%0Computer Program
%TDomain-decomposition nonlinear manifold reduced order model
%XThis 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.
%ADiaz, Alejandro
%AChoi, Youngsoo
%Rhttps://doi.org/10.11578/dc.20240827.3
%Uhttps://www.osti.gov/doecode/biblio/141711
%CUnited States
%D2024
%GEnglish
%2USDOE National Nuclear Security Administration (NNSA)
%1AC52-07NA27344
2024-05-04