Fig. 1. The process of specific machine learning in materials science. (a) Schematic view of an example data set; (b) statement of the learning problem; (c) creation of a surrogate prediction model via the fingerprinting and learning steps [43].

Fig. 2. Common machine learning algorithms in materials science.

Fig. 3. Icosahedral quasicrystal data set phase diagrams generated by unsupervised Gaussian Mixture Models (GMMs).

Fig. 4. Flow chart of the computational methodology adopted for designing pipeline steel [77].

Fig. 5. Mean absolute error (MAE in kcal/mol) for BoB and polynomial models: Training sets from N?=?500 to 7000 data points were sampled identically for the different methods. The polynomial models of degree 10 and 18 exhibit high variances due to the random stratification, which for small N leads to nonrobust fits [133].

Fig. 6. (Color online) EHL - α log-log plot of the molecule dataset, shown by green symbols, with the predicted fingerprints shown by red diamonds within the regime of desired properties, i.e.,0.6≤α≤0.7??3/atom and EHL≥7.0?eV. In the inset, the predicted and calculated properties of the molecules reconstructed from three predicted fingerprints, i.e., C, D, and E, are shown by solid and open symbols: triangles for C, circles for D, and squares for E. The dashed line sketches the limit α ～ 1/EHL addressed in the text [137].

Fig. 7. Imaging techniques (top panels) allow direct measurements of atomic positions and hence bond lengths and angles, local functionalities including chemical states, dielectric properties, and superconductive gap, visualizing atomic, molecular, and defect dynamics in real time, and offers possibilities to control of matter on the molecular and atomic level. In parallel, theoretical methods (bottom panels) allow detailed studies of atomic and electronic structure and dynamics of matter along with prediction of their properties. However, almost lacking are the pathways to bridge theory and experiment. The new advances in data analytics and scientific inference are capable of treating large volumes of data/information and hence linking theory to experiment via microscopic degrees of freedom (middle panels). For example, efficiently matching imaging information about static structure to theoretical simulations on the same material (1?st column) or similarly, the dynamics of oxygen vacancies in materials to corresponding molecular dynamics simulation (3rd column) [4].