Youngsoo Choi | 20-FS-007
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 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 one-dimensional (1D) and two-dimensional (2D) Burgers' equations. Increased speeds of up to 2.6 times for 1D Burgers' and 11.7 times 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.
Reduced-order modeling is specifically named as a research and development priority in the Lawrence Livermore National Laboratory core competencies of high-energy-density science; high-performance computing, simulation, and data science; and advanced materials and manufacturing.
Publications, Presentations, and Patents
Choi, Y., et al. 2020. "Gradient-Based Constrained Optimization Using a Database of Linear Reduced-Order Models." Journal of Computational Physics (2020): 109787. LLNL-JRNL-796678
Hoang, C., et al. 2020. "Domain-Decomposition Least-Squares Petrov-Galerkin (DD-LSPG) Nonlinear Model Reduction." arXiv:2007.11835. LLNL-JRNL-812648
Kim, Y., et al. 2020. "A fast and Accurate Physics-Informed Neural Network Reduced Order Model with Shallow Masked Autoencoder." arXiv:2009.11990. LLNL-JRNL-814844