NPTEL : Dynamic Data Assimilation: An Introduction (Mathematics)

Co-ordinators : Prof. S. Lakshmivarahan


Lecture 1 - An Overview

Lecture 2 - Data Mining, Data assimilation and prediction

Lecture 3 - A classification of forecast errors

Lecture 4 - Finite Dimensional Vector Space

Lecture 5 - Matrices

Lecture 6 - Matrices (Continued...)

Lecture 7 - Multi-variate Calculus

Lecture 8 - Optimization in Finite Dimensional Vector spaces

Lecture 9 - Deterministic, Static, linear Inverse (well-posed) Problems

Lecture 10 - Deterministic, Static, Linear Inverse (Ill-posed) Problems

Lecture 11 - A Geometric View – Projections

Lecture 12 - Deterministic, Static, nonlinear Inverse Problems

Lecture 13 - On-line Least Squares

Lecture 14 - Examples of static inverse problems

Lecture 15 - Interlude and a Way Forward

Lecture 16 - Matrix Decomposition Algorithms

Lecture 17 - Matrix Decomposition Algorithms (Continued...)

Lecture 18 - Minimization algorithms

Lecture 19 - Minimization algorithms (Continued...)

Lecture 20 - Inverse problems in deterministic

Lecture 21 - Inverse problems in deterministic (Continued...)

Lecture 22 - Forward sensitivity method

Lecture 23 - Relation between FSM and 4DVAR

Lecture 24 - Statistical Estimation

Lecture 25 - Statistical Least Squares

Lecture 26 - Maximum Likelihood Method

Lecture 27 - Bayesian Estimation

Lecture 28 - From Gauss to Kalman-Linear Minimum Variance Estimation

Lecture 29 - Initialization Classical Method

Lecture 30 - Optimal interpolations

Lecture 31 - A Bayesian Formation-3D-VAR methods

Lecture 32 - Linear Stochastic Dynamics - Kalman Filter

Lecture 33 - Linear Stochastic Dynamics - Kalman Filter (Continued...)

Lecture 34 - Linear Stochastic Dynamics - Kalman Filter (Continued...)

Lecture 35 - Covariance Square Root Filter

Lecture 36 - Nonlinear Filtering

Lecture 37 - Ensemble Reduced Rank Filter

Lecture 38 - Basic nudging methods

Lecture 39 - Deterministic predictability

Lecture 40 - Predictability A stochastic view and Summary