mlsanityData to 14 Oct 2026

Hybrid coupling with operator inference and the overlapping Schwarz alternating method

arXiv 2511.20687 ↗First posted 20 Nov 2025math.NA cs.AI cs.NAcited by 4

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Abstract (arXiv)

This paper presents a novel hybrid approach for coupling subdomain-local non-intrusive Operator Inference (OpInf) reduced order models (ROMs) with each other and with subdomain-local high-fidelity full order models (FOMs) with using the overlapping Schwarz alternating method (O-SAM). The proposed methodology addresses significant challenges in multiscale modeling and simulation, particularly the long runtime and complex mesh generation requirements associated with traditional high-fidelity simulations. By leveraging the flexibility of O-SAM, we enable the seamless integration of disparate models, meshes, and time integration schemes, enhancing computational efficiency while maintaining high accuracy. Our approach is demonstrated through a series of numerical experiments on complex three-dimensional (3D) solid dynamics problems, showcasing speedups of up to 106x compared to conventional FOM-FOM couplings. This work paves the way for more efficient simulation workflows in engineering applications, with potential extensions to a wide range of partial differential equations.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 15 of its 67 references that are in the map. First posted on arXiv 20 Nov 2025.

Builds on

15 of 67 references.

References · 15

  1. 2019D3M: A deep domain decomposition method for partial differential equationscited by 44
  2. 2020Data-driven reduced-order models via regularized operator inference for a single-injector combustion processcited by 42
  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 30
  5. 2021Reduced operator inference for nonlinear partial differential equationscited by 21
  6. 2025Defining Foundation Models for Computational Science: A Call for Clarity and Rigorcited by 17
  7. 2024Separable DeepONet: Breaking the Curse of Dimensionality in Physics-Informed Machine Learningcited by 15
  8. 2023Domain decomposition-based coupling of physics-informed neural networks via the Schwarz alternating methodcited by 9
  9. 2025Time Marching Neural Operator FE Coupling: AI Accelerated Physics Modelingcited by 8
  10. 2023Train Small, Model Big: Scalable Physics Simulators via Reduced Order Modeling and Domain Decompositioncited by 7
  11. 2023Domain decomposition for data-driven reduced modeling of large-scale systemscited by 6
  12. 2024Domain Decomposition-based coupling of Operator Inference reduced order models via the Schwarz alternating methodcited by 5
3 more
  1. 2023Fundamentally New Coupled Approach to Contact Mechanics via the Dirichlet-Neumann Schwarz Alternating Methodcited by 4
  2. 2025Kernel manifolds: nonlinear-augmentation dimensionality reduction using reproducing kernel Hilbert spacescited by 3
  3. 2025Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spacescited by 2

Built on by

Cited by year (2026 to 14 Oct)

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

4 papers.

  1. 2026NN-OpInf: an operator inference approach using structure-preserving composable neural networkscited by 1
  2. 2025ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marchingcited by 0
  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