Applied Math Seminar

Spring 2024

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

• Apr

  23
• Data Science: From Questions to Research

  Kyle Teller

  Salisbury University Mathematics

  Time: 12:00 PM

  View Abstract

  Data Science is a newer field of study that is gaining interest for many students. However, the novelty of the field can make it hard for students to figure out how to get started and understand what research looks like. In this talk we will define what data science is and how our program at Salisbury University runs. We will then go through some important terminology and look at the data science life cycle and its importance in working on a research project. We will explore how to start the data science life cycle and how the questions we ask impact how well we can do research. We will then end with a few examples of research questions and results from actual students.

• Apr

  19
• On Co-evolution of knowledge graph and large language models

  Duy Duong-Tran USNA

  USNA Mathematics

  Time: 12:00 PM

  View Abstract

  Large language models (LLMs - e.g., GPT, BERT, Gemini, LLaMa) have demonstrated strong capabilities across various tasks and applications. Recently, many chain-of-thought (CoT)-based methods have been proposed to further unleash the reasoning abilities of LLMs. While these LLMs show promising performance in many general applications, some recent studies expose their limitations in long-tail and domain specific knowledge, significantly hindering their adaptation in vertical fields such as biomedicine. Previous works have proposed various approaches to address this challenge. Existing methods can be roughly classified into three types: domain-specific LLMs training, retrieval augmented generation (RAG), and knowledge graph-equipped LLMs. However, the above-mentioned approaches still suffer from several limitations such as Efficiency & Scale, Data Quality & Availability. These challenges underscore the need for a more efficient, robust, and automatic framework to equip LLMs with domain-specific knowledge. In this paper, we focus on the Alzheimer’s Disease (AD)-related question answering (QA) by proposing a coevolutionary framework that leverages mutual benefits between LLMs and knowledge graphs. This is collaboration work with Tianlong Chen{MIT, Harvard} and {Shu Yang, Li Shen}{UPenn} among others.

• Apr

  05
• Small-mass diffusion approximation for systems of stochastic damped wave equations with variable damping

  Sandra Cerrai

  University of Maryland Mathematics

  Time: 12:00 PM

  View Abstract

  We consider systems of damped wave equations with a state-dependent damping coefficient and perturbed by a Gaussian multiplicative noise. Initially, we investigate their well-posedness, under quite general conditions on the friction. Subsequently, we study the validity of the so-called Smoluchowski-Kramers diffusion approximation. We show that, under more stringent conditions on the friction, in the small-mass limit the solution of the system of stochastic damped wave equations converges to the solution of a system of stochastic quasi-linear parabolic equations. In this convergence, an additional drift emerges as a result of the interaction between the noise and the state-dependent friction. The identification of this limit is achieved by using a suitable generalization of the classical method of perturbed test functions, tailored to the current infinite dimensional setting.

• Mar

  29
• Signal Processing Techniques in Data Science

  Mark Magsino

  USNA

  Time: 12:00 PM

  View Abstract

  The need for processing large amounts of data has given rise to the popular new interdisciplinary field of data science. Many of the mathematical techniques are derived from statistics, but other areas of mathematics also play a significant role in data science. In this talk, several techniques from signal processing and their applications to data science problems will be explored. Specifically, applications to dimensionality reduction, feature transformation, and data encoding with real-world examples will be discussed.

• Mar

  26
• Using the principles of computational mechanics to model microstructural solidification and residual stress in metal additive manufacturing

  Kirubel Teferra

  Navy Research Labs

  Time: 12:00 PM

  View Abstract

  Additive manufacturing (AM) promises to create lighter, more complex designs that are otherwise too difficult or expensive to build using traditional methods. In contrast to traditional methods, AM part fabrication consists of highly localized and rapid thermally-driven phase changes, giving rise to unique challenges in optimizing material performance. Specifically, the microstructural features of AM built parts have extremely complex morphology, defect structure, and residual stress distribution, which vastly differs from wrought processed counterparts. Further, the build parameters comprise a large design space over which an AM part can be built, leading to extreme variability in the quality of the built part in terms of material integrity and engineering performance. This presentation describes computational models developed to predict microstructural features of AM materials given build parameters in order to alleviate the burden of trial-by-error experimental testing. In particular, an implementation of the cellular automata finite element (CAFE) model has been developed that is capable of simulating large 3D solidified microstructures such that texture analysis and subsequent mechanical analysis over representative volume elements can be performed. Secondly, this model has been coupled with the Multiphysics Object Oriented Simulation Environment (MOOSE) in order to compute microstructure-resolved residual stress as a result of build parameters. The resulting model is a high fidelity representative volume element that enables computing the heterogeneous residual stress and strain distribution, including regions of high concentrations, and relating this response to microstructural features as well as build conditions. Following the formulation of the model, the model is validated against experimental data and numerical examples are presented that evaluate the effect of build parameters on the residual response.

• Mar

  22
• Scaling down the laws of thermodynamics

  Christopher Jarzynski

  University of Maryland-Mathematics

  Time: 12:00 PM

  View Abstract

  Thermodynamics provides a robust conceptual framework and set of laws that govern the exchange of energy and matter. Although these laws were originally articulated for macroscopic objects, nanoscale systems also exhibit “thermodynamic­-like” behavior – for instance, biomolecular motors convert chemical fuel into mechanical work, and single molecules exhibit hysteresis when manipulated using optical tweezers. To what extent can the laws of thermodynamics be scaled down to apply to individual microscopic systems, and what new features emerge at the nanoscale? I will describe some of the challenges and recent progress – both theoretical and experimental – associated with addressing these questions. Along the way, my talk will touch on non-equilibrium fluctuations, “violations” of the second law, the thermodynamic arrow of time, nanoscale feedback control, strong system-environment coupling, and quantum thermodynamics.