Machine learning approach to determine the minimum number of variables to describe observed space-time chaos

While space-time chaos with dissipation is often described by partial differential equations which are formally infinite-dimensional dynamical systems, it is widely believed that only a finite number of variables is actually needed to describe it. This is because trajectories in such systems are first attracted exponentially fast to a finite-dimensional object called the inertial manifold and stay therein afterward. In the seminar, I first review a numerical method that we previously developed to determine the inertial manifold dimension, i.e., the necessary number of variables, through the analysis of Lyapunov exponents and associated vectors. Then I describe our recent work to make it applicable to real experimental data, by using a machine learning technique to time series data. After demonstrating the validity of the method with numerical data of the Kuramoto-Sivashinsky equation, we test this approach with real experimental data of collective motion of bacteria, and evaluate the results through comparison with a phenomenological equation used in this context.

Event resources