Friday Lunch Seminar
September 11, 2020
12:15 〜 13:00
(On-line for CiNet members only)
“Data-driven modeling of nonlinear dynamics: From mode decomposition to interaction analysis”
by Yoshinobu Kawahara
Institute of Mathematics for Industry, Kyushu University and Advanced Intelligence Project
RIKEN
Host PI: Okito Yamashita
Abstract:
Data-driven modeling of complex systems has received much attention over the recent years, largely due to the availability of large datasets. In particular, the analysis of nonlinear dynamical system with Koopman operator has been actively discussed in applied mathematics and various scientific fields for this purpose. This is because it can provide physical interpretations of the dynamics based on deep theoretical backgrounds and is endowed with prominent estimation methods such as dynamic mode decomposition (DMD). DMD is a numerical method for estimating spectra of Koopman operator, and has been attracting attention as a way of obtaining global modal descriptions of nonlinear dynamics from data without requiring explicit prior knowledge. In this talk, I first overview the recent advances on this research topic, focusing on spectral analysis of dynamical systems with Koopman operator and DMD. Then, I describe several recently-proposed related algorithms using machine learning principles. One limitation of DMD is that it assumes inherent-scale spatial or temporal dynamics independently contribute to its whole dynamics, which is often not satisfied in dynamic phenomena investigated in scientific studies. Thus, I describe a neural network model to estimate interactions among different scale dynamics to address this issue. In the talk, I occasionally show some applications of these method to several real-world data.
About CiNet’s Friday Lunch Seminars:
The Friday Lunch Seminar is CiNet’s main regular meeting series, held every week at 12:15 in the beautiful main lecture theatre on the ground floor at CiNet. The talks are typically 40mins long and orientated towards an inter-disciplinary audience. They are informal, social, and most people bring their own lunch to eat during the talk. They are open to anyone who is feeling curious and wants to come, regardless of where you work.