GD-VAEs: Geometric Dynamic Variational Autoencoders for Learning Nonlinear Dynamics and Dimension Reductions. (arXiv:2206.05183v1 [cs.LG])

We develop data-driven methods incorporating geometric and topological
information to learn parsimonious representations of nonlinear dynamics from
observations. We develop approaches for learning nonlinear state space models
of the dynamics for general manifold latent spaces using training strategies
related to Variational Autoencoders (VAEs). Our methods are referred to as
Geometric Dynamic (GD) Variational Autoencoders (GD-VAEs). We learn encoders
and decoders for the system states and evolution based on deep neural network
architectures that include general Multilayer Perceptrons (MLPs), Convolutional
Neural …

arxiv dynamics learning lg variational autoencoders