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FB-HyDON: Parameter-Efficient Physics-Informed Operator Learning of Complex PDEs via Hypernetwork and Finite Basis Domain Decomposition

arXiv 2409.09207 ↗First posted 13 Sep 2024cs.LG cs.NA math.NAcited by 0

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Abstract (arXiv)

Deep operator networks (DeepONet) and neural operators have gained significant attention for their ability to map infinite-dimensional function spaces and perform zero-shot super-resolution. However, these models often require large datasets for effective training. While physics-informed operators offer a data-agnostic learning approach, they introduce additional training complexities and convergence issues, especially in highly nonlinear systems. To overcome these challenges, we introduce Finite Basis Physics-Informed HyperDeepONet (FB-HyDON), an advanced operator architecture featuring intrinsic domain decomposition. By leveraging hypernetworks and finite basis functions, FB-HyDON effectively mitigates the training limitations associated with existing physics-informed operator learning methods. We validated our approach on the high-frequency harmonic oscillator, Burgers' equation at different viscosity levels, and Allen-Cahn equation demonstrating substantial improvements over other operator learning models.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 18 of its 27 references that are in the map. First posted on arXiv 13 Sep 2024.

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18 of 27 references.

References · 18

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  3. 2016HyperNetworkscited by 1,003
  4. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  5. 2021Characterizing possible failure modes in physics-informed neural networkscited by 632
  6. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  7. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
  8. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 321
  9. 2022Transformer for Partial Differential Equations' Operator Learningcited by 270
  10. 2019Continual learning with hypernetworkscited by 267
  11. 2023Neural Operators for Accelerating Scientific Simulations and Designcited by 218
  12. 2021Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equationscited by 142
6 more
  1. 2020Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Predictioncited by 137
  2. 2023An Expert's Guide to Training Physics-informed Neural Networkscited by 119
  3. 2022NOMAD: Nonlinear Manifold Decoders for Operator Learningcited by 81
  4. 2023A Mathematical Guide to Operator Learningcited by 74
  5. 2023HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetworkcited by 25
  6. 2024An Advanced Physics-Informed Neural Operator for Comprehensive Design Optimization of Highly-Nonlinear Systems: An Aerospace Composites Processing Case Studycited by 6

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