NumPI June 2023

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Fwd: [Random] (PMS)^2 talk - Cazzaniga - July 3 at 17.00
by Federico Poloni 27 Jun '23

27 Jun '23

Inoltro anche su questa lista, visto che l'argomento può essere interessante. Un saluto a tutti! Federico -------- Forwarded Message -------- Subject: [Random] (PMS)^2 talk - Cazzaniga - July 3 at 17.00 Date: Tue, 27 Jun 2023 15:48:24 +0200 From: Carlo Orrieri <carlo.orrieri(a)unipv.it> To: random(a)fields.dm.unipi.it Dear colleagues, We are happy to announce the following *hybrid - that is, in person with online streaming -* talk: Speaker: *Alberto Cazzaniga*** (Area Science Park) Title: What is the probability that a random symmetric tensor is close to rank-one? *Abstract*: We address the problem of estimating the probability that a real symmetric tensor is close to rank-one tensors, motivated by the many applications of low-rank approximation. We discuss how the question can be addressed by studying metric invariants of the real Veronese variety thanks to the Weyl's tube formula. We describe the role of the reach and the curvature coefficients with respect to the Bombieri-Weyl metric in obtaining an explicit estimate, and outline the main ideas employed to tackle their calculation. We conclude by discussing some asymptotic results for the case of rational normal curves. Based on joint work with A. Lerario and A. Rosana. Date and time: *Monday July 3, 17:00-18:00 (Rome time zone)* Place: Laboratorio didattico*, dipartimento di matematica dell’università di Pavia, via Ferrata 5, Pavia.* Entra nella riunione in Zoom https://us02web.zoom.us/j/81154155086?pwd=Rit2Ymd3eE1lUWIrc0ErQlRMcGNVdz09 <https://us02web.zoom.us/j/81154155086?pwd=Rit2Ymd3eE1lUWIrc0ErQlRMcGNVdz09> ID riunione: 811 5415 5086 Passcode: 317594 This talk is part of the *(PMS)^2: Pavia-Milano Seminar series on Probability and Mathematical Statistics* organized jointly by the universities Milano-Bicocca, Pavia, Milano-Politecnico. Participation is free and welcome! Best regards The organizers (Carlo Orrieri, Maurizia Rossi, Margherita Zanella)

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[Indico] Luca Saluzzi, A Tensor Gradient Cross for Hamilton-Jacobi-Bellman equations, 05/06/2023, 16:00 Europe/Rome
by leonardo.robol＠unipi.it 05 Jun '23

05 Jun '23

Title: A Tensor Gradient Cross for Hamilton-Jacobi-Bellman equations, Speaker(s): Luca Saluzzi, Scuola Normale Superiore, Pisa, Date and time: 5 Jun 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/199 Abstract -------- Hamilton-Jacobi-Bellman (HJB) equation plays a central role in optimal control and differential games, enabling the computation of robust controls in feedback form. The main disadvantage for this approach depends on the so-called curse of dimensionality, since the HJB equation and the dynamical system live in the same, possibly high dimensional, space. In this talk, I will present a data-driven method for approximating high-dimensional HJB equations based on tensor decompositions. The approach presented in this talk is based on the knowledge of the value function and its gradient on sample points and on a tensor train decomposition of the value function. The collection of the data will be derived by two possible techniques: Pontryagin Maximum Principle and State-Dependent Riccati Equations. The numerical experiments will demonstrate an at most linear complexity in the dimension and a better stability in presence of noise. Moreover, I will present an application to an agent-based model and a comparison with Deep Learning techniques. Finally, time permitting, I will consider the coupling of the proposed method with Model Order Reduction techniques and their application to boundary feedback control for the Navier-Stokes equations. -- Indico :: Email Notifier https://events.dm.unipi.it/e/199

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NumPI June 2023