Year: 2023
Type: preprint
Abstract: A nonlinear-manifold reduced order model (NM-ROM) is a great way of incorporating underlying physics principles into a neural network-based data-driven approach. We combine NM-ROMs with domain decomposition (DD) for efficient computation. NM-ROMs offer benefits over linear-subspace ROMs (LS-ROMs) but can be costly to train due to parameter scaling with the full-order model (FOM) size. To address this, we employ DD on the FOM, compute subdomain NM-ROMs, and then merge them into a global NM-ROM. This approach has multiple advantages: parallel training of subdomain NM-ROMs, fewer parameters than global NM-ROMs, and adaptability to subdomain-specific FOM features. Each subdomain NM-ROM uses a shallow, sparse autoencoder, enabling hyper-reduction (HR) for improved computational speed. In this paper, we detail an algebraic DD formulation for the FOM, train HR-equipped NM-ROMs for subdomains, and numerically compare them to DD LS-ROMs with HR. Results show a significant accuracy boost, on the order of magnitude, for the proposed DD NM-ROMs over DD LS-ROMs in solving the 2D steady-state Burgers' equation.
Source: arXiv (Cornell University)
Institutions: Rice University, Lawrence Livermore National Laboratory
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: U.S. Department of Energy, Rice University, Office of Science, National Nuclear Security Administration, National Defense Science and Engineering Graduate, Advanced Scientific Computing Research, Laboratory Directed Research and Development, Air Force Office of Scientific Research, Lawrence Livermore National Laboratory
OpenAlex ID: W4389326110