A Helicity-Conservative Domain-Decomposed Physics-Informed Neural Network for Incompressible Non-Newtonian Flow
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918436584554496 |
|---|---|
| author | Lu, Zheng Lee, Young Ju Jia, Jiwei Li, Ziqian |
| author_facet | Lu, Zheng Lee, Young Ju Jia, Jiwei Li, Ziqian |
| contents | This paper develops a helicity-aware physics-informed neural network framework for incompressible non-Newtonian flow in rotational form. In addition to the energy law and the incompressibility constraint, helicity is a fundamental geometric quantity that characterizes the topology of vortex lines and plays an important role in the physical fidelity of long-time flow simulations. While helicity-preserving discretizations have been studied extensively in finite difference, finite element, and other structure-preserving settings, their realization within neural network solvers remains largely unexplored. Motivated by this gap, we propose a neural formulation in which vorticity is computed directly from the neural velocity field by automatic differentiation rather than learned as an independent output, thereby avoiding compatibility errors that pollute the helicity balance. To improve robustness and scalability, we combine two algorithmic ingredients: an overlapping spatial domain decomposition inspired by finite-basis physics-informed neural networks (FBPINNs), and a causal slab-wise temporal continuation strategy for long-time transient simulations. The local subnetworks are blended by explicitly normalized super-Gaussian window functions, which yield a smooth partition of unity, while the temporal evolution is advanced sequentially across time slabs by transferring the converged solution on one slab to the next. The resulting spatiotemporal framework provides a stable and physically meaningful approach for helicity-aware simulation of incompressible non-Newtonian flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08002 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Helicity-Conservative Domain-Decomposed Physics-Informed Neural Network for Incompressible Non-Newtonian Flow Lu, Zheng Lee, Young Ju Jia, Jiwei Li, Ziqian Fluid Dynamics Numerical Analysis 68T07, 35Q30 This paper develops a helicity-aware physics-informed neural network framework for incompressible non-Newtonian flow in rotational form. In addition to the energy law and the incompressibility constraint, helicity is a fundamental geometric quantity that characterizes the topology of vortex lines and plays an important role in the physical fidelity of long-time flow simulations. While helicity-preserving discretizations have been studied extensively in finite difference, finite element, and other structure-preserving settings, their realization within neural network solvers remains largely unexplored. Motivated by this gap, we propose a neural formulation in which vorticity is computed directly from the neural velocity field by automatic differentiation rather than learned as an independent output, thereby avoiding compatibility errors that pollute the helicity balance. To improve robustness and scalability, we combine two algorithmic ingredients: an overlapping spatial domain decomposition inspired by finite-basis physics-informed neural networks (FBPINNs), and a causal slab-wise temporal continuation strategy for long-time transient simulations. The local subnetworks are blended by explicitly normalized super-Gaussian window functions, which yield a smooth partition of unity, while the temporal evolution is advanced sequentially across time slabs by transferring the converged solution on one slab to the next. The resulting spatiotemporal framework provides a stable and physically meaningful approach for helicity-aware simulation of incompressible non-Newtonian flows. |
| title | A Helicity-Conservative Domain-Decomposed Physics-Informed Neural Network for Incompressible Non-Newtonian Flow |
| topic | Fluid Dynamics Numerical Analysis 68T07, 35Q30 |
| url | https://arxiv.org/abs/2604.08002 |