Advanced methods for non-linear systems
- UE code SMATM227
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Schedule
30 30Quarter 2
- ECTS Credits 6
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Language
English
- Teacher Mauroy Alexandre
By the end of the course, students will be familiar with original techniques for studying dynamical systems and should be able to use these techniques in real-life applications (e.g. neuroscience, power grids, finance, etc.).
Studying nonlinear (dynamical) systems is crucial in many scientific disciplines, but only few techniques provide a global and systematic approach to those systems. This course will introduce such techniques, which are based on advanced mathematical tools (e.g. operator theory). Emphasis will also be put on the use and development of numerical methods.
The course will mainly focus on operator-theoretic methods, which allow to turn a nonlinear system into a linear (but infinite-dimensional) system. However the exact content of the course might change from one year to another, depending on the students’ interest as well as recent developments in research.
Dynamical systems theory : general reminder (attractor, stability, chaos), ergodic theory.
Operator theory : Koopman and Perron-Frobenius operators, spectral decomposition, interplay between geometric invariants and spectral properties.
Numerical methods : computation of spectrum and eigenfunctions (Fourier averages, DMD algorithm, Arnoldi method), projection of an operator on a basis.
Individual project with an oral presentation (in French) and a final report (in English). In his/her project, the student will use the techniques presented in the course, focusing on a specific application chosen according to his/her preferences. The project will be evaluated by the course holder and/or the subsitute teacher. Quality of peer reviewing could also be considered in the evaluation.
Training | Study programme | Block | Credits | Mandatory |
---|---|---|---|---|
Master 120 en sciences mathématiques, à finalité spécialisée en data science | Standard | 0 | 6 | |
Master 120 en sciences mathématiques, à finalité didactique | Standard | 0 | 6 | |
Master 60 en sciences mathématiques | Standard | 0 | 6 | |
Master 120 en sciences mathématiques, à finalité approfondie | Standard | 0 | 6 | |
Master 120 en sciences mathématiques, à finalité spécialisée en Project Engineering | Standard | 0 | 6 | |
Master 120 en sciences mathématiques, à finalité didactique | Standard | 1 | 6 | |
Master 60 en sciences mathématiques | Standard | 1 | 6 | |
Master 120 en sciences mathématiques, à finalité approfondie | Standard | 1 | 6 | |
Master 120 en sciences mathématiques, à finalité spécialisée en Project Engineering | Standard | 1 | 6 | |
Master 120 en sciences mathématiques, à finalité spécialisée en data science | Standard | 1 | 6 |