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Impact of quantum-chemical metrics on the machine learning prediction of electron density

Ksenia R. Briling1*, Alberto Fabrizio1, Clemence Corminboeuf1*

1 Institut des Sciences et Ingénierie Chimiques, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

* Corresponding authors emails: ksenia.briling@epfl.ch, clemence.corminboeuf@epfl.ch
DOI10.24435/materialscloud:d8-0h [version v1]

Publication date: Jun 28, 2021

How to cite this record

Ksenia R. Briling, Alberto Fabrizio, Clemence Corminboeuf, Impact of quantum-chemical metrics on the machine learning prediction of electron density, Materials Cloud Archive 2021.96 (2021), doi: 10.24435/materialscloud:d8-0h.


Machine learning (ML) algorithms have undergone an explosive development impacting every aspect of computational chemistry. To obtain reliable predictions, one needs to maintain the proper balance between the black-box nature of ML frameworks and the physics of the target properties. One of the most appealing quantum-chemical properties for regression models is the electron density, and some of us recently proposed a transferable and scalable model based on the decomposition of the density onto an atom-centered basis set. The decomposition, as well as the training of the model, is at its core a minimization of some loss function, which can be arbitrarily chosen and may lead to results of different quality. Well-studied in the context of density fitting (DF), the impact of the metric on the performance of ML models has not been analyzed yet. In this work, we compare predictions obtained using the overlap and the Coulomb repulsion metrics for both the decomposition and training. As expected, the Coulomb metric used as both the DF and ML loss functions leads to the best results for the electrostatic potential and dipole moments. The origin of this difference lies in the fact that the model is not constrained to predict densities that integrate to the exact number of electrons N. Since an a posteriori correction for the number of electrons decreases the errors, we proposed a modification of the model where N is included directly into the kernel function, which allowed to lower the errors on the test and out-of-sample sets.

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592.2 MiB Tar ball containing decomposition coefficients for the electron density using all metrics, electrostatic potentials, geometries, predicted coefficients, regression weights, and tables containing numerical data relevant to the paper.


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Machine Learning Quantum Chemical Metrics Correction Number of Electrons EPFL MARVEL/DD1 SNSF ERC

Version history:

2021.96 (version v1) [This version] Jun 28, 2021 DOI10.24435/materialscloud:d8-0h