%0Computer Program
%TNonlinear manifold reduced order model
%XTraditional 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.
%AChoi, Youngsoo
%AKim, Youngkyu
%AWidemann, David
%Rhttps://doi.org/10.11578/dc.20240904.2
%Uhttps://www.osti.gov/doecode/biblio/142366
%CUnited States
%D2024
%GEnglish
%2USDOE National Nuclear Security Administration (NNSA)
%1AC52-07NA27344
2024-07-02