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 336 Numerical Methods for Stochastic Differential Equations with connections to Machine Learning Teaching stochastic differential equations Ito integral Monte Carlo Multilevel Monte Carlo Importance sampling Variance Reduction Kolmogorov Backward Equation Fokker-Planck equations Hamilton-Jabobi-Bellman Stochastic Optimal Control The goal of this course is to give basic knowledge of stochastic differential equations and their numerical solution, useful for scientific and engineering modeling, guided by some problems in applications in financial mathematics, material science, geophysical flow problems, turbulent diffusion, control theory, and Monte Carlo methods.
