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Tuesday, Oct 23, 2018 from 3:30PM to 5PM | POB 6.304
Hosted by Karen Willcox
Sponsor: ICES Seminar
Numerical simulation of large-scale dynamical systems plays a crucial role in studying a great variety of complex physical phenomena. However, simulations in these large-scale settings present significant computational difficulties. Model reduction aims to resolve this computational burden by constructing simpler (reduced order) models, which are much easier and faster to simulate and yet accurately represent the original system. These simpler reduced order models can then serve as efficient surrogates for the original, replacing them, for example, in optimal control and design. In this talk, we will focus on systems theoretical methods for model reduction, with a special emphasis on interpolatory methods based on rational approximation. After reviewing the concept of interpolation in the setting of dynamical systems, we will discuss how to construct optimal interpolants. If time allows, we will also describe recent extensions to nonlinear dynamics. We will use various examples to illustrate the theoretical discussion.
Bio
Serkan Gugercin is a professor of Mathematics at Virginia Tech. He holds the the A.V. Morris Professorship and is a core faculty member in the Division of Computational Modeling and Data Analytics. In 1992, he received his B.S. degree in Electrical and Electronics Engineering from Middle East Technical University, Ankara, Turkey; and his M.S. and Ph.D. degrees in Electrical Engineering from Rice University, in 1999 and 2003, respectively. His primary research interests are model reduction, data-driven modeling, numerical linear algebra, approximation theory, and systems and control theory.
Dr. Gugercin received the Ralph Budd Award for Research in Engineering from Rice University in 2003 for the best doctoral thesis in the School of Engineering; Teaching Award from Jacobs University Bremen, in 2003; the National Science Foundation Early CAREER Award in Computational and Applied Mathematics in 2007; and the Alexander von Humboldt Research Fellowship in 2016. He is currently serving as an Associate Editor for SIAM Journal on Scientific Computing, and Systems and Control Letters.
Thursday, Oct 25, 2018 from 3:30PM to 5PM | POB 6.304
Hosted by Karen Willcox
Sponsor: ICES Seminar
Work with Sergey Dolgov, University of Bath, UK, Akwum Onwunta and Martin Stoll, Faculty of Mathematics, TU Chemnitz, Germany
We discuss optimization and control of unsteady partial differential equations (PDEs), where some coefficient of the PDE as well as the control may be uncertain. This may be due to the lack of knowledge about the exact physical parameters like material properties describing a real-world problem ("epistemic uncertainty") or the inability to apply a computed optimal control exactly in practice. Using a stochastic Galerkin space-time discretization of the optimality system resulting from such PDE-constrained optimization problems under uncertainty leads to large-scale linear or nonlinear systems of equations in saddle point form. Nonlinearity is treated witha Picard-type iteration in which linear saddle point systems have to be solved in each iteration step. Using data compression based on separation of variables and the tensor train (TT) format, we show how these large-scale indefinite and (non)symmetric systems that typically have $10^8$ to $10^{15}$ unknowns can be solved without the use of HPC technology. The key observation is that the unknown and the data can be well approximated in a new block TT format that reduces complexity by several orders of magnitude. As examples, we consider control and optimization problems for the linear heat equation, the unsteady Stokes and Stokes-Brinkman equations, as well as the incompressible unsteady Navier-Stokes equations. The talk reviews the results published in {BenOS16,BenDOS16} and provides new results for the Navier-Stokes case.
Bibliography
{BenOS16} P. Benner, A. Onwunta, M. Stoll, Block-diagonal preconditioning for optimal control problems constrained by {PDE}s with uncertain inputs, SIAM Journal on Matrix Analysis and Application, 37(2):491--518, 2016.
{BenDOS16} P. Benner, S. Dolgov, A. Onwunta, M. Stoll, Low-rank solvers for unsteady Stokes-Brinkman optimal control problem with random data,
Computer Methods in Applied Mechanics and Engineering, 304:26--54, 2016.
Bio
Peter Benner received the Diplom in mathematics from RWTH Aachen, Germany, in 1993. From 1993 to 1997, he worked on his Ph.D. at the University of Kansas, Lawrence, KS USA, and the TU Chemnitz-Zwickau, Germany, where he received the Ph.D. degree in February 1997. In 2001, he received the Habilitation in Mathematics from the University of Bremen, Germany, where he held an Assistant Professor position from 1997 to 2001. After spending a term as a Visiting Associate Professor at TU Hamburg-Harburg, Germany, he was a Lecturer in mathematics at TU Berlin 2001–2003. Since 2003, he has been a Professor for "Mathematics in Industry and Technology" at TU Chemnitz. In 2010, he was appointed as one of the four directors of the Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany. Since 2011, he has also been an Honorary Professor at the Otto-von-Guericke University of Magdeburg.
Benner's research interests are in the areas of scientific computing, numerical mathematics, systems theory, and optimal control. A particular emphasis has been on applying methods from numerical linear algebra and matrix theory in systems and control theory. Recent research focuses on numerical methods for optimal control of systems modeled by evolution equations (PDEs, DAEs, SPDEs), model order reduction, preconditioning in optimal control and UQ problems, and Krylov subspace methods for structured or quadratic eigenproblems. Research in all these areas is accompanied by the development of algorithms and mathematical software suitable for modern and high-performance computer architectures.
Friday, Nov 2, 2018 from 10AM to 11AM | POB 6.304
Hosted by Kendrick Shepherd and Max Bremer
Sponsor: ICES Seminar-Babuska Forum Series
The main distinctive feature of turbulent flows is scale separation. However defined and measured, the smallest fluid motions are orders of magnitude smaller than the largest ones, posing tremendous challenges to our understanding, simulation, and modeling of turbulence. In this talk I will explore the concept of scale separation as it affects and controls the growth of interfaces that separate reactants and products in turbulent reactive flows. Based on large scale simulations of the reactive Navier-Stokes equations, we show that the Reynolds number, which is a measure of scale separation, controls the overall rate of conversion by scaling the area of the interface’s surface.
Bio
Dr. Bisetti is an Assistant Professor in the Department of Aerospace Engineering and Engineering Mechanics at the University of Texas at Austin. He holds a Laurea in Mechanical Engineering from Politecnico di Milano, Italy. He received M.S.E and Ph.D. degrees from the Department of Mechanical Engineering at the University of Texas at Austin and the University of California at Berkeley in 2002 and 2007, respectively. Dr. Bisetti’s research interests are in fluid mechanics, reactive flows, turbulence, plasmas, high-performance computing, uncertainty quantification, and numerical methods.
Thursday, Nov 8, 2018 from 3:30PM to 5PM | POB 4.304
Important Update: NOTE Different LocationHosted by Tan Bui-Thanh
Sponsor: ICES Seminar
Dynamical systems with Hamiltonians changing in time can be studied by averaging over the fast oscillations, or by adiabatic approximation in the case of slowly changing dynamics. In both cases, the averaged dynamics is useful up to finite time only, given by the inverse of the small parameter.
I will describe a recently developed new approach, in which the averaging can be done on larger and larger time scales, in a way that gives rigorously controlled errors to all orders in the small parameter, and to arbitrary large time intervals. As such, it is a new way to derive and understand Nekhoroshev type theorems.
I then present applications: new proof of adiabatic theorems and scattering for time dependent potentials. Then I will present numerical scheme for dispersive wave equations with controlled errors to very large time scales (10^3-10^7).
Thursday, Nov 8, 2018 from 11AM to 12PM | POB 4.304
Important Update: NOTE: Different time/roomHosted by Ufuk Topcu
Sponsor: ICES Seminar
Semidefinite optimization is a type of convex optimization problems over the cone of positive semidefinite (PSD) matrices, and sum-of-squares (SOS) optimization is another type of convex optimization problems concerned with the cone of SOS polynomials. Both semidefinite and SOS optimization have found a wide range of applications, including control theory, fluid dynamics, machine learning, and power systems. In theory, they can be solved in polynomial time using interior-point methods. However, these methods are only practical for small- to medium-sized problem instances.
In this talk, I will introduce decomposition methods for semidefinite optimization and SOS optimization with chordal sparsity, which scale more favorably to large-scale problem instances. It is known that chordal decomposition allows one to equivalently decompose a PSD cone into a set of smaller and coupled cones. In the first part of this talk, I will apply this fact to reformulate a sparse ssemidefinite program (SDP) into an equivalent SDP with smaller PSD constraints. Then, I will discuss how operator-splitting methods can be used to solve the decomposed SDPs efficiently. The resulting algorithms have been implemented in the open-source solver CDCS. In the second part of this talk, I will extend the decomposition result on SDPs to SOS optimization with polynomial constraints. The relationship between the decomposition of SOS optimization and the DSOS/SDSOS techniques (Ahmadi and Majumdar, 2017) will be explored, revealing a practical way to bridge the gap between SOS optimization and DSOS/SDSOS optimization for sparse problem instances.
Bio
Yang Zheng received his B.E. and M.S. degrees from Tsinghua University, Beijing, China, in 2013 and 2015, respectively. He is currently working toward the Ph.D. degree under the supervision of Prof. Antonis Papachristodoulou in the Department of Engineering Science, University of Oxford, United Kingdom. His research interests include distributed control of dynamical system over networks, exploiting sparsity in large-scale semidefinite optimization and sum-of-squares (SOS) optimization, with applications to intelligent transportation systems. Mr. Zheng received the Best Student Paper Award at the 17th IEEE International Conference on Intelligent Transportation Systems in 2014, and the Best Paper Award at the 14th Intelligent Transportation Systems Asia-Pacific Forum in 2015. He is a recipient of the National Scholarship, Outstanding Graduate in Tsinghua University, and the Clarendon Scholarship at the University of Oxford. In 2018, he received the ABTA Doctoral Research Award in Engineering Science.
Tuesday, Nov 27, 2018 from 3:30PM to 5PM | POB 6.304
Hosted by Karen Willcox
Sponsor: ICES Seminar
This tutorial will focus on compressed sensing approaches to sparse polynomial approximation of complex functions in high dimensions. Of particular interest to the UQ community is the parameterized PDE setting, where the target function is smooth, characterized by a rapidly decaying orthonormal expansion, whose most important terms are captured by a lower (or downward closed) set. By exploiting this fact, we will present and analyze several procedures for exactly reconstructing a set of (jointly) sparse vectors, from incomplete measurements. These include novel weighted $\ell_1$ minimization, improved iterative hard thresholding, mixed convex relaxations, as well as nonconvex penalties. Theoretical recovery guarantees will also be presented based on improved bounds for the restricted isometry property, as well as unified null space properties that encompass all currently proposed nonconvex minimizations. Numerical examples are provided to support the theoretical results and demonstrate the computational efficiency of the described compressed sensing methods.
Tuesday, Feb 5, 2019 from 3:30PM to 5PM | POB 6.304
Important Update: NOTE: Title and Abstract ChangeHosted by Tan Bui-Thanh
Sponsor: ICES Seminar
In the framework of steady-state diffusion problems, we show how the ideas of static condensation and hybridization lead to the introduction of the hybridizable discontinuous Galerkin methods.
Bio
Professor Cockburn received his Ph.D from University of Chicago in 1986 under the direction of Jim Douglas, Jr. He has spent all his academic career at University of Minnesota where he is now Distinguished McKnight University Professor. His research interests include the development of Discontinuous Galerkin methods for nonlinear conservation laws, second-order elliptic problems, electro-magnetism, wave propagation and elasticity.