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We develop data-driven methods for incorporating physical information forpriors to learn parsimonious representations of nonlinear systems arising fromparameterized PDEs and mechanics. Our approach is based on VariationalAutoencoders (VAEs) for learning from observations nonlinear state spacemodels. We develop ways to incorporate geometric and topological priors throughgeneral manifold latent space representations. We investigate the performanceof our methods for learning low dimensional representations for the nonlinearBurgers equation and constrained mechanical systems.

Variational Autoencoders for Learning Nonlinear Dynamics of Physical Systems