A Pretraining-Finetuning Computational Framework for Material Homogenization
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arXiv
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| Format: | Preprint |
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2024
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| author | Wang, Yizheng Li, Xiang Yan, Ziming Ma, Shuaifeng Bai, Jinshuai Liu, Bokai Rabczuk, Timon Liu, Yinghua |
| author_facet | Wang, Yizheng Li, Xiang Yan, Ziming Ma, Shuaifeng Bai, Jinshuai Liu, Bokai Rabczuk, Timon Liu, Yinghua |
| contents | Homogenization is a fundamental tool for studying multiscale physical phenomena. Traditional numerical homogenization methods, heavily reliant on finite element analysis, demand significant computational resources, especially for complex geometries, materials, and high-resolution problems. To address these challenges, we propose PreFine-Homo, a novel numerical homogenization framework comprising two phases: pretraining and fine-tuning. In the pretraining phase, a Fourier Neural Operator (FNO) is trained on large datasets to learn the mapping from input geometries and material properties to displacement fields. In the fine-tuning phase, the pretrained predictions serve as initial solutions for iterative algorithms, drastically reducing the number of iterations needed for convergence. The pretraining phase of PreFine-Homo delivers homogenization results up to 1000 times faster than conventional methods, while the fine-tuning phase further enhances accuracy. Moreover, the fine-tuning phase grants PreFine-Homo unlimited generalization capabilities, enabling continuous learning and improvement as data availability increases. We validate PreFine-Homo by predicting the effective elastic tensor for 3D periodic materials, specifically Triply Periodic Minimal Surfaces (TPMS). The results demonstrate that PreFine-Homo achieves high precision, exceptional efficiency, robust learning capabilities, and strong extrapolation ability, establishing it as a powerful tool for multiscale homogenization tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07943 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Pretraining-Finetuning Computational Framework for Material Homogenization Wang, Yizheng Li, Xiang Yan, Ziming Ma, Shuaifeng Bai, Jinshuai Liu, Bokai Rabczuk, Timon Liu, Yinghua Computational Engineering, Finance, and Science Machine Learning Homogenization is a fundamental tool for studying multiscale physical phenomena. Traditional numerical homogenization methods, heavily reliant on finite element analysis, demand significant computational resources, especially for complex geometries, materials, and high-resolution problems. To address these challenges, we propose PreFine-Homo, a novel numerical homogenization framework comprising two phases: pretraining and fine-tuning. In the pretraining phase, a Fourier Neural Operator (FNO) is trained on large datasets to learn the mapping from input geometries and material properties to displacement fields. In the fine-tuning phase, the pretrained predictions serve as initial solutions for iterative algorithms, drastically reducing the number of iterations needed for convergence. The pretraining phase of PreFine-Homo delivers homogenization results up to 1000 times faster than conventional methods, while the fine-tuning phase further enhances accuracy. Moreover, the fine-tuning phase grants PreFine-Homo unlimited generalization capabilities, enabling continuous learning and improvement as data availability increases. We validate PreFine-Homo by predicting the effective elastic tensor for 3D periodic materials, specifically Triply Periodic Minimal Surfaces (TPMS). The results demonstrate that PreFine-Homo achieves high precision, exceptional efficiency, robust learning capabilities, and strong extrapolation ability, establishing it as a powerful tool for multiscale homogenization tasks. |
| title | A Pretraining-Finetuning Computational Framework for Material Homogenization |
| topic | Computational Engineering, Finance, and Science Machine Learning |
| url | https://arxiv.org/abs/2404.07943 |