chemistry, and biology are innumerable. To give some examples, simulations for crystal structure prediction, drug development, materials aging, and high strain/strain-rate deformation would all benefit tremendously from better interatomic potentials.

Machine learning (ML) of interatomic potentials is a rapidly advancing research topic. ML potentials have been fit to a variety of datasets including materials [@Behler2007; @Handley2014; @Szlachta2014; @Li2015; @Thompson2015SpectralPotentials; @Kruglov2017; @Huan2017; @Jindal2017; @Botu2017MachineOutlook; @Schutt2018; @Deringer2018ComputationalTheory; @Suwa2019MachineElectrons; @Pozdnyakov2019FastPotential; @Liu2020StructurePotential] and molecules [@Morawietz2012ACharges; @Smith2017; @Yao2017ThePhysics; @Lubbers2018; @Nguyen2018ComparisonExpansions; @Gastegger2017MachineSpectra; @Smith2019ApproachingLearning; @Schran2019AutomatedGround]. The datasets are calculated from computationally expensive *ab initio* quantum mechanics (QM) methods, most commonly density functional theory (DFT) [@Engel2011DensityTheory]. Trained on this data, the model can predict energy and forces for new atomic configurations. ML potentials should exactly encode translation, rotation, and permutation symmetries. Forces should also be calculated as the exact gradient of the predicted energy. Another important ingredient is an assumption of spatial locality: each atomic force only depends on neighboring atoms within a fixed radius, typically of order 5 to [${10}\,\mathrm{{\textup{\AA}}}$]{}. Long-range Coulomb interactions or dispersion corrections may be added [@Yao2017ThePhysics; @Unke2019PhysNet:Charges].

Compared to ML models, classical potentials have highly restrictive functional forms that might not be appropriate for the full space of atomic configurations. A common challenge, 