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.

基于操作符学习的数值均匀化模型HomoGenius，可快速提供任意几何、材料和分辨率的均匀化结果，比传统数值均匀化方法效率提高了80倍，且具有高精度、超高效和学习能力。

HomoGenius: 利用神经算子快速预测有效力学性能的均质化基础模型