Events
Department of Mathematics and Statistics
Texas Tech University
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
The Links–Gould (LG) polynomials are two-variable link invariants arising from the quantum supergroup $U_q(\mathfrak{sl}(2|1))$, exhibiting hybrid behavior between the Jones and Alexander polynomials. I will survey some recent results illustrating this theme.
The basic LG invariant provides a lower bound on the Seifert genus and this bound extends to its colored versions. It has been verified by Garoufalidis and Li that the 2-colored Links–Gould polynomial detects the genus for all 352.2 million prime knots with up to 19 crossings. We also prove a conjecture of Geer and Patureau-Mirand that the Links–Gould invariant admits a specialization to the Akutsu–Deguchi–Ohtsuki (ADO) invariant at a sixth root of unity. Finally, we establish analogs of Jones–Wenzl idempotents for LG and formulate an analog of the Fox conjecture, supported by computational evidence.
This is joint work, in various combinations, with Stavros Garoufalidis, Rinat Kashaev, Ben-Michael Kohli, Jiebo Song, Guillaume Tahar, and Emmanuel Wagner.
 | Thursday
Oct. 1
6:30 PM
Math 010
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| Mathematics Education
Math Circle
Burak Avsar
Mathematics and Statistics, Texas Tech University
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Outreach program for advanced middle and high school math studentsWe present our recent results on multi-scale reinforcement learning algorithms for mean field game and mean field control problems with applications to finance.
Zoom link: texastech.zoom.us/j/3067000354
Meeting ID: 306 700 0354
Passcode: TTUMF