My research bridges mathematical and data-driven models through interpretable, computationally efficient, and robust scientific machine learning. A central focus is the development of machine learning-enhanced data assimilation algorithms for high-dimensional, chaotic physical systems, together with principled approaches to inverse problems grounded in rigorous mathematical analysis. In parallel, I develop theoretical foundations for modern learning architectures by studying attention mechanisms and transformers as measure-to-measure operators. Beyond these directions, my work includes graph-based machine learning methods that leverage data geometry for active learning, as well as the integration of large language models with knowledge graphs to support complex mathematical reasoning and retrieval.