Revealing the state space of turbulence using machine learning

Understand

Despite the apparent complexity of turbulent flow, identifying a simpler description of the underlying dynamical system remains a fundamental challenge.

• Capturing how the turbulent flow meanders amongst unstable states (simple invariant solutions) in phase space, as envisaged by Hopf in 1948, using some efficient representation offers the best hope of doing this, despite the inherent difficulty in identifying these states.
• Here, we make a significant step towards this goal by demonstrating that deep convolutional autoencoders can identify low-dimensional representations of two-dimensional turbulence which are closely associated with the simple invariant solutions characterizing the turbulent attractor.
• To establish this, we develop latent Fourier analysis that decomposes the flow embedding into a set of orthogonal latent Fourier modes which decode into physically meaningful patterns resembling simple invariant solutions.