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

Machine learning (ML) surrogate modeling is a powerful approach to reduce the computational cost of first-principles calculations. While well established for the prediction of scalar observables like energetics or band gaps, performance metrics for the learning of tensor-based observables have not yet been formalized. Here we use the electric field tensor (EFG) underlying nuclear magnetic resonance (NMR) spectroscopy to demonstrate and quantify the superiority of a tensorial learning 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. Our results relate the inferiority of symmetry-agnostic scalar learning especially to its inability to capture the orientation of the EFG tensor. Tensorial learning instead achieves results within experimental precision at a high learning rate.