List of representations used for inverse design (HTVS and GM) of inorganic solid materials. Invertibility is the existence of inverse transform from representation to crystal structure, and invariance refers to the invariance of representation to translation, rotation, and unit cell repeat. The models and target applications are also listed for each reference.

Representation	Invertibility	Invariance	Model	Application
Supervised learning (property prediction in HTVS)
Atomic properties56,57	No	Yes	SVR	Predicting melting temperature, bulk and shear modulus, bandgap
Crystal site-based representation20	Yes	Yes	KRR	Predicting formation energy of ABC2D6 elpasolite structures
Average atomic properties22	No	Yes	Ensembles of decision trees	Predicting the formation energy of inorganic crystal structures
Voronoi-tessellation-based representation58	No	Yes	Random forest	Predicting the formation energy of quaternary Heusler compounds
Crystal graph24	No	Yes	GCNN	Predicting formation enthalpy of inorganic compounds
Unsupervised learning (GM)
3D atomic density59,79	Yes	No	VAE	Generation of inorganic crystals
3D atomic density and energy grid shape60	Yes	No	GAN	Generation of porous materials
Lattice site descriptor61	Yes	No	GAN	Generation of graphene/BN-mixed lattice structures
Unit cell vectors and coordinates36,62	Yes	No	GAN	Generation of inorganic crystals