The deep material network can be used to learn the proper topological structure of a given RVE. In the following example, treemaps of trained material networks for three different 2D RVEs with network depth  after 10000 epochs (1% training error) are shown.

Material networks can also be trained for 3D RVEs. Applications to polymer nanocomposite and CFRP systems are addressed.

Geometric RVE information, such as the volume fraction, can be accurately extracted from pure mechanical data. The material network is intrinsically parameterized for material design purpose.

Other than the virtual material testing data from RVE analysis, experimental data can also be incorporated in the offline-training process.

Histories of training and validation errors

Evolution of topological structures of 2D and 3D material networks