| *Model*         | *Citation*                                          | *Type*      | *CSSP* | *NN* | *Defects* | *Spin* | *Symmetry*  |
|-----------------+-----------------------------------------------------+-------------+--------+------+-----------+--------+-------------|
| AutoML          | \cite{conradBenchmarkingAutoMLRegression2022}       | Composition | X      |      |           | -      | -           |
|-----------------+-----------------------------------------------------+-------------+--------+------+-----------+--------+-------------|
| Coulomb matrix  | \cite{ruppFastAccurateModeling2012}                 | Descriptor  |        |      |           | -      | explicit    |
| SOAP            | \cite{bartokRepresentingChemicalEnvironments2013a}  | Descriptor  |        |      |           | -      | explicit    |
| Alchemical SOAP | \cite{lopanitsynaModelingHighentropyTransition2023} | Potential   | X      |      |           | -      | explicit    |
| Disordered SOAP | \cite{sommer3DSCDatasetSuperconductors2023}         | Descriptor  |        |      | X         | -      | explicit    |
| GAP             | \cite{bartokGaussianApproximationPotentials2010}    | Potential   | X      |      |           | ?      | explicit    |
| ACE             | \cite{bochkarevEfficientParametrizationAtomic2022}  | Potential   |        |      |           | -      | explicit    |
|-----------------+-----------------------------------------------------+-------------+--------+------+-----------+--------+-------------|
| MEGNetSparse    | \cite{kazeevSparseRepresentationMachine2023}        | Potential   | X      | X    | X         | -      | explicit    |
| MACE            | \cite{batatiaMACEHigherOrder2022}                   | Potential   | X      | X    |           | -      | explicit    |
| MACE-MP         | \cite{batatiaFoundationModelAtomistic2023}          | UIP         | X      | X    |           | -      | explicit    |
|-----------------+-----------------------------------------------------+-------------+--------+------+-----------+--------+-------------|
| Magnetic ACE    | \cite{rinaldiNoncollinearMagneticAtomic2024}        | Potential   |        |      |           | noco   | explicit    |
| SpinGNN++       | \cite{yuGeneralTimereversalEquivariant2024}         | Potential   | X      | X    |           | noco   | explicit    |
| CHGNet          | \cite{dengCHGNetPretrainedUniversal2023a}           | UIP         | X      | X    |           | coll   | explicit    |
| SNRep           | \cite{dominaSpectralNeighborRepresentation2022}     | Potential   |        |      |           | coll   | explicit    |
| PET             | \cite{pozdnyakovSmoothExactRotational2024}          | Potential   | ?      | X    |           | coll   | approximate |