Numerical Homogenization

Numerical homogenization aims to efficiently predict the macroscopic properties of heterogeneous materials from their microscopic structure, avoiding computationally expensive simulations of the entire material. Current research focuses on developing surrogate models, often employing neural networks (including deep operator networks and graph kernel networks) or fast Fourier transforms, to accelerate this process and enable inverse design capabilities. These advancements are significantly improving the speed and accuracy of multiscale simulations across various fields, such as material science and engineering, facilitating the design and optimization of novel materials with tailored properties.