mlsanityData to 14 Oct 2026

Multifidelity domain decomposition-based physics-informed neural networks and operators for time-dependent problems

arXiv 2401.07888 ↗First posted 15 Jan 2024math.NA cs.LG cs.NAcited by 4

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Abstract (arXiv)

Multiscale problems are challenging for neural network-based discretizations of differential equations, such as physics-informed neural networks (PINNs). This can be (partly) attributed to the so-called spectral bias of neural networks. To improve the performance of PINNs for time-dependent problems, a combination of multifidelity stacking PINNs and domain decomposition-based finite basis PINNs is employed. In particular, to learn the high-fidelity part of the multifidelity model, a domain decomposition in time is employed. The performance is investigated for a pendulum and a two-frequency problem as well as the Allen-Cahn equation. It can be observed that the domain decomposition approach clearly improves the PINN and stacking PINN approaches. Finally, it is demonstrated that the FBPINN approach can be extended to multifidelity physics-informed deep operator networks.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 15 of its 31 references that are in the map. First posted on arXiv 15 Jan 2024.

Builds on

15 of 31 references.

References · 15

  1. 2018On the Spectral Bias of Neural Networkscited by 1,341
  2. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 634
  3. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 583
  4. 2021Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equationscited by 145
  5. 2020Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networkscited by 123
  6. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  7. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 89
  8. 2021Improved architectures and training algorithms for deep operator networkscited by 86
  9. 2022Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problemscited by 58
  10. 2023Multi-stage Neural Networks: Function Approximator of Machine Precisioncited by 48
  11. 2022Bi-fidelity Modeling of Uncertain and Partially Unknown Systems using DeepONetscited by 27
  12. 2021Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Controlcited by 24
3 more
  1. 2022On the Role of Fixed Points of Dynamical Systems in Training Physics-Informed Neural Networkscited by 23
  2. 2023Stacked networks improve physics-informed training: applications to neural networks and deep operator networkscited by 21
  3. 2023Efficient kernel surrogates for neural network-based regressioncited by 7

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Cited by year

Citing papers per year: 2024: 3; 2025: 1.

4 papers.

  1. 2024Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problemscited by 35
  2. 2024SPIKANs: Separable Physics-Informed Kolmogorov-Arnold Networkscited by 12
  3. 2025Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learningcited by 3
  4. 2024Deep operator network models for predicting post-burn contractioncited by 1