Quantum mechanics and machine learning
Quantum mechanics (QM), the theory of matter at atomic scale, allows calculation of virtually any property of a molecule or material. However, accurate numerical procedures scale as highorder polynomials in system size, preventing applications to large systems, long time scales, or big data sets. Machine learning (ML) provides algorithms that identify nonlinear relationships in large highdimensional data sets via induction. Our research focuses on models that combine QM with ML. These QM/ML models use ML to interpolate between QM reference calculations, yielding speedups of up to several orders of magnitude when the same QM procedure is carried out for a large number of similar inputs, e.g., in virtual screening, molecular dynamics, or selfconsistent field calculations. We are particularly interested in models that generalize across chemical compound space.

M. Rupp, A. Tkatchenko, K.R. Müller, O.A. von Lilienfeld: Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning, Physical Review Letters 108(5): 058301, 2012. [doi] [pdf]
We use machine learning to predict DFT atomization energies of a diverse set of 7k small organic molecules with an accuracy of 10 kcal/mol, introducing the Coulomb matrix representation to compare different molecules. In followup studies, we extend our approach to different properties at various levels of theories, analyzing datasets as large as 134k molecules, and achieving accuracies below 1 kcal/mol.

 J.C. Snyder, M. Rupp, K. Hansen, L. Blooston, K.R. Müller, K. Burke: Orbitalfree Bond Breaking via Machine Learning, Journal of Chemical Physics, 139(22): 224104, 2013. [doi] [pdf]
 J.C. Snyder, M. Rupp, K. Hansen, K.R. Müller, K. Burke: Finding Density Functionals with Machine Learning, Physical Review Letters 108(25): 253002, 2012. [doi] [pdf]
Machine learning is used to estimate the map from electron densities to their kinetic energy in a onedimensional model potential. With few reference calculations, errors are smaller than typical errors of many exchangecorrelation functionals. In followup studies, we introduce nonlinear gradient denoising to find highly accurate selfconsistent densities, successfully dissociating chemical bonds.