Core Concepts
The proposed HomoGenius model can quickly and accurately predict the effective mechanical properties of complex periodic materials, such as Triply Periodic Minimal Surfaces (TPMS), by integrating operator learning techniques into the homogenization process.
Abstract
The paper introduces a foundation model called HomoGenius for efficient and accurate numerical homogenization of complex periodic materials. Key highlights:
HomoGenius utilizes the Fourier neural operator as its backbone, which can predict the required displacement fields for homogenization up to 1,000 times faster than traditional finite element methods, while maintaining high accuracy.
The model demonstrates exceptional performance across various TPMS geometries, materials with different Poisson's ratios, and different resolutions. Compared to finite element reference solutions, HomoGenius achieves an average relative error of only 1.58% in predicting the effective elastic modulus.
By integrating data across different resolutions, HomoGenius showcases a flexible learning capability, allowing it to be trained on low-resolution data and tested on high-resolution data without significant performance degradation.
The core innovation of HomoGenius is the integration of operator learning techniques, particularly the Fourier neural operator, into the numerical homogenization process to dramatically improve computational efficiency while retaining high accuracy.
Stats
The effective elastic modulus computed by HomoGenius is within 5% of the reference finite element solution, with an average relative error of only 1.60%.
The prediction of displacement fields by HomoGenius is nearly 1,000 times faster than traditional finite element analysis.
Quotes
"Compared to traditional finite element analysis, HomoGenius can enhance the overall homogenization speed by approximately 80 times."
"Training on a dataset with a resolution of 32 results in larger errors primarily due to the insufficient resolution of the training data. This leads to non-negligible geometric discretization errors, meaning that even the best model will still incur this type of error."