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

Romit Maulik, Bethany Lusch, Prasanna Balaprakash

Research output: Contribution to journalArticlepeer-review

114 Scopus citations

Abstract

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

Original languageEnglish (US)
Article number037106
JournalPhysics of Fluids
Volume33
Issue number3
DOIs
StatePublished - Mar 1 2021

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

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