# Regensburg 2019 – wissenschaftliches Programm

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# MM: Fachverband Metall- und Materialphysik

## MM 33: Topical session (Symposium MM): Big Data Analytics in Materials Science

### MM 33.4: Vortrag

### Donnerstag, 4. April 2019, 11:15–11:30, H43

**Symmetry-invariant basis representations for machine- learning of electronic structure data beyond energies** — •Michael Luya^{1, 2} and Reinhard J. Maurer^{2} — ^{1}Department of Mathematics, University of Warwick, Coventry, United Kingdom — ^{2}Department of Chemistry, University of Warwick, Coventry, United Kingdom

Recent successes on the high-dimensional machine-learning-based (ML) interpolation of total energies and forces from ab-initio computations are extremely encouraging for the future role that machine-learning can play in condensed matter simulation and electronic structure theory. Beyond scalar energy fields, ML can be useful to find efficient representations of quantum mechanical interaction integrals and Hamiltonians in atomic orbital basis representations. These represent tensor fields, which, contrary to scalar fields, feature covariance properties and additional directional coordinate dependence that need to be addressed.

Here we present an approach based on a generalisation of Slater-Koster transformation and symmetry-adaptation to transform interaction integrals and Hamiltonians from electronic structure theory in atomic-orbital representation into rotationally invariant forms that are amenable to established machine learning methods. We validate our approach on a large set of training data on simple organic molecules of varying size.