<![CDATA[PhD Defense | Adaptive Subspace Tracking and Inverse Design for High-Dimensional Electromagnetics]]>

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.