Past Events

Seminars are held Tuesdays and Thursdays in POB 6.304 from 3:30-5:00 pm, unless otherwise noted. Speakers include scientists, researchers, visiting scholars, potential faculty, and ICES/UT Faculty or staff. Everyone is welcome to attend. Refreshments are served at 3:15 pm.

Friday, Feb 9

  • Additional Information

    Hosted by Sriram Nagaraj and Federico Fuentes

    Sponsor: ICES Seminar-Babuska Forum Series

    Speaker: Thaleia Zariphopoulou

    Speaker Affiliation: Mathematics and IROM, Presidential Chair in Mathematics and V.F. Neuhaus Professor of Finance, UT Austin

  • Abstract

    In this talk, I will introduce a family of stochastic optimization problems under relative performance criteria, for agents having CARA or CRRA utilities and acting in a common time horizon in log-normal environments. I will present the explicit time-independent equilibrium strategies for both the finite population games and the corresponding mean field games, which are shown to be unique in the class of time-independent equilibria. I will also discuss extensions related to filtering and incomplete information, random horizons, and real-time learning of market dynamics.

    Bio
    Thaleia Zariphopoulou is the holder of the Presidential Chair of Mathematics and the V.F. Neuhaus Professorship of Finance at the University of Texas at Austin. Previously, she was the Laun Professor at the University of Wisconsin, Madison and from 2009-2012, the first holder of the Oxford-Man Chair in Quantitative Finance at the University of Oxford. Currently, she is also a Visiting Professor at the Mathematical Institute at Oxford University and a Visiting Member of the FDT Center for Intelligent Asset Management, Columbia University. Her area of expertise is financial mathematics, quantitative finance and stochastic optimization. She has published extensively in the areas of investments and valuation in incomplete markets, and introduced novel approaches to indifference valuation and dynamic risk preferences.

    She has served very actively the community of financial mathematics and quantitative finance. She sits on the editorial board of eleven academic journals and monograph series, and she is the Editor of the SIAM Series in Financial Mathematics. She has served in various prize committees and panels. She has also been the Vice-Chair (2007-2010) of the SIAG Activity Group in Financial Mathematics and Engineering, and has served as Vice-President (2004-2006) and President (2006-2008) of the Bachelier Finance Society. In 2012, she was elected SIAM Fellow and in 2014, she was an invited speaker at the International Congress of Mathematicians in Seoul.


Thursday, Feb 8

Integrative approach to develop novel low energy defibrillation methods

Thursday, Feb 8, 2018 from 3:30PM to 5PM | POB 6.304

  • Additional Information

    Hosted by George Biros and Michael Sacks

    Sponsor: ICES Seminar - Computational Medicine Series

    Speaker: Flavio Fenton

    Speaker Affiliation: School of Mines, Georgia Institute of Technology

  • Abstract

    In this talk, I will describe how we use mathematical methods from dynamical systems, experiments in whole hearts, and high-performance parallel computing in an integrative approach to investigate the mechanisms that initiate, perpetuate, and terminate electrically driven cardiac arrhythmias. In particular, I will describe some of the mechanisms that can initiate fibrillation such as period doubling bifurcations and then describe a control method we have developed to terminate arrhythmias based on synchronization that requires only 10% of the energy needed for conventional defibrillation. For this I will establish a relationship between the response of cardiac tissue to an electric field and the spatial distribution of heterogeneities due to the coronary vascular structure, and discuss how in response to a pulsed electric field E, these heterogeneities serve as nucleation sites for the generation of intramural electrical waves with a source density ρ(E) and a characteristic time constant τ for tissue excitation that obeys a power law. This allow us to develop numerical simulations for effective defibrillation that are then tested in vitro and finally in vivo under clinical conditions.

    Bio
    Flavio H Fenton currently works at the School of Physics, Georgia Institute of Technology. Professor Fenton works in excitable media, complex systems, and pattern formation, using a combined approach of theory, experiments, and computer simulations. The main areas of research are Experiments in complex systems, Mathematical modeling of complex systems, and High performance computing. The current project is 'computational cardiac dynamics.'

  • Multimedia

Tuesday, Feb 6

Pulse Reflection in a Random Waveguide with a Turning Point

Tuesday, Feb 6, 2018 from 1PM to 2PM | POB 6.304

  • Additional Information

    Hosted by Kui Ren and Irene Gamba

    Sponsor: ICES Seminar-Numerical Analysis Series

    Speaker: Liliana Borcea

    Speaker Affiliation: University of Michigan

  • Abstract

    Guided waves arise in a variety of applications like underwater acoustics, optics, the design of musical instruments, and so on. We present an analysis of wave propagation and reflection in an acoustic waveguide with random sound soft boundary and a turning point. The waveguide has slowly bending axis and variable cross section. The variation consists of a slow and monotone change of the width of the waveguide and small and rapid fluctuations of the boundary, on the scale of the wavelength. These fluctuations are modeled as random. The turning point is many wavelengths away from the source, which emits a pulse that propagates toward the turning point, where it is reflected. We consider a regime where scattering at the random boundary has a significant effect on the reflected pulse. We determine from first principles when this effect amounts to a deterministic pulse deformation. This is known as a pulse stabilization result. The reflected pulse shape is not the same as the emitted one. It is damped, due to scattering at the boundary, and is deformed by dispersion in the waveguide. An example of an application of this result is in inverse problems, where the travel time of reflected pulses at the turning points can be used to determine the geometry of the waveguide.


Friday, Feb 2

Reduced-order modeling of parametrized large-scale systems

Friday, Feb 2, 2018 from 10AM to 11AM | POB 6.304

  • Additional Information

    Hosted by Federico Fuentes and Sriram Nagaraj

    Sponsor: ICES Seminar-Babuska Forum Series

    Speaker: Tan Bui Thanh

    Speaker Affiliation: Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin

  • Abstract

    Most reduced-order modeling (aka model reduction) techniques employ a reduced-space basis on which the large-scale mathematical problem is projected to become a much smaller system whose solution can be obtained in a fraction of the cost of the original problem. The basis is usually formed as the span of a set of solutions of the large-scale system, which are computed for selected values (samples) of parameters and forcing inputs. In this talk, a basis idea behind reduced-order modeling will be presented and a connection to the fundamental mathematical tools such as Fourier expansion and Karhunen-Loeve expansion will be highlighted. The important connection with compressive sensing will be also outlined. For problems where canonical bases are not efficient, adaptive/empirical bases are necessary. To that end, the proper orthogonal decomposition (POD) method will be presented as an effective tool. The relationship between POD, PCA (principle component analysis), and SVD (singular value decomposition) will be outlined. Various successful applications to complex problems in science and engineering will be shown to demonstrate the effectiveness of reduced-order models towards real time simulations.

    If time permits, challenging topics such as how to find the "best" reduced basis and how to construct reduced models for nonlinear problems will be discussed.

    Bio
    Tan Bui received his PhD in 2007 in computational fluid dynamics from the Department of Aeronautics and Astronautics at MIT. He joined ICES as a postdoc in 2008, and became a faculty in the Department of Aerospace Engineering and Engineering Mechanics, UT Austin, in 2013. His research in computational mechanics include: Inverse problem, uncertainty quantification, optimization, and high-order finite element methods. His research has been supported by DOE, NSF, DTRA, AFOSR, KAUST, Exxon Mobil.


Friday, Feb 2

Multi-species kinetic and fluid models and applications

Friday, Feb 2, 2018 from 1PM to 2PM | POB 6.304

  • Additional Information

    Hosted by Irene Gamba and Kui Ren

    Sponsor: ICES Seminar-Numerical Analysis Series

    Speaker: Christian Klingenberg

    Speaker Affiliation: Wuerzburg University, Germany

  • Abstract

    We consider a multi component gas mixture. This mixture is modelled by a system of kinetic BGK equations. Consistency of the model is proven, also existence, uniqueness and the positivity of solutions. We can extend our model to an ES-BGK model and to polyatomic mixtures. By taking moments, this allows us to derive macroscopic two-species conservation laws. We present numerical simulations using an adaptive kinetic-fluid models for plasma simulations. This is joint work with Marlies Pirner (Wuerzburg University, Germany) and Gabriella Puppo (Universita Insubria, Italy).


Thursday, Feb 1

Analysis of Sheet-Like Anatomical Shapes Using Medial Representations

Thursday, Feb 1, 2018 from 3:30PM to 5PM | POB 6.304

  • Additional Information

    Hosted by Michael Sacks and George Biros

    Sponsor: ICES Seminar: Computational Medicine Seminar Series

    Speaker: Paul Yushkevitch

    Speaker Affiliation: Associate Professor, Penn Image Computing & Science Laboratory, University of Pennsylvania

  • Abstract

    Many structures in the human body are thin and flat, having what might be called a sheet-like shape. Interesting aspects of sheet-like shapes can be captured by the medial axis, a geometrical construct generated by thinning a shape until nothing but an infinitely thin skeleton remains. The medial axis captures the overall three-dimensional shape of sheet-like objects, while also giving rise to a well-formed definition of local thickness. I will discuss a set of computational modeling techniques that allow features derived from the medial axis to be used for statistical analysis of shape, such as for deriving the mean shape from a sample of anatomical objects, or characterizing the effects of disease on sheet-like organs. The key challenge addressed by these techniques is how to describe multiple exemplars of a shape in a consistent manner, such that point-wise correspondences between different exemplars’ medial axes can be found. I will present several applications of medial modeling in medical image analysis, including approaches for the segmentation, geometrical modeling, and statistical analysis of heart valves. Time permitting, I will present very recent work that uses related shape analysis techniques to solve complex groupwise image registration problems that arise in high-resolution ex vivo imaging.

    Bio
    Paul Yushkevich received his Ph.D. in Computer Science in 2003 from the University of North Carolina at Chapel Hill. After a postdoc in the Department of Radiology at the University of Pennsylvania, he joined the faculty there, and is currently Associate Professor. His research interests include statistical shape analysis, computational object representation, automatic image segmentation, groupwise image registration, and structure-specific analysis of anatomic, functional and diffusion-weighted MRI data; as well as application of these techniques to cross-sectional and longitudinal studies of brain and cardiac disorders. An area of particular interest is high-resolution ex vivo imaging and detailed characterization of the human medial temporal lobe, the seat of memory in the human brain and the site of earliest Alzheimer's disease pathology. He is active in the development of open-source image analysis software, such as ITK-SNAP, a 3D image segmentation tool that is used widely in the biomedical imaging community.

  • Multimedia

Thursday, Feb 1

Safe Autonomy via Stochastic Reachability

Thursday, Feb 1, 2018 from 10:30AM to 12PM | POB 4.304

  • Additional Information

    Hosted by Ufuk Topcu

    Sponsor: ICES Seminar

    Speaker: Abraham Vinod

    Speaker Affiliation: Department of Electrical and Computer Engineering, University of New Mexico

  • Abstract

    Deploying autonomy in expensive safety-critical or high-risk systems require guarantees of safety. Two major challenges in providing these assurances are the stochasticity and the high dimensionality of the system. Stochasticity may capture human actions, disturbance effects, and mitigate the inevitable limitations in mathematical models; and high-dimensionality is inevitable as model fidelity improves. The desired guarantee may be obtained by solving the stochastic reach-avoid problem, a stochastic optimal control problem with a multiplicative cost function. Existing approaches provide approximations and suffer from the curse of dimensionality. We propose scalable algorithms to under approximate the stochastic reach-avoid probability and the associated sets using convex optimization and Fourier analysis. Our approach is grid-free and recursion-free and enables verification of high-dimensional stochastic dynamical systems. We apply our method to problems in stochastic target capture using quadrotors and satellite rendezvous and docking.

    Bio:
    Abraham P. Vinod received the B.Tech. and the M.Tech degree in Electrical Engineering from Indian Institute of Technology, Madras in 2014. He is currently a Ph.D. candidate in the Department of Electrical and Computer Engineering at the University of New Mexico. His research interests are in the area of optimization and stochastic control, particularly stochastic reachability analysis. He was awarded Best Student Paper Award in the 2017 ACM Hybrid Systems: Computation and Control Conference for the use of Fourier transforms in stochastic reachability, the Prof. Achim Bopp Prize for Best Student Hardware Project for his M.Tech work on attitude estimation, and the Central Board of Secondary Education Merit Scholarship for his undergraduate studies.


Friday, Jan 26

Front capturing schemes for nonlinear PDEs with a free boundary limit

Friday, Jan 26, 2018 from 1PM to 2PM | POB 6.304

  • Additional Information

    Hosted by Kui Ren and Richard Tsai

    Sponsor: ICES Seminar-Numerical Analysis Series

    Speaker: Li Wang

    Speaker Affiliation: Department of Mathematics, SUNY Buffalo

  • Abstract

    Evolution in physical or biological systems often involves interplay between nonlinear interaction among the constituent “particles”, and convective or diffusive transport, which is driven by density dependent pressure. When pressure-density relationship becomes highly nonlinear, the evolution equation converges to a free boundary problem as a stiff limit. In terms of numerics, the nonlinearity and degeneracy bring great challenges, and there is lack of standard mechanism to capture the propagation of the front in the limit. In this talk, I will introduce a numerical scheme for tumor growth models based on a prediction-correction reformulation, which naturally connects to the free boundary problem in the discrete sense. As an alternative, I will present a variational method for a class of continuity equations (such as Keller-Segel model) using the gradient flow structure, which has built-in stability, positivity preservation and energy decreasing property, and serves as a good candidate in capturing the stiff pressure limit.


  • Additional Information

    Hosted by Federico Fuentes and Sriram Nagaraj

    Sponsor: ICES Seminar-Babuska Forum Series

    Speaker: Todd A. Oliver

    Speaker Affiliation: Institute for Computational Engineering and Sciences, The University of Texas at Austin

  • Abstract

    Computational simulations are commonly used to probe the physics of complex phenomena and to inform critical design and operational decisions for complex systems. Given these uses, it is essential that the software implementation of the models that form the basis of such simulations be correct and that the effects of numerical approximations are understood. Verification encompasses both of these activities. The process of assessing software correctness is code verification, while the process of assessing solution accuracy is solution verification. In this talk, we examine two tools aimed at enabling verification studies.

    The first tool is a software library for generating and using manufactured solutions: the MASA (Manufactured Analytical Solution Abstraction) library (https://github.com/manufactured-solutions/MASA). MASA serves as a centralized repository for manufactured solutions and accompanying source terms. It currently contains solutions for a number of equation sets, including the Euler, Navier-Stokes, and Reynolds-averaged Navier-Stokes equations. The library provides C, C++, Fortran, and python interfaces, enabling use across a wide range of scientific codes. Further, it provides automatic differentiation capabilities to ease the generation of new solutions. We will show examples of bugs discovered using MASA, describe how to incorporate MASA support into an existing software package, and discuss how to generate new manufactured solutions using MASA.

    The second tool aims to enable solution verification for statistics computed from simulations of chaotic systems, as encountered in large eddy or direct numerical simulation (DNS). In such simulations, due to the presence of non-trivial statistical error, standard techniques for estimating discretization error, such as Richardson extrapolation, fail or are unreliable. In this work, we develop an extension of Richardson extrapolation that accounts for the effects of sampling error. The result is a Bayesian inference problem in which the uncertain discretization error parameters are estimated given statistical results from simulations with varying resolution. The performance of the method is demonstrated on multiple problems, including DNS of channel flow.

    Bio
    Todd Oliver is a Research Scientist at the Center for Predictive Engineering and Computational Science within the Institute of Computational Engineering and Sciences at UT-Austin. He received his Ph.D. in Aerospace Engineering from MIT in 2008. He joined ICES at a Postdoctoral Researcher shortly after and has been at UT since that time. His research interests include uncertainty quantification, model inadequacy, and computational fluid dynamics.


  • Additional Information

    Hosted by Ufuk Topcu

    Sponsor: ICES Seminar

    Speaker: Mohammad Khalil

    Speaker Affiliation: Sandia National Laboratories, Livermore, California

  • Abstract

    Bayes’ theorem provides parameter estimates that blend prior knowledge of the system parameters with indirect observational data. Bayesian model selection utilizes such estimates in comparing the suitability of many plausible models using the so-called model evidence the probability that randomly selected parameters from the prior would generate the observed data. There are various approaches to prescribe the prior distribution depending on the level of knowledge of the modeler. Popular priors include diffuse priors Jeffrey’s priors conjugate priors and informative priors. The choice of prior distribution and associated parameters that parametrize such priors (called hyper-parameters) has a major impact on any Bayesian estimation procedure and subsequent model selection analysis.

    In the context of feature selection automatic relevance determination (ARD), aka sparse Bayesian learning, is an effective tool for pruning large numbers of irrelevant features leading to a sparse explanatory subset. It does so by regularizing the Bayesian inference solution space using a parameterized data-dependent prior distribution that effectively prunes away redundant or superfluous features. The hyper-parameter of each ARD prior explicitly represents the relevance of the corresponding model parameter. The hyper-parameters are estimated using the observational data by performing evidence maximization or type-II maximum likelihood. In the context of model selection ARD priors aid in finding the best model nested under the envisioned model. ARD provides a flexible Bayesian platform to find the optimal nested model by eliminating the need to propose candidate nested models and associated prior pdfs. Thus ARD priors effectively reduce the parameter space dimension of the inference procedure based on available observations.

    This talk will motivate the use of ARD priors in the context of physics-based Bayesian model selection. Results will be presented for an application to model selection of complex aeroelastic systems modeled by coupled nonlinear stochastic ordinary differential equations using noisy wind-tunnel experimental observations. The experiments consist of a NACA0012 airfoil undergoing limit cycle oscillation in the transitional Reynolds number regime. The parameter likelihood is computed by marginalizing over the posterior pdfs of the uncertain time-varying state vector which is obtained using non-linear filtering (extended Kalman filter). A brief intro into state estimation via filtering (Kalman-based and particle filters) will be presented, time-permitting.

    Bio:
    Mohammad Khalil is a Senior Member of the Technical Staff at Sandia National Laboratories, California in the Quantitative Modeling and Analysis department. He holds a B.Sc. in microbiology and Immunology and a B.Eng. in Computer and Electrical Engineering from McGill University, Canada, and M.Sc. and Ph.D. degrees in Civil and Environmental Engineering from Carleton University, Canada. He has more than 10 years of experience developing Bayesian inference algorithms for statistical model calibration, parameter estimation, and data assimilation, with applications in fluid-structure interaction, combustion modeling, nonlinear structural dynamics, wildfire forecasting, and time-series analysis.