The reconstruction of flows from spatiotemporal data by autoencoders

Abstract

Artificial neural networks have become essential tools in data science for uncovering insights from complex data. However, they are usually seen as black boxes. In this work we explore how an autoencoder processes complex spatiotemporal information. We analyze the topological structure of reconstructed flows in the latent space of an autoencoder for two distinct test cases. The first case involves a synthetic spatiotemporal pattern for the temperature field in a convective problem, illustrating a classic extended system that exhibits low-dimensional chaos. The second case focuses on an experimental recording of the labial oscillations responsible for sound production in an avian vocal organ, as an example of periodic dynamics in a biological system. We find that the state representation in its latent space can be topologically equivalent to the phase space of the problem. Autoencoders thus retain phase space representations of the data hidden in its latent layer.