Applied Math Seminar

Fall 2023

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

• Nov

  30
• Machine Learning for Earth System Prediction and Predictability

  Maria Molina

  UMD Atmospheric Sciences

  Time: 12:00 PM

  View Abstract

  Across the broader scientific community, rapid advances in machine learning, and deep learning in particular, have inspired researchers to use these tools to enable science advances that previously would have been unattainable. The appeal in machine learning usage stems in part from the ability of machine learning to model complex nonlinear systems, and in part from recent algorithmic and computational advances that have improved and accelerated deep learning model training. Meanwhile, skillful prediction of the Earth system beyond two weeks remains difficult, particularly for precipitation. It is generally agreed that predictability stemming from atmospheric initial conditions is substantially reduced beyond two weeks and that predictability from the ocean generally does not offer added predictability until a forecast trajectory reaches the seasonal timescale. Imperfect initial conditions and model systematic errors also contribute to the difficulty of deterministic initialized forecasts. Ensemble forecasting has helped assess forecast spread in relation to initial condition errors, but the high cost of running global initialized forecasts precludes the creation of many ensemble members. These challenges motivate the use of machine learning and deep learning methods for prediction and predictability beyond a lead time of two weeks. Various approaches using machine learning for Earth system prediction and predictability will be highlighted: (1) a study using unsupervised learning to assess the representation of North American weather regimes in an initialized prediction system, (2) a machine learning-based assessment of how different components of the Earth system can vary in predictability contributions seasonally, and (3) a bias correction post-processing deep learning approach to initialized forecasts.

• Nov

  09
• Numerical methods for hydrodynamics at small scales

  Sean Carney

  George Mason University Mathematics

  Time: 12:00 PM

  View Abstract

  Biological cells, battery science, and microfluidic devices all feature sub-micron ($10^{-6}$ m) scale fluid dynamics. At these scales, the effects of viscosity, chemical reactions, surface tension, and electrostatic interactions can be dominant, while inertial forces that drive typical atmospheric and aerodynamic flows are relatively unimportant. At even smaller, nanometer ($10^{-9}$ m) length scales, it becomes critical to additionally account for thermal fluctuations that arise from the discrete, atomistic nature of fluid mixtures. It is a significant challenge to develop mathematical models that faithfully capture the physics of such small-scale fluid systems without resorting to fully discrete simulations (such as molecular dynamics) that are computationally intractable. The resulting systems of equations are usually stiff, nonlinearly coupled, and stochastic, and hence developing accurate and efficient numerical methods for their simulation is a great challenge as well. In this talk I will describe my previous work in this area, as well as ongoing work to develop a machine learning surrogate to accelerate hybrid particle-continuum models of complex fluids.

• Nov

  02
• Theoretical and Applied Naval Research in Mathematics

  Caroline Hills

  University of Notre Dame Applied Mathematics

  Time: 12:00 PM

  View Abstract

  In order to keep an edge over adversaries, the Navy is constantly researching new methodology to utilize in future projects or implement into existing technology. Two examples are the data compression algorithm Dynamic Mode Decomposition and the trajectory follower algorithm Model Predictive Control. This talk will discuss the mathematics behind these two methods as well as their benefit to the Navy’s mission. This work was supported by the Office of Naval Research through the Naval Research Enterprise Internship Program and the Naval Air Warfare Center Weapons Division in China Lake, California.

• Oct

  26
• Reversals of the large-scale circulation in thermal convection

  Nick Moore

  Colgate University Mathematics

  Time: 12:00 PM

  View Abstract

  The large-scale circulation (LSC) associated with thermal convection is known to spontaneously reverse direction. In the atmosphere, reversals can result in a sudden change in wind direction, while in the liquid core, reversals may play a role in magnetic dipole shifts. We examine LSC reversals within the context of thermal convection in an annular domain. Through comparison with direct numerical simulations, we show that a low-dimensional dynamical system derived systematically from Galerkin truncation of the governing equations accurately describes a sequence of parameter bifurcations, including the onset of circulatory flow, the appearance of chaotic LSC reversals, and finally a high-Rayleigh-number state of periodic LSC reversals with small-scale turbulence. When cast in terms of the fluid’s angular momentum and center of mass, the model reveals equivalence to a pendulum system with driving term that raises the center of mass above the fulcrum. It is the competition between driving, restoring, and damping that leads to the range of convective states. This physical picture yields accurate predictions for the frequency of regular LSC reversals in the high Rayleigh-number limit and offers a transparent mechanism for reversals.

• Oct

  19
• Local or Boundary Data Assimilation via Control Methods for Dissipative PDE Systems

  Rasika Mahawattege

  UMBC Mathematics

  Time: 12:00 PM

  View Abstract

  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

  Time: 12:00 PM

  View Abstract

  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

  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.