HomoGenius: a Foundation Model of Homogenization for Rapid Prediction of
  Effective Mechanical Properties using Neural Operators
Yizheng Wang Xiang Li Ziming Yan Yuqing Du Jinshuai Bai Bokai Liu Timon Rabczuk Yinghua Liu
Homogenization is an essential tool for studying multiscale physical
phenomena. However, traditional numerical homogenization, heavily reliant on
finite element analysis, requires extensive computation costs, particularly in
handling complex geometries, materials, and high-resolution problems. To
address these limitations, we propose a numerical homogenization model based on
operator learning: HomoGenius. The proposed model can quickly provide
homogenization results for arbitrary geometries, materials, and resolutions,
increasing the efficiency by a factor of 80 compared to traditional numerical
homogenization methods. We validate effectiveness of our model in predicting
the effective elastic modulus on periodic materials (TPMS: Triply Periodic
Minimal Surface), including complex geometries, various Poisson's ratios and
elastic modulus, and different resolutions for training and testing. The
results show that our model possesses high precision, super efficiency, and
learning capability.