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Prossimi Eventi

  • ott 29 gio 2020

    MOX Colloquia
    Jan S. Hesthaven, Nonintrusive reduced order models using physics informed neural networks,  29-10-2020, ore 14:00 precise
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    • MOX Colloquia
    • Jan S. Hesthaven
    • Chair of Computational Mathematics and Simulation Science, EPFL, Lausanne, CH
    • Nonintrusive reduced order models using physics informed neural networks
    • Giovedì 29 ottobre 2020 alle ore 14:00 precise
    • Online seminar: https://mox.polimi.it/elenco-seminari/?id_evento=1979&t=763724
    • Abstract
      The development of reduced order models for complex applications, offering the promise for rapid and accurate evaluation of the output of complex models under parameterized variation, remains a very active research area. Applications are found in problems which require many evaluations, sampled over a potentially large parameter space, such as in optimization, control, uncertainty quantification, and in applications where a near real-time response is needed. However, many challenges remain unresolved to secure the flexibility, robustness, and efficiency needed for general large-scale applications, in particular for nonlinear and/or time-dependent problems.

      After giving a brief general introduction to projection based reduced order models, we discuss the use of artificial feedforward neural networks to enable the development of fast and accurate nonintrusive models for complex problems. We demonstrate that this approach offers substantial flexibility and robustness for general nonlinear problems and enables the development of fast reduced order models for complex applications.

      In the second part of the talk, we discuss how to use residual based neural networks in which knowledge of the governing equations is built into the network and show that this has advantages both for training and for the overall accuracy of the model.

      Time permitting, we finally discuss the use of reduced order models in the context of prediction, i.e. to estimate solutions in regions of the parameter beyond that of the initial training. With an emphasis on the Mori-Zwansig formulation for time-dependent problems, we discuss how to accurately account for the effect of the unresolved and truncated scales on the long term dynamics and show that accounting for these through a memory term significantly improves the predictive accuracy of the reduced order model.

      Contatto: alfio.quarteroni@polimi.it
    • Jan S. Hesthaven

      Jan S. Hesthaven

      After receiving his PhD in 1995 from the Technical University of Denmark, Professor Hesthaven joined Brown University, USA where he became Professor of Applied Mathematics in 2005. In 2013 he joined EPFL as Chair of Computational Mathematics and Simulation Science and since 2017 as Dean of the School of Basic Sciences. His research interests focus on the development, analysis, and application of high-order accurate methods for the solution of complex time-dependent problems, often requiring high-performance computing. A particular focus of his research has been on the development of computational methods for problems of linear and non-linear wave problems and the development of reduced basis methods, recently with an emphasis on combining traditional methods with machine learning and neural networks with broad applications, including structural health monitoring.

      He has received several awards for both his research and his teaching, and has published 4 monographs and more than 160 research papers. He is on the editorial board of 8 journals and serves as Editor-in-Chief of SIAM J. Scientific Computing.

      Homepage - https://www.epfl.ch/labs/mcss/
    • Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

  • nov 12 gio 2020

    MOX Colloquia
    Omar Gatthas, Parsimonious structure-exploiting deep neural network surrogates for bayesian inverse problems,  12-11-2020, ore 16:00 precise
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    • MOX Colloquia
    • Omar Gatthas
    • Oden Institute for Computational Science & Engineering, The University of Texas at Austin (USA)
    • Parsimonious structure-exploiting deep neural network surrogates for bayesian inverse problems
    • Giovedì 12 novembre 2020 alle ore 16:00 precise
    • Online seminar: https://mox.polimi.it/elenco-seminari/?id_evento=1984&t=763724
    • Abstract
      In an inverse problem, one seeks to infer unknown parameters or parameter fields from measurements or observations of the state of a natural or engineered system. Such problems are fundamental to many fields of science and engineering: often available models possess unknown or uncertain input parameters that must be inferred from experimental or observational data. The Bayesian framework for inverse problems accounts for uncertainty in the inferred parameters stemming from uncertainties in the observational data, the model, and any prior knowledge. Bayesian inverse problems (BIPs) governed by large-scale complex models in high parameter dimensions (such as nonlinear PDEs with uncertain infinite dimensional parameter fields) quickly become prohibitive, since the forward model must be solved numerous times---as many as millions---to characterize the uncertainty in the parameters.
      Efficient evaluation of the parameter-to-observable (p2o) map, definedby solution of the forward model, is the key to making BIPs tractable. Surrogate approximations of p2o maps have the potential to greatly accelerate BIP, provided that the p2o map can be accurately approximated using (far) fewer forward model solves than would be required for solving the BIP using the full p2o map. Unfortunately, constructing such surrogates presents significant challenges when the parameter dimension is high and the forward model is expensive. Deep neural networks (DNNs) have emerged as leading contenders for overcoming these challenges. We demonstrate that black box application of DNNs for problems with infinite dimensional parameter fields leads to poor results, particularly in the common situation when training data are limited due to the expense of the model. However, by constructing a network architecture that is adapted to the geometry
      and intrinsic low-dimensionality of the p2o map as revealed through adjoint PDEs, one can construct a "parsimonious" DNN surrogate with superior approximation properties with only limited training data.
      Application to an inverse problem in Antarctic ice sheet flow is discussed.
      This work is joint with Tom O'Leary-Roseberry, Peng Chen, Umberto Villa, and Nick Alger.

      Contact: alfio.quarteroni@polimi.it
    • Omar Gatthas

      Omar Gatthas

      Dr. Omar Ghattas is a Professor of Geological Sciences and Mechanical Engineering at the University of Texas at Austin. He is also the Director of the Center for Computational Geosciences and Optimization in the Oden Institute for Computational Engineering and Sciences and holds the John A. and Katherine G. Jackson Chair in Computational Geosciences. He is a member of the faculty in the Computational Science, Engineering, and Mathematics (CSEM) interdisciplinary PhD program in the Oden Institute, and holds courtesy appointments in Computer Science and Biomedical Engineering. He has general research interests in forward and inverse modeling, optimization, and uncertainty quantification of large-scale complex mechanical, geological, and biological systems. With collaborators, he received the ACM Gordon Bell Prize in 2003 (for Special Achievement) and again in 2015 (for Scalability), and was a finalist for the 2008, 2010, and 2012 Bell Prizes. He received the 2019 SIAM Computational Science & Engineering Best Paper Prize, and the 2019 SIAM Geosciences Career Prize. He is a Fellow of the Society for Industrial and Applied
      Mathematics (SIAM).
    • Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

  • dic 10 gio 2020

    MOX Colloquia
    Enrique Zuazua, Turnpike control and deep learning,  10-12-2020, ore 14:00 precise
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    • MOX Colloquia
    • Enrique Zuazua
    • University of Erlangen-Nuremberg
    • Turnpike control and deep learning
    • Giovedì 10 dicembre 2020 alle ore 14:00 precise
    • Online Seminar: https://mox.polimi.it/elenco-seminari/?id_evento=1982&t=763724
    • Abstract
      The tunrpike principle, ubiquitous in applications, asserts that in long time horizons optimal control strategies are nearly of a steady state nature. In this lecture we shall survey on some recent results on this topic and present some its consequences on deep supervised learning, and, in particular, in Residual Neural Networks. This lecture will be based in particular on recent joint work with C: Esteve, B. Geshkovski and D. Pighin.
      Affiliations:
      [1] Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
      [2] Fundación Deusto, Bilbao, Basque Country Spain
      [3] Universidad Autónoma de Madrid, Spain

      Contatto: alfio.quarteroni@polimi.it
    • Enrique Zuazua

      Enrique Zuazua

      Enrique Zuazua Iriondo (Eibar, Basque Country - Spain, 1961) dual PhD in Mathematics - University of the Basque Country & Université Pierre et Marie Curie, holds a Chair in Applied Analysis - Alexander von Humboldt Professorship at FAU- Friedrich-Alexander University, Erlangen-Nürnberg (Germany). He leads the research project "DyCon: Dynamic Control", funded by the ERC - European Research Council at Deusto Foundation, University of Deusto - Bilbao (Basque Country, Spain) and the Department of Mathematics, at UAM - Autonomous University of Madrid where he holds secondary appoints as Professor of Applied Mathematics (UAM) and Director of CCM - Chair of Computational Mathematics (Deusto). His fields of expertise in the area of Applied Mathematics cover topics related with Partial Differential Equations, Systems Control and Machine Learning, led to some fruitful collaboration in different industrial sectors such as the optimal shape design in aeronautics and the management of electrical and water distribution networks. With an important high impact on his work (h-index = 41), he has mentored a significant number of postdoctoral researchers and coached a wide network of Science managers.
      He holds a degree in Mathematics from the University of the Basque Country, and a dual PhD degree from the same university (1987) and the Université Pierre et Marie Curie, Paris (1988). In 1990 he became Professor of Applied Mathematics at the Complutense University of Madrid, to later move to UAM in 2001. He has been awarded the Euskadi (Basque Country) Prize for Science and Technology 2006 and the Spanish National Julio Rey Pastor Prize 2007 in Mathematics and Information and Communication Technology and the Advanced Grants by the European Research Council (ERC) NUMERIWAVES in 2010 and DyCon in 2016. He is an Honorary member of the of Academia Europaea and Jakiunde, the Basque Academy of Sciences, Letters and Humanities, Doctor Honoris Causa from the Université de Lorraine in France and Ambassador of the Friedrisch-Alexandre University in Erlangen-Nurenberg, Germany. He was an invited speaker at ICM2006 in the section on Control and Optimization. From 1999-2002 he was the first Scientific Manager of the Panel for Mathematics within the Spanish National Research Plan and from 2008-2012 he was the Founding Scientific Director of the BCAM - Basque Center for Applied Mathematics.
      He is also a member of the Scientific Council if a number of international research institutions such as the CERFACS in Toulouse, France and member of the Editorial Board in some of the leading journals in Applied Mathematics and Control Theory
    • Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

  • feb 18 gio 2021

    MOX Colloquia
    Ellen Kuhl, Modeling dementia,  18-02-2021, ore 14:00 precise
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    • MOX Colloquia
    • Ellen Kuhl
    • Stanford University
    • Modeling dementia
    • Giovedì 18 febbraio 2021 alle ore 14:00 precise
    • Online Seminar: https://mox.polimi.it/elenco-seminari/?id_evento=1981&t=763724
    • Abstract
      Neurodegeneration will undoubtedly become a major challenge in medicine and public health caused by demographic changes worldwide. More than 45 million people are living with dementia today and this number is expected to triple by 2050. Recent studies have reinforced the hypothesis that the prion paradigm, the templated growth and spreading of misfolded proteins, could help explain the progression of a variety of neurodegenerative disorders. However, our current understanding of prion-like growth and spreading is rather empirical. Here we show that a physics-based reaction-diffusion model can explain the growth and spreading of misfolded protein in a variety of neurodegenerative disorders. We combine the classical Fisher-Kolmogorov equation for population dynamics with anisotropic diffusion and simulate misfolding across representative sections of the human brain and across the brain as a whole. Our model correctly predicts amyloid-beta deposits and tau inclusions in Alzheimer's disease, alpha-synuclein inclusions in Parkinson's disease, and TDP-43 inclusions in amyotrophic lateral sclerosis. To reduce the computational complexity, we represent the brain through a connectivity-weighted Laplacian graph created from 418 brains of the Human Connectome Project. Our brain network model correctly predicts the key characteristic features of whole brain models at a fraction of their computational cost. Our results suggest that misfolded proteins in various neurodegenerative disorders grow and spread according to a universal law that follows the basic physical principles of nonlinear reaction and anisotropic diffusion. Our simulations can have important clinical implications, ranging from estimating the socioeconomic burden of neurodegeneration to designing clinical trials and pharmacological intervention.

      Contatto: alfio.quarteroni@polimi.it
    • Ellen Kuhl

      Ellen Kuhl

      Ellen Kuhl is the Robert Bosch Chair of Mechanical Engineering at Stanford University. She is a Professor of Mechanical Engineering and, by courtesy, Bioengineering. She received her PhD from the University of Stuttgart in 2000 and her Habilitation from the University of Kaiserslautern in 2004. Her area of expertise is Living Matter Physics, the design of theoretical and computational models to simulate and predict the behavior of living structures. Ellen has published more than 200 peer-reviewed journal articles and edited two books; she is an active reviewer for more than 20 journals at the interface of engineering and medicine and an editorial board member of seven international journals in her field. Ellen is the current Chair of the US National Committee on Biomechanics and a Member-Elect of the World Council of Biomechanics. She is a Fellow of the American Society of Mechanical Engineers and of the American Institute for Mechanical and Biological Engineering. She received the National Science Foundation Career Award in 2010, was selected as Midwest Mechanics Seminar Speaker in 2014, and received the Humboldt Research Award in 2016. Ellen is an All American triathlete on the Wattie Ink. Elite Team, a multiple Boston, Chicago, and New York marathon runner, and a Kona Ironman World Championship finisher.
    • Politecnico di Milano, Dipartimento di Matematica edificio 14, via Giuseppe Ponzio 31/P, 20133 Milano - Telefono: +39 02 2399 4505 - Fax: +39 02 2399 4568

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