Key Coursework
Key Coursework
ECE598 - Diffusion flow Matching models (Prof. Zhizhen Zhao) - Continuous normalizing flow, Energy-based model and score matching, Diffusion models, Rectified flow and flow matching, Stochastic Interpolants and Schrodinger bridge, flow matching on general geometry, Flow matching on discrete state space, Connections with Optimal Transport, Generalization properties of diffusion and flow model
ECE557 - Geometric Control Theory (Prof. Yuliy Barshnikov, Prof. M. A. Belabbas) - Review of linear systems - Fundamental solutions, Variation of constants formula, Controllability of linear systems, Smooth manifolds, Vector fields and flows, Lie brackets and Lie groups and flows on them, Cartan calculus, Distributions, Frobenius theorem, Chow-Rashevski Theorem, Feedback control and Feedback linearization - homotopies and retractions, Wilson and Brockett theorem, Poincare-Hopf theorem, Riemann geometry - Geodesics, Christoffel symbols, Connections, Levi-Civita connection, Feedback invariants and Feedback linearization
ECE543 - Statistical Learning Theory (Prof. Dimitiros Katselis) - Concentration Inequalities, Function spaces determined by kernels, Empirical Risk Minimization and Generalization Bounds via Rademacher Complexity, VC Dimension
AE598 - Formal Methods for Aerospace Robotics (Prof. Hirosyasu Tsukamoto) - Robust and Adaptive Control, Safe motion planning and Barrier functions, Stochastic motion planning and Risk metrics, Distributed multi-agent control, Model-free adaptive control
ECE555 - Control of Stochastic Systems (Prof. M. A. Belabbas) - Discrete-time Stochastic processes, Filtrations, Simple Random Walk, Martingales and stopping times, Poisson counters and Ito Stochastic differential equations, Ito rule for change of variables, Fokker-Plank equation for jump processes, Dynamic programming and optimal control, Wiener processes, differentiability of Wiener processes, Stratonovich calculus, Stochastic realization using power spectrum, Linear and nonlinear filtering - DMZ equation and Kalman-Bucy filter, Stochastic control and separation principle