MEIDNet (shorter training)

The architecture of the published model, trained for fewer epochs.

field	value
Dataset	Perov-5, protocol perov5-v1.1
Type	model
Inputs	structure, property:heat_all, property:dir_gap
Parameters	0.70 M
Training data	Perov-5, all 18,928 materials (the test split included: scores on it are not held-out)
Status	Computed here on 2026-10-05
Evidence level	MLIP validated
Added	2026-10-03 by Anand Babu (UCLouvain)
Alignment space	the outputs of the projection heads (what the decoders read)
Checkpoint	dual_autoencoder_clip_earlyfusion_propertyaware.pth · sha256 b1a672d7e28c…
Links	paper · code · weights

Property prediction

metric	value	definition
MAE ΔH	1.009 eV/atom	mean absolute error of the formation enthalpy (heat_all)
RMSE ΔH	1.391 eV/atom	root-mean-square error of the formation enthalpy
R² ΔH	-2.495	coefficient of determination of the formation enthalpy (0 = no better than the mean)
MAE gap	3.292 eV	mean absolute error of the direct band gap over all test materials; 96% of them have a gap of 0 eV
MAE gap > 0	1.978 eV	mean absolute error of the direct band gap on the test materials with a non-zero gap, the range that inverse design targets
RMSE gap	3.392 eV	root-mean-square error of the direct band gap
R² gap	-39.038	coefficient of determination of the direct band gap; not informative here, because the gap is zero for most materials
MAE ΔH ≠ 0	1.009 eV/atom	mean absolute error of the formation enthalpy on materials where it is not zero
n	3,785	test materials evaluated

MEIDNet (shorter training): formation enthalpy, predicted vs. DFT

MEIDNet (shorter training): direct band gap, predicted vs. DFT

Representation

metric	value	definition
R@1	0.297	fraction of test materials for which, among the distinct property profiles of the test split, their own profile's latent is the nearest to their structure latent (materials with identical property values share one profile)
R@5	0.848	the same within the five nearest profiles
cos	0.480	mean cosine similarity between the structure latent and the property latent of the same material, in the space where the model aligns them (before or after its projection heads; stated on the method's page)
k-NN MAE ΔH	0.024 eV/atom	formation-enthalpy error of a 5-nearest-neighbour probe: each test material takes the mean property of its five nearest training materials in the representation
k-NN MAE gap	0.047 eV	direct-band-gap error of the same probe
L2	1.019	mean L2 distance between the two latents of the same material (unit latents)
cos, encoder outputs	0.003	the matched cosine between the normalised encoder outputs, before the projection heads
cos, projection heads	0.480	the matched cosine between the outputs of the projection heads
profiles	367	distinct property profiles among the test materials: the candidates of retrieval (chance level of R@1 is one over this number)
n	3,785	test materials evaluated

Inverse design

metric	value	definition
SUN	0.556	stable, unique and novel candidates divided by the budget of 54; a candidate that was not delivered counts as a failure
Stable	0.923	fraction of delivered candidates whose MACE-MP-0 formation energy after relaxation is at most 0.10 eV/atom, against elemental reference phases (the criterion of meidnet screen and of the paper)
Unique	1.000	fraction of delivered candidates whose composition does not repeat an earlier one
Novel	0.654	fraction of delivered candidates whose composition is not in the data set (training, validation and test splits)
ΔHf	-1.50 eV/atom	median MACE-MP-0 formation energy of the delivered candidates
DFT hit	0.056	among candidates whose A, B and X sites match a Perov-5 entry (so their DFT band gap is known), the fraction within 0.5 eV of the target
DFT known	18	candidates with a known DFT band gap (the denominator of DFT hit)
Delivered	52	candidates delivered out of the budget of 54
Valid	0.963	fraction of the budget that passes every rule of the family
SUN count	30	stable, unique and novel candidates
Budget	54	candidates requested

Candidates

Every candidate with its MLIP formation energy, novelty and, where Perov-5 has the same sites, the DFT band gap.

candidate	formula	target gap (eV)	ΔHf (eV/atom)	stable	novel	DFT gap (eV)
oxide_T1_1	CsTaO3	1.5	-2.671	yes	no	3.50
oxide_T1_2	LaScO3	1.5	-3.629	yes	no	6.40
oxide_T1_3	LaFeO3	1.5	-2.155	yes	no	0.00
oxide_T1_4	BaSnO3	1.5	-2.476	yes	no	2.50
oxide_T1_5	KTaO3	1.5	-2.930	yes	no	5.00
oxide_T1_6	SrVO3	1.5	-2.416	yes	no	0.00
oxide_T2_1	BaZrO3	2.5	-3.513	yes	no	6.30
oxide_T2_2	RbNbO3	2.5	-2.632	yes	no	3.90
oxide_T2_3	CaHfO3	2.5	-3.529	yes	no	7.30
oxide_T2_4	LaMnO3	2.5	-2.467	yes	no	0.00
oxide_T2_5	SrHfO3	2.5	-3.645	yes	no	7.20
oxide_T2_6	SrGeO3	2.5	-2.485	yes	no	1.70
oxide_T3_1	CaGeO3	3.5	-2.460	yes	no	2.70
oxide_T3_2	CsNbO3	3.5	-2.475	yes	no	2.90
oxide_T3_3	NaTaO3	3.5	-2.902	yes	no	5.30
oxide_T3_4	BaPbO3	3.5	-1.970	yes	no	0.00
oxide_T3_5	LaCoO3	3.5	-2.084	yes	no	0.00
oxide_T3_6	BaTiO3	3.5	-3.364	yes	no	4.00
chalcogenide_T1_1	LaScTe3	1.5	-1.884	yes	yes	–
chalcogenide_T1_2	BaGeS3	1.5	-656.803	no	yes	–
chalcogenide_T1_3	LaVTe3	1.5	-1.539	yes	yes	–
chalcogenide_T1_4	BaWS3	1.5	3221614596037021.000	no	yes	–
chalcogenide_T1_5	CaWTe3	1.5	-1.046	yes	yes	–
chalcogenide_T1_6	BaZrTe3	1.5	-2.002	yes	yes	–
chalcogenide_T2_1	RbNbTe3	2.5	-1.355	yes	yes	–
chalcogenide_T2_2	CsTaTe3	2.5	-1.295	yes	yes	–
chalcogenide_T2_3	LaCrTe3	2.5	-1.485	yes	yes	–
chalcogenide_T2_4	KNbTe3	2.5	-1.338	yes	yes	–
chalcogenide_T2_5	BaWTe3	2.5	-1.310	yes	yes	–
chalcogenide_T2_6	LaFeTe3	2.5	-1.514	yes	yes	–
chalcogenide_T3_1	CaGeTe3	3.5	-1.081	yes	yes	–
chalcogenide_T3_2	CaMoS3	3.5	-2720.939	no	yes	–
chalcogenide_T3_3	NaTaTe3	3.5	-1.146	yes	yes	–
chalcogenide_T3_4	LaCoS3	3.5	-2.544	yes	yes	–
chalcogenide_T3_5	CaWS3	3.5	-33543487.666	no	yes	–
chalcogenide_T3_6	CaHfTe3	3.5	-1.617	yes	yes	–
halide_T1_1	NaFeI3	1.5	-0.553	yes	yes	–
halide_T1_2	NaNiI3	1.5	-0.723	yes	yes	–
halide_T1_3	RbMnI3	1.5	-1.123	yes	yes	–
halide_T1_4	CsZnI3	1.5	-1.165	yes	yes	–
halide_T1_5	RbSnI3	1.5	-1.194	yes	yes	–
halide_T1_6	RbPbI3	1.5	-1.240	yes	yes	–
halide_T2_1	CsPbI3	2.5	-1.302	yes	yes	–
halide_T2_2	KPbI3	2.5	-1.186	yes	yes	–
halide_T2_3	RbFeI3	2.5	-0.773	yes	yes	–
halide_T2_4	KFeI3	2.5	-0.737	yes	yes	–
halide_T2_5	KZnI3	2.5	-1.102	yes	yes	–
halide_T2_6	CsMnI3	2.5	-1.160	yes	yes	–
halide_T3_1	NaZnI3	3.5	-0.928	yes	yes	–
halide_T3_2	KCuI3	3.5	-0.892	yes	yes	–
halide_T3_3	NaMnI3	3.5	-0.900	yes	yes	–
halide_T3_4	NaCoI3	3.5	-0.586	yes	yes	–

Outputs

• property_prediction: benchmarks/runs/perov5/meidnet-propertyaware/property_prediction
• inverse_design: benchmarks/runs/perov5/meidnet-propertyaware/inverse_design

Reproduce

python scripts/benchmarks.py run perov5 --method meidnet-propertyaware

Computed on Intel64 Family 6 Model 197 Stepping 2, GenuineIntel (16 threads), CPU only; generating the candidates took 43 min.