HomoGenius: a Foundation Model of Homogenization for Rapid Prediction of Effective Mechanical Properties using Neural Operators

The core idea of the homogenization method is to use a mathematical model to simplify the complex structural behavior on the microscale to a homogenized representation on the macroscale. The homogenization method plays an important role in the field of mechanics and engineering. The homogenization method in mechanics allows researchers to predict the mechanical behavior at the macroscale from the material structures at the microscale. In this way, researchers can perform the mechanical analysis only on the macro-level model while maintaining an acceptance level of accuracy in the analysis, significantly reducing the complexity and cost of the calculations [1, 2, 3]. For example, researchers have applied homogenization methods to study the macroscopic material properties of various materials, such as fiber-reinforced composites [4], particulate composites [5], laminated composites [6]; metamateiral such as photonic crystals [7], phononic crystals [8], auxetic materials with negative Poisson's ratio [9], electromagnetic metamaterial [10]; porous media such as rock [11], wood [12], trabecular bone [13, 14], lattice materials [15, 16], various cellular materials [17, 18, 19], functionally graded materials [20, 21].