  This work proposes an autoencoder neural network as a non-linear
generalization of projection-based methods for solving Partial Differential
Equations (PDEs). The proposed deep learning architecture presented is capable
of generating the dynamics of PDEs by integrating them completely in a very
reduced latent space without intermediate reconstructions, to then decode the
latent solution back to the original space. The learned latent trajectories are
represented and their physical plausibility is analyzed. It is shown the
reliability of properly regularized neural networks to learn the global
characteristics of a dynamical system's phase space from the sample data of a
single path, as well as its ability to predict unseen bifurcations.
