Unveiling descriptors for predicting the bulk modulus of amorphous carbon

Descriptors for the bulk modulus of amorphous carbon are investigated through the implementation of data mining where data sets are prepared using first-principles calculations. Data mining reveals that the number of bonds in each C atom and the density of amorphous carbon are found to be descriptors representing the bulk modulus. Support vector regression (SVR) within machine learning is implemented and descriptors are trained where trained SVR is able to predict the bulk modulus of amorphous carbon. An inverse problem, starting from the bulk modulus towards structural information of amorphous carbon, is performed and structural information of amorphous carbon is successfully predicted from the desired bulk modulus. Thus, treating several physics factors in multidimensional space allows for the prediction of physical phenomena. In addition, the reported approach proposes that “big data” can be generated from a small data set using machine learning if descriptors are well defined. This would greatly change how amorphous carbon would be treated and help accelerate further development of amorphous carbon materials.

Figure 1

Proposed workflow model for predicting the structure of amorphous carbon from properties using first-principles calculation and data science.

Figure 2

Predicted bulk modulus against true bulk modulus with descriptors: (a) the number of bonds in each C atom and (b) the number of bonds in each C atom with density. Structure models of bond type in amorphous carbon are also shown.

Figure 3

Cross-validation of bulk modulus with randomly sorted data set of $80\%$ of trained data and $20\%$ of test data where the following descriptors are used: the number of bonds in each C atom with density.

Figure 4

Projector density of state of C atom in (a) $s{p}^2$ in amorphous carbon and (b) $s{p}^2$ in graphene. Structures of $s{p}^2$ in amorphous carbon and graphene are also shown.