Title: Adaptive Subspace Tracking and Inverse Design for High-Dimensional Electromagnetics

Date: Thursday, November 19, 2026

Time: 2:00 PM EST

Location:

In person: CODA C1015 (Vinings)

Virtual: https://teams.microsoft.com/meet/2420063874953443?p=zH2mKpDkLDTZuzvr7Q

Alex Saad-Falcon

Machine Learning PhD Student

School of Electrical and Computer Engineering

Georgia Institute of Technology

Committee

1. Dr. Justin Romberg (Advisor), School of Electrical and Computer Engineering, Georgia Institute of Technology
2. Dr. Mark Davenport, School of Electrical and Computer Engineering, Georgia Institute of Technology
3. Dr. Saibal Mukhopadhyay, School of Electrical and Computer Engineering, Georgia Institute of Technology
4. Dr. Nima Ghalichechian, School of Electrical and Computer Engineering, Georgia Institute of Technology
5. Dr. Ryan Westafer, Georgia Tech Research Institute

Abstract

This dissertation develops theory, algorithms, and systems for high-dimensional optimization problems in electromagnetics. The first part studies subspace tracking and principal component analysis under hardware constraints such as limited computation, scarce memory, or acquisition restricted to a few linear measurements per sample. For Gaussian data in dimension d, it shows that an Oja-type algorithm using 2k adaptive linear measurements per sample estimates the top-k principal subspace at the minimax error rate of a two-level spiked model, up to a constant factor, when the sample size is known in advance, while measurement designs fixed in advance have a lower bound larger by a factor of order d/k at large sample sizes when the (k+1)-th eigenvalue is comparable to the k-th. It also develops regularized least squares algorithms on the Grassmann manifold for tracking time-varying subspaces. On the systems side, it describes AdaAFE-CIM, which uses subspace tracking for adaptive data compression in array processing hardware and reduces baseband power by 95.4% relative to full digitization in power-model simulations, together with an open-source end-to-end simulator for array processing under realistic hardware and channel effects. Finally, it presents inverse design methods for electromagnetic structures: a periodic level set function for gradient-free topology optimization, validated by fabrication and measurement for metasurfaces, and a neural adjoint method for reconfigurable antennas with exponentially large switch configuration spaces.