# Dynamic Data Assimilation

Other, , Prof. S. Lakshmivarahan

Other, , Prof. S. Lakshmivarahan

Introduction:Data Mining, Data Assimilation, Inverse problems and Prediction - Static vs. dynamic and deterministic vs. stochastic problems- formulation & classification;Mathematical tools:Finite dimensional vector space basic concepts - Overview of properties and operations on matrices - Special classes of matrices, Eigen decomposition, and matrix square root - Gradient, Jacobian, Hessian, Quadratic forms and their properties;Static, deterministic models: least Squares method formulation and properties - Linear least squares (LLS) - over determined case, weighted and unweighted formulation, orthogonal and oblique projections - LLS- Underdetermined case -Lagrangian multiplier - Nonlinear least squares problem (NLS) - formulation - Approximation first and second-order methods for solving NLS - Examples of LLS and NLS - satellite retrieval

Matrix methods solving LLS:Normal equations symmetric positive definite (SPD) systems multiplicative matrix decomposition - Cholesky decomposition- matrix square root - Gramm-Schmidt orthogonalization process - QR decomposition - Singular value decomposition (SVD) - Solution of retrieval problems;Direct minimization methods for solving LLS:LLS as a quadratic minimization problem - Gradient method, its properties - Convergence and speed of convergence of gradient method - Conjugate gradient and Quasi-Newton methods - Practice problems and programming exercises;Deterministic, dynamic models:adjoint method - Dynamic models, role of observations, and least squares objective function, estimation of initial condition (IC) and parameters, adjoint sensitivity - A straight line problem a warm up - Linear model, first-order adjoint dynamics and computation of the gradient of the least squares objective function - Nonlinear model and first-order adjoint dynamics - Illustrative examples and practice problems, programming exercises

Deterministic, Dynamic models:Other methods - Forward sensitivity method for estimation of IC and parameters, forward sensitivity dynamics - Example of Carbon dynamics,Relation between adjoint and forward sensitivity, Predictability, Lyapunov index - Method of nudging and overview of nudging methods;Static, stochastic models:Bayesian framework - Bayesian method linear, Gaussian case - Linear minimum variance estimation (LMVE) and prelude to Kalman filter - Model space vs. observation space formulation -Duality between Bayesian and LMVE;Dynamic, Stochastic models:Kalman filtering - Derivation of the Kalman filter equations - Derivation of Nonlinear filter - Computational requirements - Ensemble Kalman filtering;Dynamic stochastic models:Other methods - Unscented Kalman filtering - Particle filtering - An overview and assessment of methods

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4.1 ( 11 )

Dynamic Data Assimilation an introduction by Prof S. Lakshmivarahan,School of Computer Science,University of Oklahoma.For more details on NPTEL visit httpnptel.ac.in

Sam

Sep 12, 2018

Excellent course helped me understand topic that i couldn't while attendinfg my college.

Dembe

March 29, 2019

Great course. Thank you very much.