Lennon Shikhman

I am a graduate student in Applied Mathematics at Florida Institute of Technology and Computer Science at Georgia Tech. My research focuses on mathematically grounded machine learning for structured and scientific systems. I study neural operators and stochastic models as approximations of mappings between high- and infinite-dimensional function spaces, with emphasis on stability, generalization under distributional shift, and spectral and geometric structure in learned representations.

My long-term goal is to develop principled machine learning methods for scientific computing, sensing, and dynamical systems. I investigate boundary-dependent operator learning for PDEs, probabilistic interpretations of training dynamics, and rigorous experimental frameworks for empirical machine learning. I also work on inverse problems in sensing systems, anomaly detection in time series and financial data, and representation learning for high-dimensional physical and physiological signals.