Inferring stability properties of chaotic systems on autoencoders' latent spaces
This work enables inferring stability for high-dimensional chaotic systems, which is important for turbulence and chaotic dynamics research, though it builds incrementally on existing forecasting methods.
The paper tackled the problem of inferring stability properties of chaotic systems on autoencoders' latent spaces, showing that a CAE-ESN model successfully infers invariant stability properties and tangent space geometry through Lyapunov exponents and covariant Lyapunov vectors.
The data-driven learning of solutions of partial differential equations can be based on a divide-and-conquer strategy. First, the high dimensional data is compressed to a latent space with an autoencoder; and, second, the temporal dynamics are inferred on the latent space with a form of recurrent neural network. In chaotic systems and turbulence, convolutional autoencoders and echo state networks (CAE-ESN) successfully forecast the dynamics, but little is known about whether the stability properties can also be inferred. We show that the CAE-ESN model infers the invariant stability properties and the geometry of the tangent space in the low-dimensional manifold (i.e. the latent space) through Lyapunov exponents and covariant Lyapunov vectors. This work opens up new opportunities for inferring the stability of high-dimensional chaotic systems in latent spaces.