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Math Colloquium - Anders Hansen - Jan 28
by Francesco Tudisco 28 Jan '21

28 Jan '21

Dear all, * *the next GSSI Math Colloquium will be held on *Thursday January 28 *at***3pm* (Italian time). The speaker is Anders Hansen, <http://www.damtp.cam.ac.uk/research/afha/anders/> with a lecture connecting computational mathematics with deep learning and AI. More details below. Anders Hansen is Associate Professor at University of Cambridge, where he leads the Applied Functional and Harmonic Analysis group, and Full Professor of Mathematics at the University of Oslo. To attend the talk please use to the following *Zoom link*: https://us02web.zoom.us/j/84038062394 Please feel free to distribute this announcement as you see fit. Looking forward to seeing you all on Thursday! Paolo Antonelli, Stefano Marchesani, Francesco Tudisco and Francesco Viola --------------------- Title: On the foundations of computational mathematics, Smale's 18th problem and the potential limits of AI Abstract: There is a profound optimism on the impact of deep learning (DL) and AI in the sciences with Geoffrey Hinton concluding that 'They should stop training radiologists now'. However, DL has an Achilles heel: it is universally unstable so that small changes in the initial data can lead to large errors in the final result. This has been documented in a wide variety of applications. Paradoxically, the existence of stable neural networks for these applications is guaranteed by the celebrated Universal Approximation Theorem, however, the stable neural networks are never computed by the current training approaches. We will address this problem and the potential limitations of AI from a foundations point of view. Indeed, the current situation in AI is comparable to the situation in mathematics in the early 20th century, when David Hilbert’s optimism (typically reflected in his 10th problem) suggested no limitations to what mathematics could prove and no restrictions on what computers could compute. Hilbert’s optimism was turned upside down by Goedel and Turing, who established limitations on what mathematics can prove and which problems computers can solve (however, without limiting the impact of mathematics and computer science). We predict a similar outcome for modern AI and DL, where the limitations of AI (the main topic of Smale’s 18th problem) will be established through the foundations of computational mathematics. We sketch the beginning of such a program by demonstrating how there exist neural networks approximating classical mappings in scientific computing, however, no algorithm (even randomised) can compute such a network to even 1-digit accuracy (with probability better than 1/2). We will also show how instability is inherit in the methodology of DL demonstrating that there is no easy remedy, given the current methodology. Finally, we will demonstrate basic examples in inverse problems where there exists (untrained) neural networks that can easily compute a solution to the problem, however, the current DL techniques will need 10^80 data points in the training set to get even 1% success rate. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/b3099d6a-bcef-2052-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Postdoc Position, Krylov Methods, Charles Univ, Czech Rep
by Federico Poloni 25 Jan '21

25 Jan '21

Buongiorno, inoltro questo annuncio, che può essere di interesse per qualche iscritto alla lista. **Postdoc Position, Krylov Methods, Charles Univ, Czech Rep** A postdoc position is available within the framework of the Primus Research Programme "A Lanczos-like Method for the Time-Ordered Exponential" at the Faculty of Mathematics and Physics, Charles University, Prague. The appointment period is one year, with the possibility of extension. The postdoc will start before the end of 2021. The start date is negotiable. We are looking for candidates with a strong background in numerical linear algebra. In particular, we seek applicants with expertise in matrix function approximation and Krylov subspace methods. The applicant must hold a Ph.D. degree by the start date. Application deadline: March 15, 2021. More information and application instructions: https://www.starlanczos.cz/open-positions <https://www.starlanczos.cz/open-positions> -- --federico poloni Dipartimento di Informatica, Università di Pisa https://www.di.unipi.it/~fpoloni/ tel:+39-050-2213143

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NEPA Seminar (D. Bini)
by Leonardo Robol 15 Jan '21

15 Jan '21

Dear all, on January 19, 3 pm, Dario Bini will give a talk on "Solving Structured Matrix Equations Encountered in the Analysis of Stochastic Processes". The talk is part of the NEPA seminar series, and many more talks will take place in the next weeks. Participation is free, but a registration is required to obtain the Zoom link [1]. [1] https://sites.google.com/unisa.it/nepaseminars Best wishes, -- Leonardo.

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[NOMADS] Seminar - Gianluca Ceruti - Today at 17:00
by Francesco Tudisco 13 Jan '21

13 Jan '21

Good morning everyone, This is just a gentle reminder about today's seminar "Numerical integrators for dynamical low-rank approximation" by Gianluca Ceruti (Uni Tuebingen). Abstract below. The seminar is at 17:00 (CET). To attend please use the zoom link: https://us02web.zoom.us/j/82131676880 Hope to see you there! Francesco and Nicola ----------- Gianluca Ceruti <https://na.uni-tuebingen.de/~ceruti/> - University of Tuebingen Numerical integrators for dynamical low-rank approximation Discretization of time-dependent high-dimensional PDEs suffers of an undesired effect, known as 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, together with efficient numerical integrators, we present a recently developed approach: dynamical low-rank approximation. Dynamical low-rank approximation for matrices will be firstly presented, and a numerical integrator with two remarkable properties will be introduced: the matrix projector splitting integrator. Based upon this numerical integrator, we will 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. To conclude, via a novel compact formulation of the Tucker integrator, we will 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, but not only restricted to, by Tensor Trains. This seminar is based upon a joint work with Ch. Lubich and H. Walach. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/46a4a726-fee9-9f0b-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[NOMADS] Seminar - Gianluca Ceruti - Jan 13 at 17:00
by Francesco Tudisco 11 Jan '21

11 Jan '21

Dear all, We hope you all had joyful holidays and wish you all a great start for the new year! We are ready to start with this year's NOMADS seminar at GSSI and would like to invite you to this week's talk. The seminar will be given on Wednesday January 13 at 17:00 (CET) by Gianluca Ceruti from University of Tuebingen. Title, abstract and zoom link are below. Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/ Please feel free to distribute this announcement as you see fit. Hope to see you all on Wednesday! Francesco and Nicola ================================ Speaker: Gianluca Ceruti, University of Tuebingen https://na.uni-tuebingen.de/~ceruti/ Zoom link: https://us02web.zoom.us/j/82131676880 Numerical integrators for dynamical low-rank approximation Discretization of time-dependent high-dimensional PDEs suffers of an undesired effect, known as 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, together with efficient numerical integrators, we present a recently developed approach: dynamical low-rank approximation. Dynamical low-rank approximation for matrices will be firstly presented, and a numerical integrator with two remarkable properties will be introduced: the matrix projector splitting integrator. Based upon this numerical integrator, we will 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. To conclude, via a novel compact formulation of the Tucker integrator, we will 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, but not only restricted to, by Tensor Trains. This seminar is based upon a joint work with Ch. Lubich and H. Walach. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/CAO2_FW%3DqD1z%3D9V…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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[NOMADS] Seminar - Alexander Viguerie - Dec 16 at 17:00
by Francesco Tudisco 16 Dec '20

16 Dec '20

Dear all, You are all invited to this week's NOMADS seminar at GSSI. The seminar will be given on *Wednesday December 16 at 17:00* (CET) by *Alexander Viguerie* from GSSI. Title, abstract and zoom link are below. This is the last seminar of 2020 and we will then be back on Jan 13, 2021. Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/ Please feel free to distribute this announcement as you see fit. Hope to see you all on Wednesday! Francesco and Nicola ================================================== Zoom link: https://us02web.zoom.us/j/89492628943 Speaker: Alexander Viguerie <https://www.gssi.it/people/post-doc/post-doc-maths/item/11289-viguerie-alex> Title: Efficient, stable, and reliable solvers for the Steady Incompressible Navier-Stokes equations: application to Computational Hemodynamics. Abstract: Over the past several years, computational fluid dynamics (CFD) simulations have become increasingly popular as a clinical tool for cardiologists at the patient-specific level. The use of CFD in this area poses several challenges. The clinical setting places heavy restrictions on both computational time and power. Simulation results are usually desired within minutes and are usually run on standard computers. For these reasons, steady-state Navier-Stokes simulations are usually preferred, as they can be completed in a fraction of the time required to run an unsteady computation. However, in many respects the steady problem is more difficult than the unsteady one, particularly in regards to solving the associated linear and nonlinear systems. Additionally, boundary data for patient-specific problems is often missing, incomplete, or unreliable. This makes the determination of a useful model challenging, as it requires the generation of reliable boundary data without introducing heavy computational costs. This seminar will address these challenges, as well as some others, and introduce new techniques for workarounds. Results from patient-specific cases will be presented and discussed. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/54b94f9a-5840-e31c-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Seminario di Des Higham
by Dario A. Bini 04 Dec '20

04 Dec '20

Buongiorno, vi informo che oggi alle 15:00 Desmond Higham (University of Edinburgh), presenterà un seminario dal titolo "/A Hierarchy of //Network Models Giving Bistability Under Triadic Closure/". L'abstract e' allegato. Per registrarsi e ricevere il link per partecipare via Zoom cliccare su https://sites.google.com/unisa.it/nepaseminars A presto, Dario --- Abstract: Triadic closure describes the tendency for new friendships to form between individuals who already have friends in common. It has been argued heuristically that the triadic closure effect can lead to bistability in the formation of large-scale social interaction networks. Here, depending on the initial state and the transient dynamics, the system may evolve towards either of two long-time states. In this work, we study a hierarchy of network evolution models that incorporate triadic closure, building on the work of Grindrod, Higham and Parsons [Internet Mathematics, 8, 2012, 402--423]. In a macroscale regime, we show rigorously that a bimodal steady state distribution is admitted. Computational simulations will be used to support the analysis. This is joint work work with Stefano Di Giovacchino (L'Aquila) and Kostas Zygalakis (Edinburgh).

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[NOMADS] Seminar - Martin Stoll - Today at 17:00
by Francesco Tudisco 02 Dec '20

02 Dec '20

Good morning everyone, This is just a gentle reminder about today's seminar "From PDEs to data science: an adventure with the graph Laplacian" by Martin Stoll (TU-Chemnitz). Abstract below. The seminar is at 17:00 (CET). To attend, please use the zoom link: https://us02web.zoom.us/j/81317396646 Hope to see you there! Francesco and Nicola ------ Martin Stoll <https://www.tu-chemnitz.de/mathematik/wire/prof.php>, TU-Chemnitz From PDEs to data science: an adventure with the graph Laplacian In this talk we briefly review some basic PDE models that are used to model phase separation in materials science. They have since become important tools in image processing and over the last years semi-supervised learning strategies could be implemented with these PDEs at the core. The main ingredient is the graph Laplacian that stems from a graph representation of the data. This matrix is large and typically dense. We illustrate some of its crucial features and show how to efficiently work with the graph Laplacian. In particular, we need some of its eigenvectors and for this the Lanczos process needs to be implemented efficiently. Here, we suggest the use of the NFFT method for evaluating the matrix vector products without even fully constructing the matrix. We illustrate the performance on several examples. — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/002e39cd-038e-e9cc-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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Seminar on 01/12 (Fabio Durastante)
by Leonardo Robol 01 Dec '20

01 Dec '20

Speaker: Fabio Durastante Affiliation: IAC-CNR (...that will soon become University of Pisa) Time: Tuesday, 01/12/2020, 16:00 Title: (Sparse) Linear Algebra at the Extreme Scales Sparse linear algebra is essential for a wide variety of scientific applications. The availability of highly parallel sparse solvers and preconditioners lies at the core of pretty much all multi-physics and multi-scale simulations. Technology is nowadays expanding to target exascale platforms. I am going to present some work on Algebraic Multigrid Preconditioners in which we try to face these challenges to make Exascale Computing possible. The talk will focus on one side on the theoretical aspects pertaining to the construction of the multigrid hierarchy for which the main novelty is the design and implementation of new parallel smoothers and a coarsening algorithm based on aggregation of unknowns employing weighted graph matching techniques. On the other, the talk also focuses on the libraries developed to cover the needs of having parallel BLAS feature for sparse matrices that are capable of running on machines with thousands of high-performance cores; and to discuss the advancements made by the new smoothers and coarsening algorithm as an improvement in terms of numerical scalability at low operator complexity over the algorithms available in previous releases of the package. I will present weak scalability results on two of the most powerful supercomputers in Europe, for linear systems with sizes up to O(10^10) unknowns for a benchmark Poisson problem, and strong scaling result for a wind-simulation benchmark problem. This is a joint work with P. D’Ambra, and S. Filippone. This work is supported by the EU under the Horizon 2020 Project Energy oriented Centre of Excellence: toward exascale for energy (EoCoE-II), Project ID: 824158 Meeting link: <https://hausdorff.dm.unipi.it/b/leo-xik-xu4>

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NOMADS seminar @GSSI - Wed 2 - Martin Stoll
by Francesco Tudisco 30 Nov '20

30 Nov '20

Dear all, You are all invited to this week's NOMADS seminar at GSSI. The seminar will be given by Martin Stoll from TU-Chemnitz (Germany). Title, abstract and zoom link are below. Further info about past and future meetings are available at the webpage: https://num-gssi.github.io/seminar/ Please feel free to distribute this announcement as you see fit. Hope to see you all on Wednesday! Francesco and Nicola ================================================== Title: From PDEs to data science: an adventure with the graph Laplacian Abstract: In this talk we briefly review some basic PDE models that are used to model phase separation in materials science. They have since become important tools in image processing and over the last years semi-supervised learning strategies could be implemented with these PDEs at the core. The main ingredient is the graph Laplacian that stems from a graph representation of the data. This matrix is large and typically dense. We illustrate some of its crucial features and show how to efficiently work with the graph Laplacian. In particular, we need some of its eigenvectors and for this the Lanczos process needs to be implemented efficiently. Here, we suggest the use of the NFFT method for evaluating the matrix vector products without even fully constructing the matrix. We illustrate the performance on several examples. Zoom: https://us02web.zoom.us/j/81317396646 — Francesco Tudisco Assistant Professor School of Mathematics GSSI Gran Sasso Science Institute Web: https://ftudisco.gitlab.io -- You received this message because you are subscribed to the Google Groups "nomads-list" group. To unsubscribe from this group and stop receiving emails from it, send an email to nomads-list+unsubscribe(a)gssi.it. To view this discussion on the web visit https://groups.google.com/a/gssi.it/d/msgid/nomads-list/c28372f5-7312-f490-…. For more options, visit https://groups.google.com/a/gssi.it/d/optout.

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