Abstract
This software combines nonlinear-manifold reduced order models (NM-ROMs) with domain
decomposition (DD) techniques. NM-ROMs, which utilize a shallow, sparse autoencoder trained with full
order model (FOM) snapshot data, approximate the FOM state on a nonlinear manifold. These models
offer advantages over linear-subspace ROMs (LS-ROMs) particularly in scenarios with slowly decaying
Kolmogorov n-width. However, the training of NM-ROMs involves a number of parameters that scale with
the size of the FOM, and storing high-dimensional FOM snapshots can significantly increase the cost of
ROM training for extreme-scale problems.
To mitigate these costs, the software employs DD to partition the FOM into smaller subdomains,
computes NM-ROMs for each, and then integrates these to form a global NM-ROM. This strategy offers
multiple benefits: it enables parallel training of subdomain NM-ROMs, reduces the number of parameters
needed, decreases the dimensional requirements of subdomain FOM training data, and allows for
customization to the unique characteristics of each FOM subdomain. The use of a shallow, sparse
autoencoder architecture in each subdomain NM-ROM facilitates the application of hyper-reduction (HR),
simplifying the nonlinear complexities and enhancing computational speed.
This software marks the inaugural application of NM-ROM combined with HR to a DD problem. It features
an algebraic DD reformulation of the FOM, training of NM-ROMs with HR for each subdomain, and
employs a sequential quadratic
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- Developers:
-
Diaz, Alejandro [1] ; Choi, Youngsoo [1]
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Release Date:
- 2024-05-04
- Project Type:
- Open Source, Publicly Available Repository
- Software Type:
- Scientific
- Version:
- 1.0
- Licenses:
-
MIT License
- Sponsoring Org.:
-
USDOE National Nuclear Security Administration (NNSA)Primary Award/Contract Number:AC52-07NA27344
- Code ID:
- 141711
- Site Accession Number:
- LLNL-CODE-864366
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Country of Origin:
- United States
Citation Formats
Diaz, Alejandro N., and Choi, Youngsoo.
Domain-decomposition nonlinear manifold reduced order model.
Computer Software.
https://github.com/LLNL/DD-NM-ROM.
USDOE National Nuclear Security Administration (NNSA).
04 May. 2024.
Web.
doi:10.11578/dc.20240827.3.
Diaz, Alejandro N., & Choi, Youngsoo.
(2024, May 04).
Domain-decomposition nonlinear manifold reduced order model.
[Computer software].
https://github.com/LLNL/DD-NM-ROM.
https://doi.org/10.11578/dc.20240827.3.
Diaz, Alejandro N., and Choi, Youngsoo.
"Domain-decomposition nonlinear manifold reduced order model." Computer software.
May 04, 2024.
https://github.com/LLNL/DD-NM-ROM.
https://doi.org/10.11578/dc.20240827.3.
@misc{
doecode_141711,
title = {Domain-decomposition nonlinear manifold reduced order model},
author = {Diaz, Alejandro N. and Choi, Youngsoo},
abstractNote = {This software combines nonlinear-manifold reduced order models (NM-ROMs) with domain
decomposition (DD) techniques. NM-ROMs, which utilize a shallow, sparse autoencoder trained with full
order model (FOM) snapshot data, approximate the FOM state on a nonlinear manifold. These models
offer advantages over linear-subspace ROMs (LS-ROMs) particularly in scenarios with slowly decaying
Kolmogorov n-width. However, the training of NM-ROMs involves a number of parameters that scale with
the size of the FOM, and storing high-dimensional FOM snapshots can significantly increase the cost of
ROM training for extreme-scale problems.
To mitigate these costs, the software employs DD to partition the FOM into smaller subdomains,
computes NM-ROMs for each, and then integrates these to form a global NM-ROM. This strategy offers
multiple benefits: it enables parallel training of subdomain NM-ROMs, reduces the number of parameters
needed, decreases the dimensional requirements of subdomain FOM training data, and allows for
customization to the unique characteristics of each FOM subdomain. The use of a shallow, sparse
autoencoder architecture in each subdomain NM-ROM facilitates the application of hyper-reduction (HR),
simplifying the nonlinear complexities and enhancing computational speed.
This software marks the inaugural application of NM-ROM combined with HR to a DD problem. It features
an algebraic DD reformulation of the FOM, training of NM-ROMs with HR for each subdomain, and
employs a sequential quadratic programming (SQP) solver for the evaluation of the coupled global NMROM.
The effectiveness of the DD NM-ROM with HR is numerically demonstrated on the 2D steady-state
Burgers' equation, showing an order of magnitude improvement in accuracy over the DD LS-ROM with
HR.},
doi = {10.11578/dc.20240827.3},
url = {https://doi.org/10.11578/dc.20240827.3},
howpublished = {[Computer Software] \url{https://doi.org/10.11578/dc.20240827.3}},
year = {2024},
month = {may}
}