Title: Grassmann extrapolation of density matrices as a tool to accelerate Born-Oppenheimer molecular dynamics,
Speaker(s): Federica Pes, Università di Pisa,
Date and time: 19 May 2023, 15:00 (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/192
Abstract
--------
Born-Oppenheimer molecular dynamics (BOMD) is a powerful but expensive technique. The main bottleneck in a density functional theory (DFT) BOMD calculation is the solution to the DFT nonlinear equations that requires an iterative procedure that starts from a guess for the density matrix. To speed up such calculations, various extrapolation strategies have been developed to use densities available at previous simulation steps as a guess for the iterative procedure. However, density matrices belong in a Grassmann manifold, which is not a vector space. Therefore the linear extrapolation is performed in a tangent space of the manifold, thanks to a locally bijective map between the manifold and its tangent space.In this contribution, we introduce an approximately time reversible approach to extrapolate density matrices. Some numerical experiments show optimal performance, compared to the state of the art.
--
Indico :: Email Notifier
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Buongiorno,
inoltro questo annuncio per una posizione a KU Leuven. La posizione è
nel gruppo di analisi numerica ed è orientata al quantum computing.
A presto,
Paola
-------- Forwarded Message --------
Subject: Faculty position Numerical Methods for Quantum Computing at KU
Leuven
Date: Tue, 9 May 2023 13:15:26 +0200
From: Nick Vannieuwenhoven <nick.vannieuwenhoven(a)kuleuven.be>
To: paola.boito(a)unipi.it
Dear Prof. Paola Boito,
We would like to draw your attention to the job offer for the full-time
faculty position in /Numerical Methods for Quantum Computing/ at KU
Leuven, with application deadline September 14, 2023. A short
description is included below. A detailed description is available at
https://www.kuleuven.be/personeel/jobsite/jobs/60205789
Since we believe that the position could be of interest to some of your
group members, colleagues or collaborators, we would kindly ask you to
forward the message, in particular to excellent post-docs and junior
group leaders.
Best regards,
Nick Vannieuwenhoven
----
Prof. dr. Nick Vannieuwenhoven,
Member of the search committee.
KU Leuven,
Department of Computer Science,
Celestijnenlaan 200A, bus 2402,
3001 Heverlee,
Belgium.
*Faculty Position, Numerical Methods for Quantum Computing, KU Leuven *
The Science, Engineering, and Technology Group of KU Leuven invites
applications for a full time research professorship in the research unit
Numerical Analysis and Applied Mathematics (NUMA). The research in NUMA
covers many aspects of computational mathematics, including
approximation theory, numerical integration, numerical (multi-) linear
algebra, numerical partial differential equations, uncertainty
quantification, optimization and control, discrete optimization and
scheduling, and high-performance computing. The research unit also
performs research in collaboration with industry. The new position aims
to strengthen the experience in the domain of quantum computing.
Quantum computing is a novel computing paradigm relying on fundamental
properties of quantum physics. It features new core building blocks that
can lead to exponential speedups relative to traditional computing. This
requires a fundamental shift in the design of numerical algorithms and
their optimized mapping to available quantum circuits. Candidates are
expected to have already obtained excellent research results within the
research field of design, analysis, development, and implementation of
new quantum algorithms for numerical computing.
The successful candidate is expected to develop a research program on
quantum computing, ensure high-quality education within the area of
mathematical engineering, and be prepared to provide scientific and
administrative services.
For further details, contact information and the application procedure
(deadline September 14, 2023), follow the link:
https://www.kuleuven.be/personeel/jobsite/jobs/60205789
The vacancy fits within the KU Leuven Quantum initiative:
https://set.kuleuven.be/en/about-us/vacancies/quantum
Title: Grassmann extrapolation of density matrices as a tool to accelerate Born-Oppenheimer molecular dynamics,
Speaker(s): Federica Pes, Università di Pisa,
Date and time: 19 May 2023, 15:00 (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/192
Abstract
--------
Born-Oppenheimer molecular dynamics (BOMD) is a powerful but expensive technique. The main bottleneck in a density functional theory (DFT) BOMD calculation is the solution to the DFT nonlinear equations that requires an iterative procedure that starts from a guess for the density matrix. To speed up such calculations, various extrapolation strategies have been developed to use densities available at previous simulation steps as a guess for the iterative procedure. However, density matrices belong in a Grassmann manifold, which is not a vector space. Therefore the linear extrapolation is performed in a tangent space of the manifold, thanks to a locally bijective map between the manifold and its tangent space.In this contribution, we introduce an approximately time reversible approach to extrapolate density matrices. Some numerical experiments show optimal performance, compared to the state of the art.
--
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https://events.dm.unipi.it/e/192
Title: Perfect Shifted QR for Rank Structured Pencils,
Speaker(s): Prof. Vandebril Raf, KU Leuven,
Date and time: 13 Apr 2023, 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/182
Abstract
--------
It is known that executing a perfect shifted QR step via the implicit QR algorithm performs poor in terms of stability, and accuracy. Typically several steps are required before deflation actually takes place. This behavior can be remedied by determining the similarity transformation via the associated eigenvector. Similar techniques can be deduced for the QZ algorithm and the rational QZ algorithm. In this talk we generalize this even further and present an approach for executing a perfect shifted QR step for general rank structured pencils. We prove that the rank structures of the matrices involved in the pencil are preserved, and moreover we examine the preservation of spectral properties of subblocks in the pencil.Authors: Nicola Mastronardi, Marc Van Barel, Raf Vandebril, and Paul Van Dooren
--
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Title: Model order reduction of parametric Hamiltonian systems on matrix manifolds,
Speaker(s): Cecilia Pagliantini, University of Pisa,
Date and time: 28 Mar 2023, 16:00 (Europe/Rome),
Lecture series: Seminar on Numerical Analysis,
Venue: Dipartimento di Matematica (Aula Seminari).
You can access the full event here: https://events.dm.unipi.it/e/176
Abstract
--------
Model order reduction of parametric differential equations aims at constructing low-complexity high-fidelity surrogate models that allow rapid and accurate solutions under parameter variation. The development of reduced order models for Hamiltonian systems is challenged by several factors: (i) failing to preserve the geometric structure encoding the physical properties of the dynamics, such as invariants of motion or symmetries, might lead to instabilities and unphysical behaviors of the resulting approximate solutions; (ii) the slowly decaying Kolmogorov n-width of transport-dominated and non-dissipative phenomena demands large reduced spaces to achieve sufficiently accurate approximations; and (iii) nonlinear operators require hyper-reduction techniques that preserve the gradient structure of the flow velocity.We will discuss how to address these aspects via a structure-preserving nonlinear reduced basis approach based on dynamical low-rank approximation. The gist of the proposed method is to adapt in time an approximate low-dimensional phase space endowed with the geometric structure of the full model and to ensure that the reduced flow is still Hamiltonian.
--
Indico :: Email Notifier
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Title: Model order reduction of parametric Hamiltonian systems on matrix manifolds,
Speaker(s): Cecilia Pagliantini, University of Pisa,
Date and time: 28 Mar 2023, 16:00 (Europe/Rome),
Lecture series: Seminar on Numerical Analysis,
Venue: Dipartimento di Matematica (Aula Seminari).
You can access the full event here: https://events.dm.unipi.it/e/176
Abstract
--------
Model order reduction of parametric differential equations aims at constructing low-complexity high-fidelity surrogate models that allow rapid and accurate solutions under parameter variation. The development of reduced order models for Hamiltonian systems is challenged by several factors: (i) failing to preserve the geometric structure encoding the physical properties of the dynamics, such as invariants of motion or symmetries, might lead to instabilities and unphysical behaviors of the resulting approximate solutions; (ii) the slowly decaying Kolmogorov n-width of transport-dominated and non-dissipative phenomena demands large reduced spaces to achieve sufficiently accurate approximations; and (iii) nonlinear operators require hyper-reduction techniques that preserve the gradient structure of the flow velocity.We will discuss how to address these aspects via a structure-preserving nonlinear reduced basis approach based on dynamical low-rank approximation. The gist of the proposed method is to adapt in time an approximate low-dimensional phase space endowed with the geometric structure of the full model and to ensure that the reduced flow is still Hamiltonian.
--
Indico :: Email Notifier
https://events.dm.unipi.it/e/176
Title: Applications of AAA Rational Approximation,
Speaker(s): Prof. Lloyd N. Trefethen, Mathematical Institute, University of Oxford,
Date and time: 21 Feb 2023, 11:00 (Europe/Rome),
Lecture series: Seminar on Numerical Analysis,
Venue: Scuola Normale Superiore (Aula Volterra).
Address:
Piazza dei Cavalieri, 7 - 56126 Pisa
You can access the full event here: https://events.dm.unipi.it/e/158
Abstract
--------
Abstract:For the first time, a method has recently become available for fast computation of near-best rational approximations on arbitrary sets in the real line or complex plane: the AAA algorithm (Nakatsukasa-Sete-T. 2018). We will present the algorithm and then demonstrate a number of applications, includingdetection of singularities, model order reduction, analytic continuation, functions of matrices, nonlinear eigenvalue problems, interpolation of equispaced data, smooth extension of multivariate real functions, extrapolation of ODE and PDE solutions into the complex plane, solution of Laplace problems, conformal mapping, Wiener-Hopf factorization.
Note
----
A reminder of tomorrow's seminar.
--
Indico :: Email Notifier
https://events.dm.unipi.it/e/158
Title: Applications of AAA Rational Approximation,
Speaker(s): Prof. Lloyd N. Trefethen, Mathematical Institute, University of Oxford,
Date and time: 21 Feb 2023, 11:00 (Europe/Rome),
Lecture series: Seminar on Numerical Analysis,
Venue: Scuola Normale Superiore (Aula Volterra).
Address:
Piazza dei Cavalieri, 7 - 56126 Pisa
You can access the full event here: https://events.dm.unipi.it/e/158
Abstract
--------
Abstract:For the first time, a method has recently become available for fast computation of near-best rational approximations on arbitrary sets in the real line or complex plane: the AAA algorithm (Nakatsukasa-Sete-T. 2018). We will present the algorithm and then demonstrate a number of applications, includingdetection of singularities, model order reduction, analytic continuation, functions of matrices, nonlinear eigenvalue problems, interpolation of equispaced data, smooth extension of multivariate real functions, extrapolation of ODE and PDE solutions into the complex plane, solution of Laplace problems, conformal mapping, Wiener-Hopf factorization.
--
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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
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.
--
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