The structure of reconstructed flows in latent spaces.

Reconstructing the flow of a dynamical system from experimental data has been a key tool in the study of nonlinear problems. It allows one to discover the equations ruling the dynamics of a system as well as to quantify its complexity. In this work, we study the topology of the flow reconstructed by autoencoders, a dimensionality reduction method based on deep neural networks that has recently proved to be a very powerful tool for this task. We show that, although in many cases proper embeddings can be obtained with this method, it is not always the case that the topological structure of the flow is preserved.