Jacob Page

Learned low-dimensional representations of turbulence and connections to simple invariant solutions

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.