A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder

•A novel physics-informed neural network reduced order model is introduced.•It is based on nonlinear manifold solution representation.•A sparse shallow neural network structure is used for the nonlinear manifold.•The existing numerical discretization of the full order model is utilized.•Advection-do...

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Bibliographic Details
Published in:Journal of computational physics Vol. 451; p. 110841
Main Authors: Kim, Youngkyu, Choi, Youngsoo, Widemann, David, Zohdi, Tarek
Format: Journal Article
Language:English
Published: Cambridge Elsevier Inc 15.02.2022
Elsevier Science Ltd
Subjects:
Advection
Air flow
Atmospheric models
Burgers equation
Computational physics
Hyper-reduction
Mathematical models
Neural networks
Nonlinear dynamical system
Nonlinear manifold solution representation
Numerical methods
Operators (mathematics)
Physics-informed neural network
Reduced order model
Reduced order models
Reduction
Solution space
Subspaces
Traffic flow
Hyper-reduction
Physics-informed neural network
Nonlinear dynamical system
Nonlinear manifold solution representation
Reduced order model
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:•A novel physics-informed neural network reduced order model is introduced.•It is based on nonlinear manifold solution representation.•A sparse shallow neural network structure is used for the nonlinear manifold.•The existing numerical discretization of the full order model is utilized.•Advection-dominated problems are accelerated with great accuracy. Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, e.g., any advection-dominated flow phenomena such as in traffic flow, atmospheric flows, and air flow over vehicles, a low-dimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physics-informed neural network ROM, namely nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 1D and 2D Burgers' equations. A speedup of up to 2.6 for 1D Burgers' and a speedup of 11.7 for 2D Burgers' equations are achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique. Finally, a posteriori error bounds for the NM-ROMs are derived that take account of the hyper-reduced operators.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2021.110841