A Convolutional Hierarchical Deep-learning Neural Network (C-HiDeNN) Framework for Non-linear Finite Element Analysis
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914123154980864 |
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| author | Liu, Yingjian Pabbala, Monish Yadav Guo, Jiachen Park, Chanwook Domel, Gino Liu, Wing Kam Qian, Dong |
| author_facet | Liu, Yingjian Pabbala, Monish Yadav Guo, Jiachen Park, Chanwook Domel, Gino Liu, Wing Kam Qian, Dong |
| contents | We present a framework for the Convolutional Hierarchical Deep-learning Neural Network (C-HiDeNN) tailored for nonlinear finite element analysis. Building upon the structured foundation of HiDeNN, C-HiDeNN introduces a convolution operator to enhance numerical approximation. A distinctive feature of C-HiDeNN is its higher-order accurate approximation achieved through an expanded set of parameters, such as the polynomial order 'p,' dilation parameter 'a,' patch size 's,' and nodal position 'X'. These parameters function as the functional equivalents of weights and biases within each C-HiDeNN patch. In addition, C-HiDeNN can be selectively applied to regions requiring high resolution to adaptively improve local prediction accuracy. To demonstrate the effectiveness of this framework, we provide numerical examples in the context of nonlinear finite element analysis. The results show that our approach achieves significantly higher accuracy than conventional Finite Element Method (FEM) while substantially reducing computational costs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02435 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Convolutional Hierarchical Deep-learning Neural Network (C-HiDeNN) Framework for Non-linear Finite Element Analysis Liu, Yingjian Pabbala, Monish Yadav Guo, Jiachen Park, Chanwook Domel, Gino Liu, Wing Kam Qian, Dong Numerical Analysis Analysis of PDEs We present a framework for the Convolutional Hierarchical Deep-learning Neural Network (C-HiDeNN) tailored for nonlinear finite element analysis. Building upon the structured foundation of HiDeNN, C-HiDeNN introduces a convolution operator to enhance numerical approximation. A distinctive feature of C-HiDeNN is its higher-order accurate approximation achieved through an expanded set of parameters, such as the polynomial order 'p,' dilation parameter 'a,' patch size 's,' and nodal position 'X'. These parameters function as the functional equivalents of weights and biases within each C-HiDeNN patch. In addition, C-HiDeNN can be selectively applied to regions requiring high resolution to adaptively improve local prediction accuracy. To demonstrate the effectiveness of this framework, we provide numerical examples in the context of nonlinear finite element analysis. The results show that our approach achieves significantly higher accuracy than conventional Finite Element Method (FEM) while substantially reducing computational costs. |
| title | A Convolutional Hierarchical Deep-learning Neural Network (C-HiDeNN) Framework for Non-linear Finite Element Analysis |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2509.02435 |