Finding invariant tori in chaos using dynamical mode decomposition

We can understand the statistical properties of the chaotic dynamics of turbulence is the study of non-chaotic yet dynamically unstable invariant solutions embedded in the system's chaotic attractor, such as invariant tori that capture quasi-periodic dynamics. In this talk, we present a method for generating guesses for invariant tori by processing turbulent data using dynamic mode decomposition (DMD). From the DMD eigenvalue spectrum, we can identify the generating frequencies of invariant tori and generate a guess used to numerically converge these invariant solutions. We will discuss an example implementation of this method where we find 2-tori from a direct numerical simulation of the Kuramoto-Sivashinsky equation in a chaotic regime.