Center for Environmental and Applied Fluid Mechanics Virtual Seminar: Jacob Page

Description

Jacob Page, a lecturer in applied and computational mathematics at the University of Edinburgh, will give a talk entitled "Learned Low-Dimensional Representations of Turbulence and Connections to Simple Invariant Solutions" in this week's Center for Environmental and Applied Fluid Mechanics seminar at a special time.

Tamer Zaki, associate professor of mechanical engineering at Johns Hopkins University, will host.

Please attend the event by using the Zoom link.

Abstract:

A long-standing challenge in low-order modelling is to design reduced representations of turbulent flows which are connected to the underlying dynamical system. In this talk I will describe how deep convolutional neural networks in a simple "autoencoder" configuration decompose snapshots of monochromatically forced, two-dimensional turbulence into a finite set of recurrent patterns which resemble the simple invariant solutions embedded in the turbulent attractor. The interpretation of the neural network embeddings is made possible by the application of "latent Fourier analysis", a decomposition of the low-dimensional latent representation of vorticity into a set of orthogonal modes parameterised by latent wavenumbers. Projections onto individual latent Fourier wavenumbers reveal the simple invariant solutions organising both the quiescent and bursting dynamics in a systematic way inaccessible to previous approaches. I will also discuss the use of latent Fourier analysis in an ongoing hunt for unstable periodic orbits.