Phase Space Learning with Neural Networks

Abstract

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.