Convolutional Hierarchical Deep Learning Neural Networks-Tensor Decomposition (C-HiDeNN-TD): a scalable surrogate modeling approach for large-scale physical systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917043446480896 |
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| author | Guo, Jiachen Park, Chanwook Xie, Xiaoyu Sang, Zhongsheng Wagner, Gregory J. Liu, Wing Kam |
| author_facet | Guo, Jiachen Park, Chanwook Xie, Xiaoyu Sang, Zhongsheng Wagner, Gregory J. Liu, Wing Kam |
| contents | A common trend in simulation-driven engineering applications is the ever-increasing size and complexity of the problem, where classical numerical methods typically suffer from significant computational time and huge memory cost. Methods based on artificial intelligence have been extensively investigated to accelerate partial differential equations (PDE) solvers using data-driven surrogates. However, most data-driven surrogates require an extremely large amount of training data. In this paper, we propose the Convolutional Hierarchical Deep Learning Neural Network-Tensor Decomposition (C-HiDeNN-TD) method, which can directly obtain surrogate models by solving large-scale space-time PDE without generating any offline training data. We compare the performance of the proposed method against classical numerical methods for extremely large-scale systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00329 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convolutional Hierarchical Deep Learning Neural Networks-Tensor Decomposition (C-HiDeNN-TD): a scalable surrogate modeling approach for large-scale physical systems Guo, Jiachen Park, Chanwook Xie, Xiaoyu Sang, Zhongsheng Wagner, Gregory J. Liu, Wing Kam Computational Engineering, Finance, and Science A common trend in simulation-driven engineering applications is the ever-increasing size and complexity of the problem, where classical numerical methods typically suffer from significant computational time and huge memory cost. Methods based on artificial intelligence have been extensively investigated to accelerate partial differential equations (PDE) solvers using data-driven surrogates. However, most data-driven surrogates require an extremely large amount of training data. In this paper, we propose the Convolutional Hierarchical Deep Learning Neural Network-Tensor Decomposition (C-HiDeNN-TD) method, which can directly obtain surrogate models by solving large-scale space-time PDE without generating any offline training data. We compare the performance of the proposed method against classical numerical methods for extremely large-scale systems. |
| title | Convolutional Hierarchical Deep Learning Neural Networks-Tensor Decomposition (C-HiDeNN-TD): a scalable surrogate modeling approach for large-scale physical systems |
| topic | Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2409.00329 |