Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 451, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2021.110841
Keywords
Nonlinear manifold solution representation; Physics-informed neural network; Reduced order model; Nonlinear dynamical system; Hyper-reduction
Funding
- LDRD program [20-FS-007]
- DTRA
- U.S. Department of Energy, National Nuclear Security Administration [DE-AC52-07NA27344, LLNL-JRNL-814844]
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Traditional linear subspace reduced order models are not effective in approximating solutions for advection-dominated flow phenomena. Therefore, we have developed a fast and accurate nonlinear manifold reduced order model that can better approximate high-fidelity solutions. The model takes advantage of existing numerical methods and achieves efficiency through hyper-reduction techniques. Numerical results demonstrate the model's ability to approximate solutions more efficiently and achieve high speedup.
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. (C) 2021 Elsevier Inc. All rights reserved.
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