Domain-decomposition nonlinear manifold reduced order model

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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  More>>
Developers:
Diaz, Alejandro [1] Choi, Youngsoo [1]
  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.:
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

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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}
}