Unit I

Introduction to Mathematical Modelling – Different types of Mathematical Models – Discrete and Continuous Models – Numerical Methods for Nonlinear Models – Stability Analysis–Eigen Values and Eigen Vectors – Dynamical System Approach.

Unit II

Linear and Nonlinear Time Series Analysis – Time – Frequency Analysis of Data –Statistical Methods for Data Analysis – Dimensionality Reduction – SVD – Independent Component Analysis – ML Techniques for Data Analysis – DL Techniques for Data Analysis.

Unit III

Decomposition Techniques for Data Analysis – Dynamic Mode Decomposition–Empirical Mode Decomposition – Variational Mode Decomposition – Equation Free Modelling – SINDy – Early Warning Frame Work for Catastrophic Transitions.

This course aims at enabling the graduate students to analyse the data that they obtain either from physical systems or from mathematical models. Further, the course will focus on imparting modelling skills to graduate students that will enable them to create models from data. The students will be exposed to conventional and the state-of-the art modelling techniques including AI/ML techniques.

After completing the course,the students will be able to

CO1:Analyse data from physical systems and mathematical models

CO2:Model systems from the first principles

CO3:Develop data driven models of systems of interest

CO4:Apply the state-of-the-art data analytics techniques to explore the dynamics of the systems of interest

1. Data Driven Modelling & Scientific Computation : Methods for Complex Systems and Big Data –J .NathanKutz,Oxford University Press,First Edition, 2013.
2. Nonlinear Dynamics and Chaos–Steven H Strogatz, Westview Press, 2015.
3. Modelling Complex System – Nino Boccara, Springer Publications, 2010.
4. Data Driven Science and Engineering –Steven L Brunton & J.NathanKutz, Cambridge University Press,2019.
5. Principles of System Identification :Theory and Practice–Arun K Tangirala, CRC Press,2015.

* – In order to achieve the course outcomes, a mandatory publication will be more suitable as anexternal evaluation component than a conventional exam. Since, PhD students are the targetaudience, they will be able employ the techniques learned from this course to their respectivefieldofstudytoarriveatapublication.