Applied Mathematics and Machine Learning

Department of Mathematics and Statistics

Texas Tech University

Fall 2026

Since Fall 2018, the seminar provides a venue for researchers and students to present and discuss mathematical approaches for the investigation of challenging real-life problems. Topics range from pure mathematical subjects to applications. The seminar also aims to encourage students to develop their own research projects. We welcome all those who want to broaden their perspective on the mathematical methods used in contemporary research.

Send an e-mail to igtomas@ttu.edu if:
- You want to be notified about TTU's Applied Mathematics Seminar on a weekly basis.
- You are faculty or doctoral student willing to present.

Wednesday
Sep. 2
4 PM
Math 011

New, Transformative Methods of Nuclear Energy Production and Rocket Propulsion
Robert Duncan
Department of Physics & Astronomy, Texas Tech University

Abstract: I will discuss our current research within the Center for Emerging Energy Sciences in the Department of Physics and Astronomy at Texas Tech University. This research is leading us back to the dynamics of the superfluid transition driven away from equilibrium, so I will finish by discussing briefly our experimental work in dynamics critical phenomena near the superfluid transition, and its applications to such far-ranging topics as the new 3He supply chain for fusion energy and a new area of ‘experimental cosmology’.

When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this Direct Link that embeds meeting and ID and passcode.
- Choice #2: Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 949 9288 2213
* Passcode: Applied

Wednesday
Sep. 16
4 PM
Math 011

Dynamic Mems: Microfabrication, Mechanisms, and Motion
Tim Dallas
Electrical & Computer Engineering, Texas Tech University

Dynamic microelectromechanical systems (MEMS) use controlled mechanical motion at the microscale to perform useful functions. This talk will begin with an introduction to Dynamic MEMS, including basic device architectures, actuation mechanisms, scaling effects, and the fabrication approaches used to create movable structures at the microscale. The second part of the talk will present three examples of Dynamic MEMS. The Digital Micromirror Device (DMD) will provide a vivid example of a highly successful commercial MEMS technology based on the controlled motion of large arrays of microscopic mirrors. Devices fabricated using Sandia National Laboratories’ SUMMiT V surface-micromachining process will illustrate more complex planar micromechanisms, followed by recent work using two-photon polymerization with the Nanoscribe platform to create three-dimensional microstructures and mechanisms. Together, these examples show how advances in microfabrication have expanded the types of motion and mechanical functionality that can be realized at the microscale.

Tim Dallas, PhD is a Professor of Electrical and Computer Engineering at Texas Tech University. Dr. Dallas’ research includes developing MEMS-based education and research tools, innovative solar racking techniques, and UAS-enabled transplant organ transport. In 2008, he established Class on a Chip, Inc. to commercialize an array of micro-experimental devices for use in engineering, physics, and MEMS classes. He works with colleagues in the College of Education on the development of an education portal, Classroom on a Chip, and the Solar Powered Digital Classroom in a Box (SPDCB). The SPDCB technology has been deployed to off-the-grid locations in Africa, Asia, and Central America. Each summer, he teaches a class entitled Solar Energy, which includes a solar energy system design project. He has also established classes in entrepreneurship and Unmanned Aircraft Systems (UAS). Prof. Dallas serves as a mentor for the TTU Innovation Hub’s accelerator program and other startup programs. Dr. Dallas has served as the principal investigator for three National Science Foundation sponsored Scholarships in STEM (S-STEM) projects, three Research Experience for Undergraduates Sites, a Course Curriculum and Laboratory Improvement (CCLI) project, and a number of other research and equipment grants from NSF. He has also been funded by the Keck and Welch Foundations for MEMS-based education technologies. He serves as an Associate Dean for the Graduate School and has served as an Associate Editor for IEEE Transactions on Education. He is a Senior Member of IEEE and a Fellow of TTU’s STEM-CORE.

When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 949 9288 2213
* Passcode: Applied

Wednesday
Sep. 23
4 PM
Math 011

Simultaneous reconstruction of natural death, recruitment, and initial maturity rates in a diffusive McKendrick-von Foerster system with multiple-age structure
Adam Umar
Department of Mathematics & Statistics, Texas Tech University

Abstract: In population dynamics, the diffusive McKendrick-von Foerster system plays a vital role in modeling the evolution of structured populations comprising both immature and mature individuals. In this work, we propose a numerical method to address a multiple-coefficient inverse problem for this system. In particular, our method is aimed to simultaneously reconstruct four coefficients: the natural death rates of both population groups, the recruitment rate, and the initial distribution of mature individuals. Our inverse approach is based on some special transformations and the use of the Fourier-Klibanov basis, which together yield a nonlinear bi-directional ODE-PDE system. This system is then approximated using the variational quasi-reversibility method, which is designed using a suitable pair of perturbing and stabilized operators, along with associated conditional energy estimates. In this work, we prove that the approximation of the immature individuals converges at a Lipschitz rate, whereas the approximation of the mature ones converges at a Hölder rate. The latter convergence rate represents a significant extension of earlier studies on the variational quasi-reversibility inversion. Finally, some numerical examples are presented to show how the proposed inversion works.

When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this Direct Link that embeds meeting ID and passcode.
- Choice #2: With this link, Join Meeting, you will then need to input the ID and Passcode by hand:
* Meeting ID: 949 9288 2213
* Passcode: Applied

Wednesday
Sep. 30
4 PM
online

In-span learning: adapting reduced-order models using their own predictions
Amirpasha Kamal Hedayat
Department of Aerospace Engineering, University of Michigan, Ann Arbor

Abstract: Reduced-order models (ROMs) are often trained on a limited range of system behavior and can lose accuracy when dynamics evolve beyond training distribution. Adaptive ROMs try to address this, typically relying on new high-fidelity information to correct their reduced representation during online prediction. We introduce a new adaptive paradigm, called in-span learning, showing that a model’s own predictions contain useful adaptive information that can complement the information obtained from external high-fidelity sources. Because these predictions lie entirely in the current trial subspace, they cannot introduce new directions. Nevertheless, when streamed through an incremental SVD with forgetting, they reweight and rotate the basis within that subspace, creating a trajectoryinformed spectral preconditioner that better prepares the model to absorb future high-fidelity information. We expose this mechanism on a threedimensional spiral model and demonstrate its effectiveness in long-horizon prediction tasks for stiff and complex dynamical systems. Across these problems, in-span updates considerably improve predictive accuracy without additional high-fidelity solves. More broadly, in-span learning can be viewed as a dynamical-systems analogue of in-context learning, in which an evolving model reorganizes its representation at inference time using context generated by its own trajectory.

This is a collaborative effort with Laura Balzano (Electrical Engineering and Computer Science) and Karthik Duraisamy (Aerospace Engineering), both from the University of Michigan, Ann Arbor.

When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this Direct Link that embeds meeting ID and passcode.
- Choice #2: use this link, Join Meeting, then you must input the ID and Passcode by hand:
* Meeting ID: 949 9288 2213
* Passcode: Applied