mlsanityData to 7 Oct 2026

Fast meta-solvers for 3D complex-shape scatterers using neural operators trained on a non-scattering problem

arXiv 2405.12380 ↗First posted 20 May 2024cs.LG physics.comp-phcited by 8

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Abstract (arXiv)

Three-dimensional target identification using scattering techniques requires high accuracy solutions and very fast computations for real-time predictions in some critical applications. We first train a deep neural operator~(DeepONet) to solve wave propagation problems described by the Helmholtz equation in a domain textitwithout scatterers but at different wavenumbers and with a complex absorbing boundary condition. We then design two classes of fast meta-solvers by combining DeepONet with either relaxation methods, such as Jacobi and Gauss-Seidel, or with Krylov methods, such as GMRES and BiCGStab, using the trunk basis of DeepONet as a coarse-scale preconditioner. We leverage the spectral bias of neural networks to account for the lower part of the spectrum in the error distribution while the upper part is handled inexpensively using relaxation methods or fine-scale preconditioners. The meta-solvers are then applied to solve scattering problems with different shape of scatterers, at no extra training cost. We first demonstrate that the resulting meta-solvers are shape-agnostic, fast, and robust, whereas the standard standalone solvers may even fail to converge without the DeepONet. We then apply both classes of meta-solvers to scattering from a submarine, a complex three-dimensional problem. We achieve very fast solutions, especially with the DeepONet-Krylov methods, which require orders of magnitude fewer iterations than any of the standalone solvers.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 30 of its 63 references that are in the map. First posted on arXiv 20 May 2024.

Builds on

30 of 63 references.

References · 30

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18 more
  1. 2019Physics-Informed Neural Networks for Power Systemscited by 80
  2. 2022Reliable extrapolation of deep neural operators informed by physics or sparse observationscited by 62
  3. 2022Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systemscited by 54
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  6. 2020Physics Informed Neural Networks for Simulating Radiative Transfercited by 35
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  8. 2023Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loadscited by 33
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  12. 2023ViTO: Vision Transformer-Operatorcited by 29
  13. 2023Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operatorscited by 28
  14. 2023Phase-Field DeepONet: Physics-informed deep operator neural network for fast simulations of pattern formation governed by gradient flows of free-energy functionalscited by 26
  15. 2023Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regressioncited by 25
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  17. 2023A Generative Modeling Framework for Inferring Families of Biomechanical Constitutive Laws in Data-Sparse Regimescited by 8
  18. 2023Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learningcited by 6

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 5; 2026: 2.

8 papers.

  1. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 103
  2. 2025NOWS: Neural Operator Warm Starts for Accelerating Iterative Solverscited by 9
  3. 2025Leveraging Operator Learning to Accelerate Convergence of the Preconditioned Conjugate Gradient Methodcited by 6
  4. 2025A Neural-Operator Preconditioned Newton Method for Accelerated Nonlinear Solverscited by 4
  5. 2025Hybrid Iterative Solvers with Geometry-Aware Neural Preconditioners for Parametric PDEscited by 3
  6. 2025HEATNETs: Explainable Random Feature Neural Networks for High-Dimensional Parabolic PDEscited by 1
  7. 2026NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspacescited by 0
  8. 2026McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equationcited by 0