On-the-Fly Machine Learning of Atomic Potential in Density Functional Theory Structure Optimization

Machine learning (ML) is used to derive local stability information for density functional theory calculations of systems in relation to the recently discovered ${\mathrm{SnO}}_2(110)\text{−}(4\times 1)$ reconstruction. The ML model is trained on (structure, total energy) relations collected during global minimum energy search runs with an evolutionary algorithm (EA). While being built, the ML model is used to guide the EA, thereby speeding up the overall rate by which the EA succeeds. Inspection of the local atomic potentials emerging from the model further shows chemically intuitive patterns.

Figure 1

Atoms of a ${\mathrm{SnO}}_2(110)$ surface structure are highlighted to match their individual contributions ${\mathbf{g}}_{i,Z}$ to the full fingerprint feature vector.

Figure 2

(a) Correlations between KRR predicted total energies and DFT total energies, and (b) the learning curve of the KRR model for predicting total energies, where $N$ is the number of training structures. Atomic potential correlations between values from KRR and DFT for (c) O atoms and (d) Sn atoms. The squared correlation coefficient is shown in (a), (c), and (d).

Figure 3

Top: Coordination numbers of O and Sn as a function of the predicted atomic potentials. The color scale (blue to red) shows the density of data points. Bottom: An example structure with a motif (encircled in green) which is also present in the global minimum. Atoms are colored according to their atomic potential.

Figure 4

Cumulative success rate for the benchmark and ML enhanced EA runs.