Performance metrics for tensorial learning: prediction of Li4Ti5O12 nuclear magnetic resonance observables at experimental accuracy

Abstract

Predicting observable quantities from first principles calculations is the next frontier within the field of machine learning (ML) for materials modelling. While ML models have shown success for the prediction of scalar properties such as energetics or band gaps, models and performance metrics for the learning of higher order tensor-based observables have not yet been formalized. In this work, we establish performance metrics for accurately predicting the electric field gradient tensor (EFG) underlying nuclear magnetic resonance (NMR) spectroscopy. We further demonstrate the superiority of a tensorial learning approach that fully encodes the corresponding symmetries over a separate scalar learning of individual tensor-derived observables. To this end we establish an extensive EFG data set representative of real experimental applications and develop performance metrics for model evaluation which directly focus on the targeted NMR observables. Finally, by leveraging the computational efficiency of the ML method employed, we predict quadrupolar observables for 1512 atom models of Li₄Ti₅O₁₂, a high performance Li-ion battery anode material, which is capable of accurately distinguishing local atomic environments via their NMR observables. This workflow and dataset sets the standard for the next generation of tensorial based learning for spectroscopic observables.