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The U.S. Naval Academy
Mathematics Department

Applied Math Seminar

Fall 2023

All talks are from 12:00-1:00 p.m. in the Seminar Room CH351, unless otherwise specified.

  • Oct
    26
  • TBA
    Nick Moore
    Colgate University Mathematics
    Location: CH351
    Time: 12:00 PM

    View Abstract

    TBA
  • Oct
    19
  • Local or Boundary Data Assimilation via Control Methods for Dissipative PDE Systems
    Rasika Mahawattege
    UMBC Mathematics
    Location: CH351
    Time: 12:00 PM

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    This talk bridges the fields of data assimilation, boundary control, and Luenberger compensator theory for partial differential equations to enhance system estimation and control in the presence of "localized" observations. While data assimilation techniques have traditionally been employed to estimate the state variables of a system using a diverse range of interior observations, their integration with boundary control methods and Luenberger compensators introduces a powerful framework for real-time system monitoring and control. The proposed methodology combines the principles of data assimilation, which update system state estimates by assimilating boundary (or localized interior) measurements, with boundary control theory, which focuses on manipulating system behavior through boundary or spatially localized feedback. Such integration can be achieved through the design of a Luenberger compensator, a widely used tool in control theory, to simultaneously estimate the state and control input in the localized observation region.
  • Oct
    11
  • Analysis and computation of Tornado-like Vortices
    Reza Malek-Madani
    USNA Mathematics
    Location: CH351
    Time: 12:00 PM

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    I will describe what I know about how tornadoes have been modeled over the past few decades. In particular, I will concentrate on the experimental and numerical studies of Susanne Horn and Jonathan Aurnou at UCLA in 2018, and the recent approach introduced by Andrea Bertozzi.
  • Sep
    07
  • Optimization and Reduced Order Models for Digital Twins
    Harbir Antil
    George Mason University Mathematics
    Location: CH351
    Time: 12:00 PM

    View Abstract

    This talk begins by discussing the role of PDE-constrained optimization in the development of digital twins. In particular, applications to identify weaknesses in structures and aneurysms are considered. Next, we analyze a data-driven optimization problem constrained by Darcy’s law to design a permeability that achieves uniform flow properties despite having nonuniform geometries. We establish well-posedness of the problem, as well as differentiability, which enables the use of rapidly converging, derivative-based optimization methods. The second part of the talk will focus on an inexact adaptive and provably convergent semismooth Newton method for general purpose optimization problems. In particular, dynamic optimization problems, which are known to be highly expensive are the focus. A memory efficient reduced order modeling approach based on randomized matrix sketching is introduced. This is joint work with Dave Ruth and Nick Wood.

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