mlsanityData to 14 Oct 2026

Virtual domain extension for imposing boundary conditions in flow simulation using pre-trained local neural operator

arXiv 2504.09807 ↗First posted 14 Apr 2025physics.flu-dyn cs.LGcited by 0

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Abstract (arXiv)

This paper builds up a virtual domain extension (VDE) framework for imposing boundary conditions (BCs) in flow simulation using pre-trained local neural operator (LNO). It creates extended virtual domains to the input function to compensate for the corrosion nature of computational domains during LNO inference, thus turns the implementation of BC into the determination of field values on the extended domain. Several strategies to calculate the field values are proposed and validated in solving numerical examples, including padding operation, direct imposition, pressure symmetry, and optimization by backpropagation, and compared with boundary imposition in traditional solvers. It is found that the large time interval of LNO induces a relatively wide near-boundary domain to be processed, thus imposing BC on only a few nodes near the boundary following the immersed boundary conception in traditional solvers can hardly achieve high accuracy. With appropriate values assigned on the extended virtual domains, VDE can accurately impose BCs and lead to reasonable flow field predictions. This work provides a guidance for imposing BCs reliably in LNO prediction, which could facilitate the reuse of pre-trained LNO in more applications.

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References · 19

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  3. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 427
  4. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 303
  5. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 297
  6. 2021Physics-informed neural networks with hard constraints for inverse designcited by 280
  7. 2022U-NO: U-shaped Neural Operatorscited by 230
  8. 2023Neural Operators for Accelerating Scientific Simulations and Designcited by 221
  9. 2020PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domaincited by 174
  10. 2021PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEscited by 98
  11. 2022Deep transfer operator learning for partial differential equations under conditional shiftcited by 83
  12. 2022Reliable extrapolation of deep neural operators informed by physics or sparse observationscited by 62
7 more
  1. 2022Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problemscited by 58
  2. 2022Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problemscited by 48
  3. 2023Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-field Solutions Under Time-dependent Loadscited by 47
  4. 2021Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domainscited by 37
  5. 2022Learning the Solution Operator of Boundary Value Problems using Graph Neural Networkscited by 17
  6. 2022Local neural operator for solving transient partial differential equations on varied domainscited by 9
  7. 2023On the locality of local neural operator in learning fluid dynamicscited by 6

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