Course Identification

Data-driven Modal Decomposition Methods of Nonlinear Systems
20222181

Lecturers and Teaching Assistants

Dr. Michael David Chekroun
N/A

Course Schedule and Location

2022
First Semester
Sunday, 14:15 - 16:00, FGS, Rm A
24/10/2021
18/03/2022

Field of Study, Course Type and Credit Points

Chemical Sciences: Lecture; Elective; Regular; 2.00 points
Mathematics and Computer Science: Lecture; Elective; Regular; 2.00 points

Comments

N/A

Prerequisites

-Linear Algebra and elements of ordinary differential equations (ODEs) and nonlinear dynamics.

 

-Basic tools from probability theory and statistics

Restrictions

20

Language of Instruction

English

Attendance and participation

Expected and Recommended

Grade Type

Numerical (out of 100)

Grade Breakdown (in %)

60%
40%
Examination and Lab (Matlab).

Evaluation Type

Examination

Scheduled date 1

30/01/2022
FGS, Rm A
1000-1300
N/A

Scheduled date 2

07/03/2022
FGS, Rm A
1000-1300
N/A

Estimated Weekly Independent Workload (in hours)

5

Syllabus

This course will provide a self-contained introduction to some of the actively-researched areas in data-driven analysis of dynamical data. The focus will be on the extraction from data of modes of variability relevant for dimensionality reduction, data-driven modeling and prediction.  These lectures will cover guiding theoretical principles as well as address practical aspects and challenges. Along the way, we will introduce and use tools from probability, statistical learning, and nonlinear dynamics, as well as teach the relevant numerical methods. A variety of concrete examples coming from nonlinear dynamics, fluid dynamics, and geophysical applications will serve as illustrations.  The course will cover the following topics:

 

  • Basic problems of data representation of time-evolving datasets issued from nonlinear systems 

 

  • Principal component analysis and extensions 

 

  • Markov matrices techniques (Transfer operator methods, Diffusion Map)

 

  • Dynamic mode decomposition, Koopman modes and other data-driven spectral methods (e.g. multivariate singular spectral analysis, data-adaptive harmonic analysis)

Learning Outcomes

Upon successful completion of this course, the students should be able to:

 • Describe key concepts, principles and methods in the field of data-driven analysis of dynamical data.

• Apply their acquired knowledge of data-driven analysis methods and principles in their own area of research, in particular for the analysis/modeling of multiscale patterns occurring in complex systems.

 

Reading List

N/A

Website

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