DD-NM-ROM integrates nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD). NM-ROMs approximate the full order model (FOM) state in a nonlinear-manifold by training a shallow, sparse autoencoder using FOM snapshot data. These NM-ROMs can be advantageous over linear-subspace ROMs (LS-ROMs) for problems with slowly decaying Kolmogorov-width. However, the number of NM-ROM parameters that need to be trained scales with the size of the FOM. Moreover, for "extreme-scale" problems, the storage of high-dimensional FOM snapshots alone can make ROM training expensive. To alleviate the training cost, DD-NM-ROM applies DD to the FOM, computes NM-ROMs on each subdomain, and couples them to obtain a global NM-ROM. This approach has several advantages: subdomain NM-ROMs can be trained in parallel, involve fewer parameters to be trained than global NM-ROMs, require smaller subdomain FOM dimensional training data, and can be tailored to subdomain-specific features of the FOM. The shallow, sparse architecture of the autoencoder used in each subdomain NM-ROM allows application of hyper-reduction (HR), reducing the complexity caused by nonlinearity and yielding computational speedup of the NM-ROM. DD-NM-ROM provides the first application of NM-ROM (with HR) to a DD problem. In particular, DD-NM-ROM implements an algebraic DD reformulation of the FOM, training a NM-ROM with HR for each subdomain, and a sequential quadratic programming (SQP) solver to evaluate the coupled global NM-ROM. The proposed DD-NM-ROM approach is numerically tested for the Burgers' equation.
Follow the instructions in conda/README.md.
Explore the DD-NM-ROM approach for steady and unsteady problems for the Burgers' equation. See the examples directory.
@article{Diaz_CMAME_2024,
title = {A fast and accurate domain decomposition nonlinear manifold reduced order model},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {425},
pages = {116943},
year = {2024},
issn = {0045-7825},
doi = {https://doi.org/10.1016/j.cma.2024.116943},
url = {https://www.sciencedirect.com/science/article/pii/S0045782524001993},
author = {Alejandro N. Diaz and Youngsoo Choi and Matthias Heinkenschloss}
}
@phdthesis{Diaz_Thesis_2024,
title = {Domain decomposition-based reduced-order models using nonlinear-manifolds and interpolatory projections},
author = {Alejandro N. Diaz},
year = {2024},
month = {April},
school = {Rice University},
type = {PhD thesis},
url = {https://hdl.handle.net/1911/116152}
}
- Alejandro Diaz (Sandia National Laboratories)
- Ivan Zanardi (University of Illinois Urbana-Champaign)
- Seung Whan Chung (Lawrence Livermore National Laboratory)
- Youngsoo Choi (Lawrence Livermore National Laboratory)
- Matthias Heinkenschloss (Rice University)
- A. Diaz was supported for this work by a Defense Science and Technology Internship (DSTI) at Lawrence Livermore National Laboratory and a 2021 National Defense Science and Engineering Graduate Fellowship, United States.
- I. Zanardi was supported for this work by a Data Science Summer Insitute (DSSI) at Lawrence Livermore National Laboratory.
- Y. Choi was supported for this work by the US Department of Energy under the Mathematical Multifaceted Integrated Capability Centers -- DoE Grant DE -- SC0023164; The Center for Hierarchical and Robust Modeling of Non-Equilibrium Transport (CHaRMNET).
DD-NM-ROM is distributed under the terms of the MIT license. All new contributions must be made under the MIT. See LICENSE-MIT
LLNL Release Nubmer: LLNL-CODE-864366