TY  - COMP
TI  - Nonlinear manifold reduced order model
AB  - 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.
AU  - Choi, Youngsoo
AU  - Kim, Youngkyu
AU  - Widemann, David
DO  - https://doi.org/10.11578/dc.20240904.2
UR  - https://www.osti.gov/doecode/biblio/142366
CY  - United States
PY  - 2024
DA  - 2024-07-02
LA  - English
C1  - Research Org.: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
C2  - Sponsor Org.: USDOE National Nuclear Security Administration (NNSA)
C4  - Contract Number: AC52-07NA27344
ER  -