Direttore Vicario: Prof. Gabriele Grillo
Responsabile Gestionale: Dr.ssa Franca Di Censo


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Prossimi Seminari

  • Nonintrusive reduced order models using physics informed neural networks
    Jan S. Hesthaven, Chair of Computational Mathematics and Simulation Science, EPFL, Lausanne, CH
    giovedì 29 ottobre 2020 alle ore 14:00 precise, Online seminar:

Seminari Passati

  • Artificial Intelligence and Personalised Cardiac Modelling: Learning by Heart
    Maxime Sermesant, INRIA
    giovedì 17 settembre 2020 alle ore 14:00, Online seminar:
    Machine learning and biophysical modelling are very complementary approaches. The recent progress in computing power and available data makes it possible to develop accurate data-driven approaches for healthcare, while biophysical models offer a principled way to represent anatomy and physiology. In this talk, I will present research where we combine both methodologies in order to leverage their strengths. Different clinical applications in computational cardiology will be presented.
    This seminar is organized within the ERC-2016-ADG Research project iHEART - An Integrated Heart Model forthe simulation of the cardiac function, that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 740132).
  • Deep Learning meets Parametric Partial Differential Equations
    Gitta Kutyniok, Institute of Mathematics, Technische Universität Berlin (DE)
    giovedì 16 luglio 2020 alle ore 14:00, Online seminar:
    High-dimensional parametric partial differential equations (PDEs) appear in various contexts including control and optimization problems, inverse problems, risk assessment, and uncertainty quantification. In most such scenarios the set of all admissible solutions associated with the parameter space is inherently low dimensional. This fact forms the foundation for the reduced basis method.
    Recently, numerical experiments demonstrated the remarkable efficiency of using deep neural networks to solve parametric problems. In this talk, after an introduction into deep learning, we will present a theoretical justification for this class of approaches. More precisely, we will derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric PDEs. In fact, without any knowledge of its concrete shape, we use the inherent low-dimensionality of the solution manifold to obtain approximation rates which are significantly superior to those provided by classical approximation results. We use this low-dimensionality to guarantee the existence of a reduced basis. Then, for a large variety of parametric PDEs, we construct neural networks that yield approximations of the parametric maps not suffering from a curse of dimensionality and essentially only depending on the size of the reduced basis.
    Finally, we present a comprehensive numerical study of the effect of approximation-theoretical results for neural networks on practical learning problems in the context of parametric partial differential equations. These experiments strongly support the hypothesis that approximation-theoretical effects heavily influence the practical behavior of learning problems in numerical analysis.
  • Physics-Informed Neural Networks (PINNs): An alphabet of Algorithms for Diverse Applications
    George Karniadakis, Brown University (USA)
    giovedì 25 giugno 2020 alle ore 14:00 precise, Online seminar:
    We will present a new approach to develop a data-driven, learning-based framework for predicting outcomes of physical and biological systems and for discovering hidden physics from noisy data. We will introduce a deep learning approach based on neural networks (NNs) and generative adversarial networks (GANs). We also introduce new NNs that learn functionals and nonlinear operators from functions and corresponding responses for system identification. Unlike other approaches that rely on big data, here we “learn” from small data by exploiting the information provided by the physical conservation laws, which are used to obtain informative priors or regularize the neural networks. We will also make connections between Gauss Process Regression and NNs, and discuss the new powerful concept of meta-learning. We will demonstrate the power of PINNs for several inverse problems in fluid mechanics, solid mechanics and biomedicine including wake flows, shock tube problems, material characterization, brain aneurysms, etc, where traditional methods fail due to lack of boundary and initial conditions or material properties. There are many versions of PINNs, e.g., variational (VPINNs), stochastic (sPINNs), conservative (cPINNs), nonlocal (nPINNs), generalized (xPINNs), etc, and we will provide some highlights. In addition, we will present our recent theoretical results on the convergence and generation of PINNs.
  • Design and Health
    Stefano Capolongo , Politecnico di Milano
    mercoledì 18 marzo 2020 alle ore 12:15, aula B21
  • Comunicare la scienza: manuale di sopravvivenza
    Maurizio Melis , Giornalista scientifico
    mercoledì 11 marzo 2020 alle ore 12:15, aula B21
  • Bergman projections on pseudoconvex domains containing complex manifolds in their boundary
    Gian Maria Dall'Ara, School of Mathematics, University of Birmingham
    mercoledì 4 marzo 2020 alle ore 10:45, aula seminari - 3° piano
  • CANCELLED - this event has been cancelled
    Wolfgang Bangerth, Department of Mathematics, Campus Delivery, Fort Collins, CO, USA NUMETH-HPC
    venerdì 28 febbraio 2020 alle ore 14:00, Aula Saleri VI piano
  • Modeling and simulation of thermo-poroelastic processes in fractured geothermal reservoirs
    Eirik Keilegavlen, Department of Mathematics, University of Bergen, Norway
    giovedì 20 febbraio 2020 alle ore 11:30, Aula Saleri - VI piano
    We present a mathematical model for coupled thermo-hydro-mechanical processes in fractured porous media, motivated by applications to geothermal energy. The model is based on a mixed-dimensional representation of the host medium and fracture network. The dynamics in the host medium is governed by fully-coupled thermo-poroelasticity, while flow and energy transport can also take place in the fracture network. Fracture deformation, including opening and sliding, is modeled using techniques from contact mechanics. We present a finite volume approach for the mixed-dimensional model, combined with a primal-dual active set strategy for the contact problem.