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@ARTICLE{Harper:1046210,
      author       = {Harper, Angela F and Köcher, Simone Swantje and Reuter,
                      Karsten and Scheurer, Christoph},
      title        = {{P}erformance metrics for tensorial learning: prediction of
                      {L}i4{T}i5{O}12 nuclear magnetic resonance observables at
                      experimental accuracy},
      journal      = {Journal of materials chemistry / A},
      volume       = {13},
      issn         = {2050-7488},
      address      = {London ˜[u.a.]œ},
      publisher    = {RSC},
      reportid     = {FZJ-2025-03746},
      pages        = {35389–35399},
      year         = {2025},
      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. 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. 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.},
      cin          = {IET-1},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IET-1-20110218},
      pnm          = {1223 - Batteries in Application (POF4-122)},
      pid          = {G:(DE-HGF)POF4-1223},
      typ          = {PUB:(DE-HGF)16},
      doi          = {10.1039/D5TA05090A},
      url          = {https://juser.fz-juelich.de/record/1046210},
}