mlsanityData to 7 Oct 2026

The role of interface boundary conditions and sampling strategies for Schwarz-based coupling of projection-based reduced order models

arXiv 2410.04668 ↗First posted 7 Oct 2024math.NA cs.LG cs.NAcited by 4

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Abstract (arXiv)

This paper presents and evaluates a framework for the coupling of subdomain-local projection-based reduced order models (PROMs) using the Schwarz alternating method following a domain decomposition (DD) of the spatial domain on which a given problem of interest is posed. In this approach, the solution on the full domain is obtained via an iterative process in which a sequence of subdomain-local problems are solved, with information propagating between subdomains through transmission boundary conditions (BCs). We explore several new directions involving the Schwarz alternating method aimed at maximizing the method's efficiency and flexibility, and demonstrate it on three challenging two-dimensional nonlinear hyperbolic problems: the shallow water equations, Burgers' equation, and the compressible Euler equations. We demonstrate that, for a cell-centered finite volume discretization and a non-overlapping DD, it is possible to obtain a stable and accurate coupled model utilizing Dirichlet-Dirichlet (rather than Robin-Robin or alternating Dirichlet-Neumann) transmission BCs on the subdomain boundaries. We additionally explore the impact of boundary sampling when utilizing the Schwarz alternating method to couple subdomain-local hyper-reduced PROMs. Our numerical results suggest that the proposed methodology has the potential to improve PROM accuracy by enabling the spatial localization of these models via domain decomposition, and achieve up to two orders of magnitude speedup over equivalent coupled full order model solutions and moderate speedups over analogous monolithic solutions.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 14 of its 82 references that are in the map. First posted on arXiv 7 Oct 2024.

Builds on

14 of 82 references.

References · 14

  1. 2020A fast and accurate physics-informed neural network reduced order model with shallow masked autoencodercited by 80
  2. 2019D3M: A deep domain decomposition method for partial differential equationscited by 44
  3. 2021Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domainscited by 37
  4. 2022Quadratic Approximation Manifold for Mitigating the Kolmogorov Barrier in Nonlinear Projection-Based Model Order Reductioncited by 29
  5. 2023Domain decomposition-based coupling of physics-informed neural networks via the Schwarz alternating methodcited by 9
  6. 2023Train Small, Model Big: Scalable Physics Simulators via Reduced Order Modeling and Domain Decompositioncited by 7
  7. 2020On the stability of projection-based model order reduction for convection-dominated laminar and turbulent flowscited by 6
  8. 2023Domain decomposition for data-driven reduced modeling of large-scale systemscited by 6
  9. 2024Domain Decomposition-based coupling of Operator Inference reduced order models via the Schwarz alternating methodcited by 5
  10. 2023Fundamentally New Coupled Approach to Contact Mechanics via the Dirichlet-Neumann Schwarz Alternating Methodcited by 4
  11. 2022A Novel Partitioned Approach for Reduced Order Model -- Finite Element Model (ROM-FEM) and ROM-ROM Couplingcited by 2
  12. 2022An optimisation-based domain-decomposition reduced order model for the incompressible Navier-Stokes equationscited by 2
2 more
  1. 2024Dynamic flux surrogate-based partitioned methods for interface problemscited by 2
  2. 2024An optimization-based coupling of reduced order models with efficient reduced adjoint basis generation approachcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 3.

4 papers.

  1. 2025Defining Foundation Models for Computational Science: A Call for Clarity and Rigorcited by 16
  2. 2026Latent Space Element Methodcited by 1
  3. 2026Adaptive hybrid coupling with operator inference, the overlapping Schwarz alternating method and reinforcement learningcited by 0
  4. 2026Hybrid coupling with numerics-informed neural networks and the overlapping Schwarz alternating methodcited by 0