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

Journal Article · · Physics of Fluids
DOI:https://doi.org/10.1063/5.0039986· OSTI ID:1840551
 [1];  [1];  [1]
  1. Argonne National Lab. (ANL), Lemont, IL (United States)
+ Show Author Affiliations
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 the evolution of the inviscid shallow water equations. Additionally, the proposed framework is extended to a parametric reduced-order model by directly embedding parametric information into the latent space to detect trends in system evolution. Furthermore, 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.
Research Organization:
Argonne National Laboratory (ANL), Argonne, IL (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
AC02-06CH11357
OSTI ID:
1840551
Alternate ID(s):
OSTI ID: 1769451
Journal Information:
Physics of Fluids, Journal Name: Physics of Fluids Journal Issue: 3 Vol. 33; ISSN 1070-6631
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

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Cited By (5)

A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations journal October 2021
Non-autoregressive time-series methods for stable parametric reduced-order models journal August 2020
An Evolve-Then-Correct Reduced Order Model for Hidden Fluid Dynamics journal April 2020
An enhanced parametric nonlinear reduced order model for imperfect structures using Neumann expansion text January 2021
Towards physically consistent data-driven weather forecasting: Integrating data assimilation with equivariance-preserving deep spatial transformers preprint January 2021

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Related Subjects

97 MATHEMATICS AND COMPUTING
Artificial neural networks
Machine learning
Nonlinear systems
Partial differential equations