Abstract
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 lowdimensional
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 software 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.
- Developers:
-
Choi, Youngsoo [1] ; Kim, Youngkyu [1] ; Widemann, David [1]
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Release Date:
- 2024-07-02
- Project Type:
- Open Source, Publicly Available Repository
- Software Type:
- Scientific
- Version:
- 1.0
- Licenses:
-
MIT License
- Sponsoring Org.:
-
USDOE National Nuclear Security Administration (NNSA)Primary Award/Contract Number:AC52-07NA27344
- Code ID:
- 142366
- Site Accession Number:
- LLNL-CODE-867904
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Country of Origin:
- United States
Citation Formats
Choi, Youngsoo, Kim, Youngkyu, and Widemann, David P.
Nonlinear manifold reduced order model.
Computer Software.
https://github.com/LLNL/NM-ROM.
USDOE National Nuclear Security Administration (NNSA).
02 Jul. 2024.
Web.
doi:10.11578/dc.20240904.2.
Choi, Youngsoo, Kim, Youngkyu, & Widemann, David P.
(2024, July 02).
Nonlinear manifold reduced order model.
[Computer software].
https://github.com/LLNL/NM-ROM.
https://doi.org/10.11578/dc.20240904.2.
Choi, Youngsoo, Kim, Youngkyu, and Widemann, David P.
"Nonlinear manifold reduced order model." Computer software.
July 02, 2024.
https://github.com/LLNL/NM-ROM.
https://doi.org/10.11578/dc.20240904.2.
@misc{
doecode_142366,
title = {Nonlinear manifold reduced order model},
author = {Choi, Youngsoo and Kim, Youngkyu and Widemann, David P.},
abstractNote = {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 lowdimensional
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 software 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.},
doi = {10.11578/dc.20240904.2},
url = {https://doi.org/10.11578/dc.20240904.2},
howpublished = {[Computer Software] \url{https://doi.org/10.11578/dc.20240904.2}},
year = {2024},
month = {jul}
}