AMCS 301 Numerical methods for random partial differential equations: hierarchical approximation and machine learning approaches Teaching Random PDEs stochastic algorithms Monte carlo methods Quasi-Monte Carlo Hierarchical regression Multilevel Monte Carlo Stochastic collocation Multi-index Low-rank approximation hierarchical and sparse approximation Bayesian Inversion Bayesian optimal experimental design A course on modern numerical methods for random partial differential equations
AMCS 308 Stochastic Numerics with Application in Simulation and Data Science Teaching stochastic algorithms Stochastic Methods Stochastic Modeling Stochastic Optimal Control Stochastic processes Filtering theory data assimilation Monte carlo methods Variance Reduction Importance sampling Monte Carlo methods. Simulation, estimation, data assimilation, and optimal control for time-discrete and time-continuous Markov chains