Dynamic Data Assimilation: An Introduction

Course Description

Our aim is to provide a broad based background on the mathematical principles and tools from linear algebra, multivariate calculus and finite dimensional optimization theory, estimation theory, non-linear dynamics and chaos that constitute the basis for dynamic data assimilation as we know today. Our aim is to present the ideas at the level of a first year graduate/final year undergraduate student aspiring to enter this exciting area.

Dynamic Data Assimilation: An Introduction
Prof. S. Lakshmivarahan in Lecture 1.
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Video Lectures & Study Materials

Visit the official course website for more study materials: http://nptel.ac.in/syllabus/111106082/

# Lecture Play Lecture
I. Introduction
1 An Overview Play Video
2 Data Mining, Data assimilation and prediction Play Video
II. Mathematical Tools
3 A classification of forecast errors Play Video
4 Finite Dimensional Vector Space Play Video
5 Matrices Play Video
6 Matrices Continued Play Video
III. Static & Deterministic Models
7 Multi-variate Calculus Play Video
8 Optimization in Finite Dimensional Vector spaces Play Video
9 Deterministic, Static, linear Inverse (well-posed) Problems Play Video
10 Deterministic, Static, Linear Inverse (Ill-posed) Problems Play Video
11 A Geometric View - Projections Play Video
IV. Matrix Methods Solving LLS
12 Deterministic, Static, nonlinear Inverse Problems Play Video
13 On-line Least Squares Play Video
14 Examples of static inverse problems Play Video
15 Interlude and a Way Forward Play Video
16 Matrix Decomposition Algorithms Play Video
17 Matrix Decomposition Algorithms Continued Play Video
V. Direct Minimization Methods for Solving LLS
18 Minimization algorithms Play Video
19 Minimization algorithms Continued Play Video
20 Inverse problems in deterministic Play Video
21 Inverse problems in deterministic Continued Play Video
22 Forward sensitivity method Play Video
VI. Deterministic & Dynamic Models: Adjoint Method
23 Relation between FSM and 4DVAR Play Video
24 Statistical Estimation Play Video
25 Statistical Least Squares Play Video
26 Maximum Likelihood Method Play Video
27 Bayesian Estimation Play Video
VII. Deterministic & Dynamic models: Other Methods
28 From Gauss to Kalman-Linear Minimum Variance Estimation Play Video
29 Initialization Classical Method Play Video
30 Optimal interpolations Play Video
VIII. Static & Stochastic Models: Bayesian Framework
31 A Bayesian Formation-3D-VAR methods Play Video
32 Linear Stochastic Dynamics - Kalman Filter Play Video
33 Linear Stochastic Dynamics - Kalman Filter Continued Play Video
IX. Dynamic & Stochastic Models: Kalman Filtering
34 Linear Stochastic Dynamics - Kalman Filter Continued. Play Video
35 Covariance Square Root Filter Play Video
36 Nonlinear Filtering Play Video
37 Ensemble Reduced Rank Filter Play Video
X. Dynamic Stochastic Models: Other Methods
38 Basic nudging methods Play Video
39 Deterministic predictability Play Video
40 Predictability: A stochastic view and summary Play Video


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