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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.02411 |
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| _version_ | 1866916472812470272 |
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| author | Pan, Cunliang Li, Chengxuan Liu, Yu Zheng, Yonggang Ye, Hongfei |
| author_facet | Pan, Cunliang Li, Chengxuan Liu, Yu Zheng, Yonggang Ye, Hongfei |
| contents | The automatic differentiation (AD) in the vanilla physics-informed neural networks (PINNs) is the computational bottleneck for the high-efficiency analysis. The concept of derivative discretization in smoothed particle hydrodynamics (SPH) can provide an accelerated training method for PINNs. In this paper, smoothing kernel physics-informed neural networks (SK-PINNs) are established, which solve differential equations using smoothing kernel discretization. It is a robust framework capable of solving problems in the computational mechanics of complex domains. When the number of collocation points gradually increases, the training speed of SK-PINNs significantly surpasses that of vanilla PINNs. In cases involving large collocation point sets or higher-order problems, SK-PINN training can be up to tens of times faster than vanilla PINN. Additionally, analysis using neural tangent kernel (NTK) theory shows that the convergence rates of SK-PINNs are consistent with those of vanilla PINNs. The superior performance of SK-PINNs is demonstrated through various examples, including regular and complex domains, as well as forward and inverse problems in fluid dynamics and solid mechanics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02411 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | SK-PINN: Accelerated physics-informed deep learning by smoothing kernel gradients Pan, Cunliang Li, Chengxuan Liu, Yu Zheng, Yonggang Ye, Hongfei Computational Physics The automatic differentiation (AD) in the vanilla physics-informed neural networks (PINNs) is the computational bottleneck for the high-efficiency analysis. The concept of derivative discretization in smoothed particle hydrodynamics (SPH) can provide an accelerated training method for PINNs. In this paper, smoothing kernel physics-informed neural networks (SK-PINNs) are established, which solve differential equations using smoothing kernel discretization. It is a robust framework capable of solving problems in the computational mechanics of complex domains. When the number of collocation points gradually increases, the training speed of SK-PINNs significantly surpasses that of vanilla PINNs. In cases involving large collocation point sets or higher-order problems, SK-PINN training can be up to tens of times faster than vanilla PINN. Additionally, analysis using neural tangent kernel (NTK) theory shows that the convergence rates of SK-PINNs are consistent with those of vanilla PINNs. The superior performance of SK-PINNs is demonstrated through various examples, including regular and complex domains, as well as forward and inverse problems in fluid dynamics and solid mechanics. |
| title | SK-PINN: Accelerated physics-informed deep learning by smoothing kernel gradients |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2411.02411 |