Phase space learning with neural networks
This provides a novel method for efficiently simulating PDE dynamics, potentially benefiting computational physics and engineering, though it appears incremental as a generalization of existing projection-based approaches.
The paper tackles the problem of solving Partial Differential Equations (PDEs) by proposing an autoencoder neural network that learns the phase space dynamics in a reduced latent space, enabling prediction of unseen bifurcations from a single sample path.
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.