Dynamic mode decomposition-like methods and applications

14 xuño 2022 - 00:00:00
10:00

Dynamic mode decomposition-like methods and applications, impartido por José M. Vega. E.T.S.I. Aeronáutica e do Espazo. Universidad Politécnica de Madrid.

Data: 14 de xuño de 2022

Hora: 10:00 h.

Lugar: online MS Teams a través do enlace Teams meeting

Duración: 1 hora

Abstract:

Dynamic mode decomposition was introduced by Schmid (2010) and is related to seminal ideas by Koopman (1931). This method is useful to post-process spatio-temporal data resulting from nonlinear dynamics. The decomposition is an expansion in spatial modes times complex exponentials in the time variable, which exhibit generally nonzero growth rates. As such, the method is an advantageous alternative to more classical methods to obtain such expansions (with zero growth rates), such as fast Fourier transform (and extensions) or power spectral density.

However, standard dynamic mode decomposition does not always give the correct results, even in cases in which the provided data admit an exact expansion in spatial modes times exponentials in time. This difficulty will be clarified using the concepts of spatial and spectral complexities. Also, a recent extension (2017), called higher order dynamic mode decomposition, will be presented that solves the difficulty. Such extension synergically combines standard dynamic mode decomposition and direct consequences of the well-known Takens’ delay embedding theorem (1981). A further extension called spatio-temporal Koopman decomposition (2018) combines spatial and temporal DMD expansions, in terms of standing and/or traveling waves.

Concepts will be illustrated using some toy-model dynamics. Several applications, using both numerical and experimental data, coming from systems of scientific and technological interest, will also be addressed.