An Optimization-Based Coupling of Reduced Order Models with an Efficient Reduced Adjoint Basis Generation Approach

Hawkins, Elizabeth; Kuberry, Paul; Bochev, Pavel

doi:10.1137/24m1672791

An Optimization-Based Coupling of Reduced Order Models with an Efficient Reduced Adjoint Basis Generation Approach

Journal Article · Tue Apr 15 00:00:00 EDT 2025 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/24m1672791· OSTI ID:2566664

^[1]; Kuberry, Paul ^[2]; Bochev, Pavel ^[2]

Clemson University, SC (United States)
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Optimization-based coupling (OBC) is an attractive alternative to traditional Lagrange multiplier approaches in multiple modeling and simulation contexts. However, application of OBC to time-dependent problems has been hindered by the computational cost of finding the stationary points of the associated Lagrangian, which requires primal and adjoint solves. This issue can be mitigated by using OBC in conjunction with computationally efficient reduced order models (ROMs). To demonstrate the potential of this combination, in this paper, we develop an optimization-based ROM-ROM coupling for a transient advection-diffusion transmission problem. We pursue the “optimize-then-reduce” path toward solving the minimization problem at each time step and solve reduced space adjoint system of equations, where the main challenge in this formulation is the generation of adjoint snapshots and reduced bases for the adjoint systems required by the optimizer. One of the main contributions of the paper is a new technique for an efficient adjoint snapshot collection for gradient-based optimizers in the context of optimization-based ROM-ROM couplings. In conclusion, we present numerical studies demonstrating the accuracy of the approach along with comparison between various approaches for selecting a reduced order basis for the adjoint systems, including decay of snapshot energy, average iteration counts, and timings.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: NA0003525

OSTI ID:: 2566664

Report Number(s):: SAND--2025-05888J

Journal Information:: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

References (25)

Heterogeneous coupling by virtual control methods Gervasio, P.; Lions, J. -L.; Quarteroni, A. Numerische Mathematik, Vol. 90, Issue 2 https://doi.org/10.1007/s002110100303	journal	December 2001
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations Brooks, Alexander N.; Hughes, Thomas J. R. Computer Methods in Applied Mechanics and Engineering, Vol. 32, Issue 1-3 https://doi.org/10.1016/0045-7825(82)90071-8	journal	September 1982
Reduced order modeling of a two-dimensional flow with moving shocks Lucia, David J.; King, Paul I.; Beran, Philip S. Computers & Fluids, Vol. 32, Issue 7 https://doi.org/10.1016/S0045-7930(02)00035-X	journal	August 2003
A domain decomposition method for optimization problems for partial differential equations Gunzburger, M. D.; Lee, Jeehyun Computers & Mathematics with Applications, Vol. 40, Issue 2-3 https://doi.org/10.1016/S0898-1221(00)00152-8	journal	July 2000
An optimization based domain decomposition method for partial differential equations Gunzburger, M. D.; Peterson, J. S.; Kwon, H. Computers & Mathematics with Applications, Vol. 37, Issue 10 https://doi.org/10.1016/S0898-1221(99)00127-3	journal	May 1999
A reduced-basis element method Maday, Yvon; Rønquist, Einar M. Comptes Rendus. Mathématique, Vol. 335, Issue 2 https://doi.org/10.1016/S1631-073X(02)02427-5	journal	January 2002
A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions D’Elia, Marta; Perego, Mauro; Bochev, Pavel Computers & Mathematics with Applications, Vol. 71, Issue 11 https://doi.org/10.1016/j.camwa.2015.12.006	journal	June 2016
An optimisation–based domain–decomposition reduced order model for parameter–dependent non–stationary fluid dynamics problems Prusak, Ivan; Torlo, Davide; Nonino, Monica Computers & Mathematics with Applications, Vol. 166 https://doi.org/10.1016/j.camwa.2024.05.004	journal	July 2024
Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data Gunzburger, Max D.; Peterson, Janet S.; Shadid, John N. Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 4-6 https://doi.org/10.1016/j.cma.2006.08.004	journal	January 2007
A decoupling algorithm for fluid-structure interaction problems based on optimization Kuberry, Paul; Lee, Hyesuk Computer Methods in Applied Mechanics and Engineering, Vol. 267 https://doi.org/10.1016/j.cma.2013.10.006	journal	December 2013
Model Order Reduction and domain decomposition strategies for the solution of the dynamic elastic–plastic structural problem Corigliano, A.; Dossi, M.; Mariani, S. Computer Methods in Applied Mechanics and Engineering, Vol. 290 https://doi.org/10.1016/j.cma.2015.02.021	journal	June 2015
A one-shot overlapping Schwarz method for component-based model reduction: application to nonlinear elasticity Iollo, Angelo; Sambataro, Giulia; Taddei, Tommaso Computer Methods in Applied Mechanics and Engineering, Vol. 404 https://doi.org/10.1016/j.cma.2022.115786	journal	February 2023
Explicit synchronous partitioned scheme for coupled reduced order models based on composite reduced bases de Castro, Amy; Bochev, Pavel; Kuberry, Paul Computer Methods in Applied Mechanics and Engineering, Vol. 417 https://doi.org/10.1016/j.cma.2023.116398	journal	December 2023
A non-overlapping optimization-based domain decomposition approach to component-based model reduction of incompressible flows Taddei, Tommaso; Xu, Xuejun; Zhang, Lei Journal of Computational Physics, Vol. 509 https://doi.org/10.1016/j.jcp.2024.113038	journal	July 2024
Formulation, analysis and computation of an optimization-based local-to-nonlocal coupling method D’Elia, Marta; Bochev, Pavel Results in Applied Mathematics, Vol. 9 https://doi.org/10.1016/j.rinam.2020.100129	journal	February 2021
Turbulence, Coherent Structures, Dynamical Systems and Symmetry Holmes, Philip; Lumley, John L.; Berkooz, Gal https://doi.org/10.1017/CBO9780511622700	book	January 2010
A certified reduced basis method for parametrized elliptic optimal control problems Kärcher, Mark; Grepl, Martin A. ESAIM: Control, Optimisation and Calculus of Variations, Vol. 20, Issue 2 https://doi.org/10.1051/cocv/2013069	journal	March 2014
A Novel Partitioned Approach for Reduced Order Model—Finite Element Model (ROM-FEM) and ROM-ROM Coupling de Castro, Amy; Kuberry, Paul; Tezaur, Irina Earth and Space 2022 https://doi.org/10.1061/9780784484470.044	conference	January 2023
Turbulence and the dynamics of coherent structures. III. Dynamics and scaling Sirovich, Lawrence Quarterly of Applied Mathematics, Vol. 45, Issue 3 https://doi.org/10.1090/qam/910464	journal	January 1987
High-Resolution Conservative Algorithms for Advection in Incompressible Flow LeVeque, Randall J. SIAM Journal on Numerical Analysis, Vol. 33, Issue 2 https://doi.org/10.1137/0733033	journal	April 1996
An Optimization Based Coupling Method for Multiscale Problems Abdulle, Assyr; Jecker, Orane; Shapeev, Alexander Multiscale Modeling & Simulation, Vol. 14, Issue 4 https://doi.org/10.1137/15M105389X	journal	January 2016
Certified Reduced Basis Methods for Parametrized Distributed Elliptic Optimal Control Problems with Control Constraints Bader, Eduard; Kärcher, Mark; Grepl, Martin A. SIAM Journal on Scientific Computing, Vol. 38, Issue 6 https://doi.org/10.1137/16M1059898	journal	January 2016
An Optimization-Based Approach for Elliptic Problems with Interfaces Kuberry, Paul; Bochev, Pavel; Peterson, Kara SIAM Journal on Scientific Computing, Vol. 39, Issue 5 https://doi.org/10.1137/16M1084547	journal	January 2017
An Optimization-Based Domain Decomposition Method for the Navier--Stokes Equations Gunzburger, Max D.; Lee, Hyesuk Kwon SIAM Journal on Numerical Analysis, Vol. 37, Issue 5 https://doi.org/10.1137/S0036142998332864	journal	January 2000
A Gradient Method Approach to Optimization-Based Multidisciplinary Simulations and Nonoverlapping Domain Decomposition Algorithms Du, Qiang; Gunzburger, Max D. SIAM Journal on Numerical Analysis, Vol. 37, Issue 5 https://doi.org/10.1137/S0036142998343087	journal	January 2000

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