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

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. ML models for experimental observables, including tensorial quantities, are essential for exploiting the full potential of the paradigm shift enabled by machine learned interatomic potentials by mapping the structure-property relationship in an equally efficient way.

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 dataset representative of real experimental applications and develop performance metrics for model evaluation which directly focus on the targeted NMR observables.