount of data to be stored and treated grows exponentially and exceeds standard capacity of common computational devices. In this setting, time dependent model order reductions techniques are desirable. In the present seminar, we present a broad overview on dynamical low-rank approximation together with recent developments on robust numerical integrators for it. Dynamical low-rank approximation for matrices is firstly presented, and a numerical integrator with two remarkable properties is introduced: the matrix projector splitting integrator. Based upon this numerical integrator, we construct two equivalent extensions for tensors, multi-dimensional arrays, in Tucker format - a high-order generalization of the SVD decomposition for matrices. These extensions are proven to preserve the excellent qualities of the matrix integrator. Then, via a novel compact formulation of the Tucker integrator, we further extend the matrix and Tucker projector splitting integrators to the most general class of Tree Tensor Networks. Important examples belonging to this class and of interest for applications are given by (but not only restricted to) Tensor Trains.The present seminar is based upon joint works with Ch. Lubich, H. Walach, J. Kusch, and D. Sulz. -- Indico :: Email Notifier https://events.dm.unipi.it/e/138

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[Indico] Dr Gianluca Ceruti, Robust numerical integrators for dynamical low-rank approximation, 15/12/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 12 Dec '22

12 Dec '22

Title: Robust numerical integrators for dynamical low-rank approximation, Speaker(s): Dr Gianluca Ceruti, École Polytechnique Fédérale de Lausanne, Date and time: 15 Dec 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: room Aula Riunioni (Dipartimento di Matematica). You can access the full event here: https://events.dm.unipi.it/e/138 Abstract -------- The discretization of time-dependent high-dimensional PDEs suffers from an undesired effect, the so-called curse of dimensionality: The amount of data to be stored and treated grows exponentially and exceeds standard capacity of common computational devices. In this setting, time dependent model order reductions techniques are desirable. In the present seminar, we present a broad overview on dynamical low-rank approximation together with recent developments on robust numerical integrators for it. Dynamical low-rank approximation for matrices is firstly presented, and a numerical integrator with two remarkable properties is introduced: the matrix projector splitting integrator. Based upon this numerical integrator, we construct two equivalent extensions for tensors, multi-dimensional arrays, in Tucker format - a high-order generalization of the SVD decomposition for matrices. These extensions are proven to preserve the excellent qualities of the matrix integrator. Then, via a novel compact formulation of the Tucker integrator, we further extend the matrix and Tucker projector splitting integrators to the most general class of Tree Tensor Networks. Important examples belonging to this class and of interest for applications are given by (but not only restricted to) Tensor Trains.The present seminar is based upon joint works with Ch. Lubich, H. Walach, J. Kusch, and D. Sulz. -- Indico :: Email Notifier https://events.dm.unipi.it/e/138

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Assegno di ricerca presso il Dipartimento di Matematica
by Leonardo Robol 23 Nov '22

23 Nov '22

Buongiorno, si è appena aperto un bando per un assegno di ricerca di 12 mesi presso il Dipartimento di Matematica (di Pisa), su fondi PNRR. La scadenza è il 21/12/22. Vi prego diffondere l'annuncio con chiunque possa essere interessato/a. https://bandi.unipi.it/public/Bandi/Detail/f2d456ca-5df1-4fcd-b95c-d16d0434…. A presto, -- Leonardo Robol.

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[Indico] Aaron Melman, Recent extensions of scalar and matrix polynomial properties and their interactions, 10/11/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 03 Nov '22

03 Nov '22

Title: Recent extensions of scalar and matrix polynomial properties and their interactions, Speaker(s): Aaron Melman, Santa Clara University, USA, Date and time: 10 Nov 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Riunioni). You can access the full event here: https://events.dm.unipi.it/e/114 Abstract -------- Several results for scalar polynomials are extended and then generalized to matrix polynomials. Among them are a directional version of Pellet's theorem for both scalarand matrix polynomials, which establishes an exclusion interval for the magnitudes of polynomial zeros or eigenvalues having a given argument, as well as results involving real polynomials with sign restrictions on their coefficients. The latter lead to exclusion sectorsfor polynomial eigenvalues. In addition, it is shown how new results can be obtained by embedding scalar polynomials into a matrix polynomial framework, and examples are given of how the interactionbetween scalar and matrix polynomials benefits both. If time (and interest) permits, an improvement of theorems by Hayashi and Hurwitz from the beginning of the twentiethcentury will be presented. These theorems concern the location of polynomial zeros when the coefficients exhibit certain sign patterns. -- Indico :: Email Notifier https://events.dm.unipi.it/e/114

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Seminario di oggi (Santolo Leveque)
by Leonardo Robol 24 Oct '22

24 Oct '22

Cari tutt*, vi ricordo il seminario di oggi di Santolo Leveque, alle 16.00: https://events.dm.unipi.it/event/113/ Al contrario di come era stato scritto nei primi avvisi, il seminario sarà in Aula Riunioni, e non in Aula Magna (nel caso aveste annotato l'aula tempo fa). A dopo! -- Leonardo Robol

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Workshop on Quasi-Newton methods
by Stefano Cipolla 23 Oct '22

23 Oct '22

Dear Colleagues, we are delighted to inform you that we are organizing the event "Workshop on Quasi-Newton methods" which will be held in Edinburgh, 9th Nov 2022, please see https://www.maths.ed.ac.uk/~gondzio/qNewton2022/home.html for more information. The workshop aims at promoting the exchange of ideas and to advance the state of the art in the area of Quasi-Newton methods. The *hybrid* workshop will consist of five invited presentations by selected leading researchers. Remote and in person participation are welcome. If you are willing to take part, please register (free of charge) at your earliest convenience, but not later than 31st Oct 2022, at the link https://forms.gle/bNccQ7mTAKhnJYNW6 Very Best Regards, Jacek, Stefano -- Stefano Cipolla Postdoctoral Research Associate School of Mathematics University of Edinburgh James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh, EH9 3FD email: scipolla(a)ed.ac.uk The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336. Is e buidheann carthannais a th’ ann an Oilthigh Dhùn Èideann, clàraichte an Alba, àireamh clàraidh SC005336.

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[Indico] Santolo Leveque, A “matching strategy” for optimal control problems with PDEs as constraints, 24/10/2022, 16:00 Europe/Rome
by leonardo.robol＠unipi.it 18 Oct '22

18 Oct '22

Title: A “matching strategy” for optimal control problems with PDEs as constraints, Speaker(s): Santolo Leveque, Scuola Normale Superiore, Pisa, Date and time: 24 Oct 2022, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Riunioni). You can access the full event here: https://events.dm.unipi.it/e/113 Abstract -------- Saddle-point systems arise quite often in many areas of scientific computing. For instance, this type of system can be found in computational fluid dynamics, constrained optimization, finance, image reconstruction, and many more scientific applications. Due to their convenient structure and high dimensionality, preconditioned iterative methods are usually employed in order to solve this class of problems. By making use of saddle-point theory, one is able to derive optimal preconditioners for a general saddle-point system. However, the major drawback is that the cost of applying their inverse operator is almost as costly as inverting the original system. For this reason, one would rather find easy-to-invert approximation of the main blocks of the preconditioner considered.In this talk, we will present the “matching strategy” derived in [3] for approximating the Schur complement of a saddle-point system arsing from optimal control problems with PDE as constraints. We will mainly focus on time-dependent PDE, when employing a Crank–Nicolson discretization in time. After applying an optimize-then-discretize approach, one is faced with continuous first-order optimality conditions consisting of a coupled system of PDEs. After discretizing with Crank–Nicolson, one has to solve for a non-symmetric system. We apply a carefully tailored invertible transformation for symmetrizing the latter, and derive an ideal preconditioner by making use of saddle-point theory. The transformation is then employed within the preconditioner in order to derive optimal approximations of the (1,1)-block and of the Schur complement. We prove the latter through bounds on the eigenvalues, and test our solver against the widely-used preconditioner derived in [2] for the linear system arising from a backward Euler discretization in time. These demonstrate the effectiveness and robustness of our solver with respect to all the parameters involved in the problem considered.This talk is based on the work in [1].References[1] S. Leveque and J. W. Pearson, Fast Iterative Solver for the Optimal Control of Time-Dependent PDEs with Crank–Nicolson Discretization in Time, Numer. Linear Algebra Appl. 29, e2419, 2022.[2] J. W. Pearson, M. Stoll and A. J. Wathen, Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems, SIAM J. Matrix Anal. Appl. 33, 1126–1152, 2012.[3] J. W. Pearson and A. J. Wathen, A New Approximation of the Schur Complement in Preconditioners for PDE-Constrained Optimization, Numer. Linear Algebra Appl. 19, 816–829, 2012. -- Indico :: Email Notifier https://events.dm.unipi.it/e/113

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[Indico] Aaron Melman, Recent extensions of scalar and matrix polynomial properties and their interactions, 10/11/2022, 11:00 Europe/Rome
by leonardo.robol＠unipi.it 10 Oct '22

10 Oct '22

Title: Recent extensions of scalar and matrix polynomial properties and their interactions, Speaker(s): Aaron Melman, Santa Clara University, USA, Date and time: 10 Nov 2022, 11:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Riunioni). You can access the full event here: https://events.dm.unipi.it/e/114 Abstract -------- Several results for scalar polynomials are extended and then generalized to matrix polynomials. Among them are a directional version of Pellet's theorem for both scalarand matrix polynomials, which establishes an exclusion interval for the magnitudes of polynomial zeros or eigenvalues having a given argument, as well as results involving real polynomials with sign restrictions on their coefficients. The latter lead to exclusion sectorsfor polynomial eigenvalues. In addition, it is shown how new results can be obtained by embedding scalar polynomials into a matrix polynomial framework, and examples are given of how the interactionbetween scalar and matrix polynomials benefits both. If time (and interest) permits, an improvement of theorems by Hayashi and Hurwitz from the beginning of the twentiethcentury will be presented. These theorems concern the location of polynomial zeros when the coefficients exhibit certain sign patterns. -- Indico :: Email Notifier https://events.dm.unipi.it/e/114

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[Indico] Santolo Leveque, A “matching strategy” for optimal control problems with PDEs as constraints, 24/10/2022, 16:00 Europe/Rome
by fabio.durastante＠unipi.it 05 Oct '22

05 Oct '22

Title: A “matching strategy” for optimal control problems with PDEs as constraints, Speaker(s): Santolo Leveque, Scuola Normale Superiore, Pisa, Date and time: 24 Oct 2022, 16:00 (Europe/Rome), Lecture series: Seminar on Numerical Analysis, Venue: Dipartimento di Matematica (Aula Magna). You can access the full event here: https://events.dm.unipi.it/e/113 Abstract -------- Saddle-point systems arise quite often in many areas of scientific computing. For instance, this type of system can be found in computational fluid dynamics, constrained optimization, finance, image reconstruction, and many more scientific applications. Due to their convenient structure and high dimensionality, preconditioned iterative methods are usually employed in order to solve this class of problems. By making use of saddle-point theory, one is able to derive optimal preconditioners for a general saddle-point system. However, the major drawback is that the cost of applying their inverse operator is almost as costly as inverting the original system. For this reason, one would rather find easy-to-invert approximation of the main blocks of the preconditioner considered.In this talk, we will present the “matching strategy” derived in [3] for approximating the Schur complement of a saddle-point system arsing from optimal control problems with PDE as constraints. We will mainly focus on time-dependent PDE, when employing a Crank–Nicolson discretization in time. After applying an optimize-then-discretize approach, one is faced with continuous first-order optimality conditions consisting of a coupled system of PDEs. After discretizing with Crank–Nicolson, one has to solve for a non-symmetric system. We apply a carefully tailored invertible transformation for symmetrizing the latter, and derive an ideal preconditioner by making use of saddle-point theory. The transformation is then employed within the preconditioner in order to derive optimal approximations of the (1,1)-block and of the Schur complement. We prove the latter through bounds on the eigenvalues, and test our solver against the widely-used preconditioner derived in [2] for the linear system arising from a backward Euler discretization in time. These demonstrate the effectiveness and robustness of our solver with respect to all the parameters involved in the problem considered.This talk is based on the work in [1].References[1] S. Leveque and J. W. Pearson, Fast Iterative Solver for the Optimal Control of Time-Dependent PDEs with Crank–Nicolson Discretization in Time, Numer. Linear Algebra Appl. 29, e2419, 2022.[2] J. W. Pearson, M. Stoll and A. J. Wathen, Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems, SIAM J. Matrix Anal. Appl. 33, 1126–1152, 2012.[3] J. W. Pearson and A. J. Wathen, A New Approximation of the Schur Complement in Preconditioners for PDE-Constrained Optimization, Numer. Linear Algebra Appl. 19, 816–829, 2012. -- Indico :: Email Notifier https://events.dm.unipi.it/e/113

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