Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning

• URL: http://arxiv.org/abs/2003.12081v2
• Date: Tue, 9 Feb 2021 18:16:16 GMT
• Title: Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning
• Authors: Marcel F. Langer, Alex Goe{\ss}mann, Matthias Rupp
• Abstract summary: Computational study of molecules and materials from first principles is a cornerstone of physics, chemistry, and materials science. In settings involving many simulations, machine learning can reduce these costs, often by orders of magnitude, by interpolating between reference simulations. We comprehensively review and discuss current representations and relations between them, using a unified mathematical framework.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Computational study of molecules and materials from first principles is a cornerstone of physics, chemistry, and materials science, but limited by the cost of accurate and precise simulations. In settings involving many simulations, machine learning can reduce these costs, often by orders of magnitude, by interpolating between reference simulations. This requires representations that describe any molecule or material and support interpolation. We comprehensively review and discuss current representations and relations between them, using a unified mathematical framework based on many-body functions, group averaging, and tensor products. For selected state-of-the-art representations, we compare energy predictions for organic molecules, binary alloys, and Al-Ga-In sesquioxides in numerical experiments controlled for data distribution, regression method, and hyper-parameter optimization.

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