Course

Module-1

Implementation of Linear Systems Revisited: Direct Solution Methods, Iterative Solution Methods, Gradient (Steepest) Descent, Eigen values, Eigen vectors and Solvability, Non linear Systems.
Curve fitting : Least-Square Fitting Methods, Polynomial Fits and Splines. Singular Value Decomposition: Basics, Principal Component Analysis (PCA), Diagonalization, Proper orthogonal Modes.
Dimensionality Reduction : POD for Partial differential equations, POD expansion, POD with symmetries.

Module-2

Dynamic mode decomposition (DMD): Introduction, Dynamics of DMD versus POD, Applications of DMD.
Data assimilation : Introduction and applications.
Equation free modeling : Multiscale physics, Lifting and Restricting in Equation- Free Computing.

Module-3

Applications of POD and DMD for Thermal and Fluid systems: Introduction to coherent structures, Turbulence, Jet flows, boundary layer, flows in complex geometries, flows in internal combustion engines.

• CO1 : To gain fundamental knowledge on the basic concepts and theoretical ideas in data-driven techniques in the context of programming language infrastructure.
• CO2 : To develop an understanding of the algorithms used for transforming and reducing data.
• CO3 : To implement the various theoretical and computational tools on scientific applications relevant for thermal and fluid systems.

• Kutz, J.N., Brunton,S., Brunton,B., and Proctor,J., Data driven Modeling and Scientific Computation: Method for Complex Systems and Big Data. Oxford University Press,2013.
• Kutz,J.N., Brunton,S., Data driven Science and Engineering: Machine Learning, Dynamical Systems and Control. Cambridge University Press, 2019.
• Holmes,P., Lumley,J.L., Berkooz,G., and Rowley, C.W., Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press,2012.
• Kutz,J.N., Brunton,S., Brunton,B., and Proctor,J., Dynamic Mode Decomposition : Data Driven Modeling of Complex Systems.SIAM,2016.
• Anton,H. ,and Rorres,C., Elementary Linear Algebra. John Wiley & Sons Inc.2005.