Multi-Patch Isogeometric Convolution Hierarchical Deep-learning Neural Network
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929375529664512 |
|---|---|
| author | Zhang, Lei Park, Chanwook Hughes, T. J. R. Liu, Wing Kam |
| author_facet | Zhang, Lei Park, Chanwook Hughes, T. J. R. Liu, Wing Kam |
| contents | A seamless integration of neural networks with Isogeometric Analysis (IGA) was first introduced in [1] under the name of Hierarchical Deep-learning Neural Network (HiDeNN) and has systematically evolved into Isogeometric Convolution HiDeNN (in short, C-IGA) [2]. C-IGA achieves higher order approximations without increasing the degree of freedom. Due to the Kronecker delta property of C-IGA shape functions, one can refine the mesh in the physical domain like standard finite element method (FEM) while maintaining the exact geometrical mapping of IGA. In this article, C-IGA theory is generalized for multi-CAD-patch systems with a mathematical investigation of the compatibility conditions at patch interfaces and convergence of error estimates. Two compatibility conditions (nodal compatibility and G^0 (i.e., global C^0) compatibility) are presented and validated through numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03307 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multi-Patch Isogeometric Convolution Hierarchical Deep-learning Neural Network Zhang, Lei Park, Chanwook Hughes, T. J. R. Liu, Wing Kam Numerical Analysis Computational Engineering, Finance, and Science A seamless integration of neural networks with Isogeometric Analysis (IGA) was first introduced in [1] under the name of Hierarchical Deep-learning Neural Network (HiDeNN) and has systematically evolved into Isogeometric Convolution HiDeNN (in short, C-IGA) [2]. C-IGA achieves higher order approximations without increasing the degree of freedom. Due to the Kronecker delta property of C-IGA shape functions, one can refine the mesh in the physical domain like standard finite element method (FEM) while maintaining the exact geometrical mapping of IGA. In this article, C-IGA theory is generalized for multi-CAD-patch systems with a mathematical investigation of the compatibility conditions at patch interfaces and convergence of error estimates. Two compatibility conditions (nodal compatibility and G^0 (i.e., global C^0) compatibility) are presented and validated through numerical examples. |
| title | Multi-Patch Isogeometric Convolution Hierarchical Deep-learning Neural Network |
| topic | Numerical Analysis Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2406.03307 |