Paper ID: 2404.07943 • Published Mar 18, 2024
A Pretraining-Finetuning Computational Framework for Material Homogenization
Yizheng Wang, Xiang Li, Ziming Yan, Shuaifeng Ma, Jinshuai Bai, Bokai Liu, Timon Rabczuk, Yinghua Liu
TL;DR
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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.