March 2022 - NumPI - Mailing list — Dipartimento di Matematica, UniPI

Fwd: [Dipartimento.di] Seminar in Computational Mathematics - B.
by Federico Poloni 18 Mar '22

18 Mar '22

-------- Forwarded Message -------- Subject: [Dipartimento.di] Seminar in Computational Mathematics - B. Filipecki Date: Fri, 18 Mar 2022 13:40:32 +0100 From: Federico Poloni <federico.poloni(a)unipi.it> To: dipartimento(a)di.unipi.it Dear all, within the activities of the Computational Mathematics Lab, we are pleased to announce the following seminar. Title: Hierarchical Optimization of the Electrical Power Grid Speaker: Bartosz Filipecki, Department of Computer Science, University of Pisa Date/Time: Wednesday, 23 March 2022 17:00 Place: Aula Seminari Est, Dipartimento di Informatica Abstract: European electrical power networks operation is becoming more and more difficult due to increasing load and uncertainty associated with renewable energy sources. To address this problem, we consider a hierarchical approach to optimization of power grid operation. First, microgrid demand is aggregated to provide flexibility to the distribution system operator (DSO). At this stage, the optimal power flow problem (OPF) is solved in order to determine the flexibilities that can be made available to the transmission system operator (TSO). Afterwards, OPF is solved to determine the operation of the highest voltage grids, including additional constraints related to security and stability. The former provide protection against line failure, so that no blackout occurs. The latter make sure that the system does not deviate in the dynamic sense from the solution to the static OPF problem. The TSO level can also include Flexible Alternating-Current Transmission Systems Devices (FACTS). These provide us with advanced methods to control the power flow, but at a significant computational cost. After obtaining the solution, we propagate it back through the DSO level to the microgrids, which completes the framework. Everyone is welcome to attend, in person or on MS Teams: https://teams.microsoft.com/l/meetup-join/19%3ameeting_ZGE3ZDcyOTItOTViMS00… Mauro Passacantando Federico Poloni -- --Federico Poloni Dipartimento di Informatica, Università di Pisa https://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143 ______________________________________________ Dipartimento.di mailing list Dipartimento.di(a)listgateway.unipi.it http://listgateway.unipi.it/mailman/listinfo/dipartimento.di

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[Indico] [Event reminder] Grassmann extrapolation for
by leonardo.robol＠unipi.it 17 Mar '22

17 Mar '22

Please note that the event "Grassmann extrapolation for Born-Oppenheimer Molecular Dynamics" will start on 18 Mar 2022, 11:00 (Europe/Rome). It will take place at Dipartimento di Matematica (Aula Magna). You can access the full event here: https://indico.cs.dm.unipi.it/e/76 Description ----------- Born-Oppenheimer Molecular Dynamics (BOMD) is a powerful, yet very demanding technique in computational quantum chemistry. Performing a BOMD simulation require, for each time step, to compute the energy and forces for a quantum mechanical system, which can also be embedded in a classical environment. When Density Functional Theory is used as a quantum mechanical model, the most time-consuming step for each energy/forces evaluation is the solution to the non-linear eigenvalue problem that stems from the discretization of the Kohn-Sham equations. Limiting the number of iterations required to achieve a satisfactory convergence of the procedure is therefore paramount to reduce the cost - and therefore extend the applicability - of such simulations. The most important factor in reducing the number of iteration is starting from a good guess, usually in the form of a one-body reduced density matrix. In a BOMD simulation it is possible to extrapolate information from previous steps into a new guess, however, this is not straightforward due to the nonlinear constraints that the density matrix must satisfy. In this contribution, we address this issue by performing the extrapolation on the tangent plane to the Grassmann manifold where the density is defined, by mapping the manifold to its tangent plane with a locally bijective map, which allows us to perform a linear extrapolation and then map the result back to the manifold, ensuring thus that all the physical properties of the density matrix are correctly enforced. Preliminary benchmark calculations show that the strategy is general and robust, and that even when using a naive linear extrapolation we obtain a strategy that outperforms the current state-of-the-art methods. Streaming link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 -- Indico :: Email Notifier https://indico.cs.dm.unipi.it/e/76

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[Indico] [Event reminder] Grassmann extrapolation for
by leonardo.robol＠unipi.it 08 Mar '22

08 Mar '22

Please note that the event "Grassmann extrapolation for Born-Oppenheimer Molecular Dynamics" will start on 18 Mar 2022, 11:00 (Europe/Rome). It will take place at Dipartimento di Matematica (Aula Magna). You can access the full event here: https://indico.cs.dm.unipi.it/e/76 Description ----------- Born-Oppenheimer Molecular Dynamics (BOMD) is a powerful, yet very demanding technique in computational quantum chemistry. Performing a BOMD simulation require, for each time step, to compute the energy and forces for a quantum mechanical system, which can also be embedded in a classical environment. When Density Functional Theory is used as a quantum mechanical model, the most time-consuming step for each energy/forces evaluation is the solution to the non-linear eigenvalue problem that stems from the discretization of the Kohn-Sham equations. Limiting the number of iterations required to achieve a satisfactory convergence of the procedure is therefore paramount to reduce the cost - and therefore extend the applicability - of such simulations. The most important factor in reducing the number of iteration is starting from a good guess, usually in the form of a one-body reduced density matrix. In a BOMD simulation it is possible to extrapolate information from previous steps into a new guess, however, this is not straightforward due to the nonlinear constraints that the density matrix must satisfy. In this contribution, we address this issue by performing the extrapolation on the tangent plane to the Grassmann manifold where the density is defined, by mapping the manifold to its tangent plane with a locally bijective map, which allows us to perform a linear extrapolation and then map the result back to the manifold, ensuring thus that all the physical properties of the density matrix are correctly enforced. Preliminary benchmark calculations show that the strategy is general and robust, and that even when using a naive linear extrapolation we obtain a strategy that outperforms the current state-of-the-art methods. Streaming link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4 -- Indico :: Email Notifier https://indico.cs.dm.unipi.it/e/76

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Annunci di seminari NumPI
by Leonardo Robol 08 Mar '22

08 Mar '22

Cari tutti, d'ora in poi -ammesso che la cosa funzioni bene- useremo la piattaforma Indico per inviare gli annunci dei seminari sulla mailing list, dato che lo fa in automatico (reminder inclusi, cosa che io tendo a dimenticare piuttosto facilmente). A breve dovrebbe arrivarne uno. Il formato dell'annuncio sarà leggermente diverso rispetto al solito, ma si tratta sempre dei seminari NumPi. A presto, -- Leonardo.

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Seminar announcement
by Fabio Durastante 07 Mar '22

07 Mar '22

Speaker: Nicola Guglielmi Affiliation: Gran Sasso Science Institute Venue: Aula Volterra, Scuola Normale Superiore *Remark. *Il seminario si terrà in presenza. Chi fosse interessato a partecipare deve scrivere a classi(a)sns.it _entro le 9:00 di Lunedì __ __7 marzo 2022_ *Abstract. *Stability and robustness analysis of linear continuous and discrete dynamical systems is a vast and active interdisciplinary research area. Although the word stability is used in many different contexts, in this talk it is meant to indicate the broad spectrum of issues that arise in the analytical and numerical study of dynamical and control systems, especially in relation to qualitative information of the system under study. These issues result from the need to develop stable and reliable systems robustly preserving essential qualitative properties. The analysis of these features is often based on eigenvalue optimization or on pseudospectral measures of a certain matrix A, where the structure of A (e.g., sparse, Hamiltonian, nonnegative, Toeplitz, etc.) plays an important role. The main goal of this talk is to show how these structured distances can be approximated. The proposed method is a two-level iterative algorithm, where in an inner iteration a gradient flow drives perturbations to the original matrix of a fixed size into a minimum of a functional that depends on eigenvalues (and possibly eigenvectors), and in an outer iteration the perturbation size is optimized such that the functional reaches some target value (for example O). An interesting point - related to certain low-rank properties of extremizers - lies in the possibility of considering gradient flows on low-rank manifolds. The talk is mainly inspired by joint works with Christian Lubich (Tuebingen). Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4

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