Dissertation or Thesis Defense

Graph Neural Networks (GNNs) are the tool of choice for scalable and stable learning in graph-structured data applications involving geometric information. My research addresses the fundamental questions of how GNNs can generalize across different graph scales and how they can remain stable on large-scale graphs. I do so by considering manifolds as graph limit models. […]

AI agents, both in the physical and digital worlds, should generalize from their training data to three increasingly difficult levels of deployment: training tasks and environments, training tasks and environments with variations, and completely new tasks and environments. Moreover, like humans, they are expected to learn from as little training data as possible, especially in […]

Neural compression, which pertains to compression schemes that are learned from data using neural networks, has emerged as a powerful approach for compressing real-world data. Neural compressors often outperform classical schemes, especially in settings where reconstructions that are perceptually similar to the source are desired. Despite their empirical success, the fundamental principles governing how neural […]

Directly training deep learning models for applications in large-scale cyber-physical systems can be intractable due to the large number of components and decision variables. Instead, we focus on exploiting spatial symmetries in systems by designing size-generalizable architectures. Once trained on small-scale examples, such architectures exhibit equivalent or comparable performance on large-scale systems. The first example […]

The inverse design paradigm has emerged as a transformative approach for the synthesis of nanophotonic structures, offering a powerful alternative to conventional intuition-driven design. By approaching photonic device design as a computational optimization problem, inverse design enables the systematic exploration of high-dimensional parameter spaces to uncover non- intuitive structures that meet complex performance targets. This […]