2020 Spring, Math 801, Topics in Applied Math

--- Uncertainty Quantification, Data Assimilation and Prediction of Complex Nonlinear Turbulent Dynamical Systems

Week 1 (Jan 22,24): Overview

Week 2 (Jan 27,29,31): Introduction to Information Theory and UQ

Week 3 (Feb 3,5,7): Stochastic Toolkits

Week 4 (Feb 10,12,14): Filtering, data assimilation and state estimation

Week 5 (Feb 17,19,21): Introduction to optimal control theory

Week 6 (Feb 24, 26,28): Conditional Gaussian nonlinear modeling framework

Week 7 (Mar 2,4,6): Lagrangian data assimilation

Week 8 (Mar 9,11,13): Nonlinear smoothing and state estimation

Week 9 (Mar 16,18,20): Spring break

Week 10 (Mar 23,25,27): Parameter estimation

Week 11 (Mar 30, Apr 1,3): Predicting the Madden-Julian Oscillation (MJO) and the Monsoon Intraseasonal Oscillation (MISO)

Week 12 (Apr 6,8,10): Developing stochastic low-order models for predicting intermittent time series and extreme events

Week 13 (Apr 13,15,17): An efficient solver of high-dimensional Fokker-Planck equations

Week 14 (Apr 20,22,24): Fluctuation-Dissipation and Linear Response Theory

Week 15 (Apr 27,29, May 1): Application of UQ and stochastic models to studying El Niño-Southern Oscillation