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

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arxiv 2401.07888 v2 pith:AG333QLJ submitted 2024-01-15 math.NA cs.LGcs.NA

Alexander Heinlein , Amanda A. Howard , Damien Beecroft , Panos Stinis This is my paper · ORCID
classification math.NAcs.LGcs.NA
keywords domainmultifidelitynetworksneuralpinnsphysics-informedproblemsapproach
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Double screening in the training dynamics of variational physics-informed neural networks for heterogeneous coupled parabolic systems

    math.AP 2026-07 conditional novelty 7.0 of 10

    In the neural tangent kernel regime, the slowest training mode of variational PINNs for heterogeneous parabolic systems is asymptotically determined by the diffusive block alone, with condition number growing like Pe².

  2. Multifidelity-Augmented Gaussian Process Inputs for Surrogate Modeling from Scarce Data

    stat.ML 2026-03 conditional novelty 6.0 of 10

    Augmenting a high-fidelity GP's inputs with predictions from all low-fidelity surrogates improves accuracy and cuts cost versus cokriging and autoregressive multifidelity GPs on scarce-data problems.

  3. The modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture with domain decomposition

    math.NA 2025-11 conditional novelty 3.0 of 10

    A hybrid KAN-MLP physics-informed network with a trainable convex weight and overlapping domain decomposition improves reported accuracy on high-frequency and multiscale PDE benchmarks.

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