Mathematics - Dynamic Data Assimilation (English)

   Thursday, May 15, 2025   

Starting a new Lecture Notes Series on Mathematics - Dynamic Data Assimilation

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Lecture 1: Mod-01 Lec-01 An Overview

Lecture 2: Mod-01 Lec-02 Data Mining, Data assimilation and prediction

Lecture 3: Mod-01 Lec-03 A classification of forecast errors

Lecture 4: Mod-02 Lec-04 Finite Dimensional Vector Space

Lecture 5: Mod-02 Lec-05 Matrices

Lecture 6: Mod-02 Lec-06 Matrices Continued

Lecture 7: Mod-02 Lec-07 Multi-variate Calculus

Lecture 8: Mod-02 Lec-08 Optimization in Finite Dimensional Vector spaces

Lecture 9: Mod-03 Lec-09 Deterministic, Static, linear Inverse (well-posed) Problems

Lecture 10: Mod-03 Lec-10 Deterministic, Static, Linear Inverse (Ill-posed) Problems

Lecture 11: Mod-03 Lec-11 A Geometric View - Projections

Lecture 12: Mod-03 Lec-12 Deterministic, Static, nonlinear Inverse Problems

Lecture 13: Mod-03 Lec-13 On-line Least Squares

Lecture 14: Mod-03 Lec-14 Examples of static inverse problems

Lecture 15: Mod-04 Lec-15 Interlude and a Way Forward

Lecture 16: Mod-04 Lec-16 Matrix Decomposition Algorithms

Lecture 17: Mod-04 Lec-17 Matrix Decomposition Algorithms Continued

Lecture 18: Mod-04 Lec-18 Minimization algorithms

Lecture 19: Mod-04 Lec-19 Minimization algorithms Continued

Lecture 20: Mod-05 Lec-20 Inverse problems in deterministic

Lecture 21: Mod-05 Lec-21 Inverse problems in deterministic Continued

Lecture 22: Mod-05 Lec-22 Forward sensitivity method

Lecture 23: Mod-05 Lec-23 Relation between FSM and 4DVAR

Lecture 24: Mod-06 Lec-24 Statistical Estimation

Lecture 25: Mod-06 Lec-25 Statistical Least Squares

Lecture 26: Mod-06 Lec-26 Maximum Likelihood Method

Lecture 27: Mod-06 Lec-27 Bayesian Estimation

Lecture 28: Mod-06 Lec-28 From Gauss to Kalman-Linear Minimum Variance Estimation

Lecture 29: Mod-07 Lec-29 Initialization Classical Method

Lecture 30: Mod-07 Lec-30 Optimal interpolations

Lecture 31: Mod-07 Lec-31 A Bayesian Formation-3D-VAR methods

Lecture 32: Mod-08 Lec-32 Linear Stochastic Dynamics - Kalman Filter

Lecture 33: Mod-08 Lec-33 Linear Stochastic Dynamics - Kalman Filter Continued

Lecture 34: Mod-08 Lec-34 Linear Stochastic Dynamics - Kalman Filter Continued.

Lecture 35: Mod-08 Lec-35 Covariance Square Root Filter

Lecture 36: Mod-08 Lec-36 Nonlinear Filtering

Lecture 37: Mod-08 Lec-37 Ensemble Reduced Rank Filter

Lecture 38: Mod-09 Lec-38 Basic nudging methods

Lecture 39: Mod-10 Lec-39 Deterministic predictability

Lecture 40: Mod-10 Lec-40 Predictability A stochastic view and Summary