Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

A common strategy for the dimensionality reduction of nonlinear partial differential equations (PDEs) relies on use proper orthogonal decomposition (POD) to identify a reduced subspace and Galerkin projection evolving dynamics in this space. However, advection-dominated PDEs are represented poorly by methodology since process truncation discards important interactions between higher-order modes during time evolution. In study, we demonstrate that encoding using convolutional autoencoders (CAEs) followed reduced-space evolution recurrent neural networks overcomes limitation effectively. We truncated system only two latent space dimensions can reproduce sharp advecting shock profile viscous Burgers equation with very low viscosities, six-dimensional recreate inviscid shallow water equations. Additionally, proposed framework is extended parametric reduced-order model directly embedding information into detect trends Our results show these systems more amenable low-dimensional CAE network combination than POD-Galerkin technique.