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Mathematics Department

Applied Math Seminar

Fall 2016

All talks are from 12:00-1:00 p.m. in the Seminar Room, unless otherwise specified.

  • Dec
    02
  • Kevin McIlhany
    United States Naval Academy
  • Nov
    18
  • Stochastic Galerkin method for the steady state Navier-Stokes equations
    Bedrich Sousedik
    University of Maryland, Baltimore County

    View Abstract

    We study steady state Navier-Stokes equations in the context of stochastic finite element discretizations. We assume that the viscosity is given in terms of a generalized polynomial chaos (gPC) expansion. We formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and compare the results with that of stochastic collocation and Monte Carlo methods. We also propose a preconditioner for systems of equations solved in each step of the stochastic (Galerkin) nonlinear iteration and we demonstrate its effectiveness in a series of numerical experiments.
  • Nov
    04
  • The geometry of 3D flows and regularity of solutions of the 3D Navier-Stokes equations.
    Aseel Farhat
    University of Virginia

    View Abstract

    We show that smallness of solutions of the 3D Navier-Stokes equations in the Besov space $B^{-1}_{\infty, \infty}$ suffices to prevent a possible blow-up. In particular, it is revealed that the aforementioned condition implies a particular local spatial structure of the regions of intense velocity, namely, the structure of local volumetric sparseness on the scale comparable to the radius of spatial analyticity measured in $L^\infty$.
  • Oct
    28
  • Multiview representation learning
    Raman Arora
    Johns Hopskins University

    View Abstract

    Unsupervised learning of useful features, or representations, is one of the most basic challenges of machine learning. Unsupervised representation learning techniques capitalize on unlabeled data which is often cheap and abundant and sometimes virtually unlimited. The goal of these ubiquitous techniques is to learn a representation that reveals intrinsic low-dimensional structure in data, disentangles underlying factors of variation, and is useful across multiple tasks and domains. This talk will focus on multiview representation learning that uses multiple "views" of data to learn improved representations for each of the views. The views can be multiple measurement modalities (audio + video, text + images, tweets + friends network, transaction logs + credit history) but also different information extracted from the same source (words + context, document text + links). The different views often contain complementary information, and multiview representation learning methods can take advantage of this information to learn features that are useful for understanding the structure of the data and that are beneficial for downstream tasks. Multiple views can help by reducing noise (what is noise in one view is not in the other) or improving confidence (when one view is more confident than the other). In this talk, we will focus on novel methodology for multiview learning of representations (features) and applications to speech and language processing, social media analytics and computational healthcare.
  • Oct
    18
  • Imaging with intensity-only measurements
    Alexei Novikov
    Penn State University
    Time: 12:00 PM

    View Abstract

    Imaging requires the solution of complicated inverse problems where we aim to determine the medium parameters from the measurements of the reflections of probing signals. In optics and X-ray imaging it is often difficult, or impossible, to measure the phases received at the detectors, only the intensities are available for imaging. I will introduce this problem mathematically, and explain some approaches that arise in attempting to image with intensities. I will then show results from extensive numerical simulations.
  • Oct
    07
  • Modeling and data analysis of convectively coupled equatorial waves and the Madden-Julian oscillation
    Reed Ogrosky
    Virginia Commonwealth University

    View Abstract

    Rainfall and clouds, i.e. convection, in the tropics occur on many spatial and temporal scales. A significant portion of tropical rainfall that occurs on daily and weekly timescales can be attributed to convectively coupled equatorial waves, while much of the tropical rainfall that occurs on intraseasonal timescales can be attributed to the Madden-Julian oscillation (MJO). In this talk I will discuss methods for identifying these rainfall events in observational data that make use of PDE theories for the tropical atmosphere. These methods will also be used to compare model results with observations, and it will be shown that a recent model for the MJO is able to reproduce the intermittency, strength, and frequency of observed events. This is joint work with Sam Stechmann at the University of Wisconsin-Madison.
  • Sep
    29
  • James Wilson
    Jove Sciences, Inc
  • Sep
    23
  • Ocean and Coupled Data Assimilation
    Steve Penny
    University of Maryland College Park

    View Abstract

    An advanced hybrid ocean data assimilation system has been implemented at NCEP, which combines an Ensemble Kalman Filter with a 3D-Variational method to generate bias-corrected estimates of the ocean state. This system is currently transitioning into operations for ocean monitoring. This system will serve as the ocean DA component for NCEP's next-generation Climate Forecast System (CFSv3). In addition, we have developed new strongly coupled DA techniques that allow observations from each coupled Earth system domain to have an immediate impact on the analyses of the other domains. This approach has been shown to reduce biases and improve the accuracy of both ocean and atmospheric state estimates.
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