Uncertainty Quantification (IEMS-407, Northwestern)

Advanced graduate course on Uncertainty Quantification.

Syllabus

Theortical Foundation

• Optimal Transport, Wasserstein Gradient Flow, Sampling [textbook]
• High Dimensional Probability [textbook]
• Functional Inequalities and Sampling, optimization in probability space
• Probabilistic Numerics [textbook]
• Well-posed inverse problems; Bayesian posterior consistency; Bernstein Von Mises Theorem.

Applications: Inverse Problems and Data Assimilation

• Sampling: Importance sampling, (continuous-time) MCMC, particle methods.
• Neural ODE and diffusion model
• Optimization: Maximum a posteriori (MAP) estimators, variational methods, approximation in Kullback-Liebler divergence, Kalman Filter.