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

Journal Article · · Journal of Computational Physics
 [1];  [2];  [2];  [1]
  1. Univ. of California, Berkeley, CA (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
+ Show Author Affiliations
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. Lastly, a posteriori error bounds for the NM-ROMs are derived that take account of the hyper-reduced operators.
Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1843130
Alternate ID(s):
OSTI ID: 1868572
OSTI ID: 23203590
Report Number(s):
LLNL-JRNL-814844; 1023653
Journal Information:
Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 451; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

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97 MATHEMATICS AND COMPUTING
Hyper-reduction
Nonlinear dynamical system
Nonlinear manifold solution representation
Physics-informed neural network
Reduced order model