MEIDNet (published model)

Early fusion with property-aware decoding, trained for 2,000 epochs with a contrastive warm-up over the first 1,200: the model of the paper and of the live Studio.

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_2k.pth · sha256 f9493781d5bb…
Links	paper · code · weights

Property prediction

metric	value	definition
MAE ΔH	0.404 eV/atom	mean absolute error of the formation enthalpy (heat_all)
RMSE ΔH	0.539 eV/atom	root-mean-square error of the formation enthalpy
R² ΔH	0.475	coefficient of determination of the formation enthalpy (0 = no better than the mean)
MAE gap	2.792 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	1.676 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	3.051 eV	root-mean-square error of the direct band gap
R² gap	-31.400	coefficient of determination of the direct band gap; not informative here, because the gap is zero for most materials
MAE ΔH ≠ 0	0.404 eV/atom	mean absolute error of the formation enthalpy on materials where it is not zero
n	3,785	test materials evaluated

MEIDNet (published model): formation enthalpy, predicted vs. DFT

MEIDNet (published model): direct band gap, predicted vs. DFT

Representation

metric	value	definition
R@1	0.336	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	0.896	the same within the five nearest profiles
cos	0.772	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	0.021 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	0.055 eV	direct-band-gap error of the same probe
L2	0.675	mean L2 distance between the two latents of the same material (unit latents)
cos, encoder outputs	-0.008	the matched cosine between the normalised encoder outputs, before the projection heads
cos, projection heads	0.772	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	0.611	stable, unique and novel candidates divided by the budget of 54; a candidate that was not delivered counts as a failure
Stable	0.962	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	0.660	fraction of delivered candidates whose composition is not in the data set (training, validation and test splits)
ΔHf	-1.52 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	53	candidates delivered out of the budget of 54
Valid	0.981	fraction of the budget that passes every rule of the family
SUN count	33	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	LaMnO3	1.5	-2.467	yes	no	0.00
oxide_T1_2	CaTiO3	1.5	-3.364	yes	no	4.70
oxide_T1_3	LaAlO3	1.5	-3.587	yes	no	6.30
oxide_T1_4	CsTaO3	1.5	-2.671	yes	no	3.50
oxide_T1_5	BaTiO3	1.5	-3.364	yes	no	4.00
oxide_T1_6	NaTaO3	1.5	-2.902	yes	no	5.30
oxide_T2_1	LaCoO3	2.5	-2.084	yes	no	0.00
oxide_T2_2	NaNbO3	2.5	-2.668	yes	no	4.40
oxide_T2_3	BaMnO3	2.5	-1.919	yes	no	0.00
oxide_T2_4	LaFeO3	2.5	-2.155	yes	no	0.00
oxide_T2_5	KNbO3	2.5	-2.713	yes	no	4.10
oxide_T2_6	CsNbO3	2.5	-2.475	yes	no	2.90
oxide_T3_1	LaGaO3	3.5	-2.922	yes	no	5.60
oxide_T3_2	BaZrO3	3.5	-3.513	yes	no	6.30
oxide_T3_3	BaGeO3	3.5	-2.357	yes	no	0.00
oxide_T3_4	CaVO3	3.5	-2.378	yes	no	0.00
oxide_T3_5	BaSnO3	3.5	-2.476	yes	no	2.50
oxide_T3_6	SrTiO3	3.5	-3.429	yes	no	4.30
chalcogenide_T1_1	CsTaTe3	1.5	-1.295	yes	yes	–
chalcogenide_T1_2	RbNbTe3	1.5	-1.355	yes	yes	–
chalcogenide_T1_3	LaCoTe3	1.5	-1.518	yes	yes	–
chalcogenide_T1_4	LaMnTe3	1.5	-1.546	yes	yes	–
chalcogenide_T1_5	LaVTe3	1.5	-1.539	yes	yes	–
chalcogenide_T1_6	BaSnTe3	1.5	-1.461	yes	yes	–
chalcogenide_T2_1	CaTiTe3	2.5	-1.607	yes	yes	–
chalcogenide_T2_2	BaTiTe3	2.5	-1.912	yes	yes	–
chalcogenide_T2_3	BaZrTe3	2.5	-2.002	yes	yes	–
chalcogenide_T2_4	NaNbTe3	2.5	-1.208	yes	yes	–
chalcogenide_T2_5	LaCoS3	2.5	-2.544	yes	yes	–
chalcogenide_T2_6	BaWS3	2.5	-594.364	no	yes	–
chalcogenide_T3_1	BaMoTe3	3.5	-1.429	yes	yes	–
chalcogenide_T3_2	LaCrTe3	3.5	-1.485	yes	yes	–
chalcogenide_T3_3	SrTiTe3	3.5	-1.779	yes	yes	–
chalcogenide_T3_4	CaMoTe3	3.5	-1.152	yes	yes	–
chalcogenide_T3_5	BaMoS3	3.5	-512.082	no	yes	–
chalcogenide_T3_6	NaTaTe3	3.5	-1.146	yes	yes	–
halide_T1_1	RbZnI3	1.5	-1.136	yes	yes	–
halide_T1_2	KSnI3	1.5	-1.142	yes	yes	–
halide_T1_3	NaMnI3	1.5	-0.900	yes	yes	–
halide_T1_4	NaCoI3	1.5	-0.586	yes	yes	–
halide_T1_5	RbMnI3	1.5	-1.123	yes	yes	–
halide_T1_6	KNiI3	1.5	-0.883	yes	yes	–
halide_T2_1	NaZnI3	2.5	-0.928	yes	yes	–
halide_T2_2	NaSnI3	2.5	-0.936	yes	yes	–
halide_T2_3	CsZnI3	2.5	-1.165	yes	yes	–
halide_T2_4	RbSnI3	2.5	-1.194	yes	yes	–
halide_T2_5	CsMnI3	2.5	-1.160	yes	yes	–
halide_T2_6	NaCuI3	2.5	-0.724	yes	yes	–
halide_T3_1	RbFeI3	3.5	-0.773	yes	yes	–
halide_T3_2	KMnI3	3.5	-1.083	yes	yes	–
halide_T3_3	CsPbI3	3.5	-1.302	yes	yes	–
halide_T3_4	NaNiI3	3.5	-0.723	yes	yes	–
halide_T3_5	NaFeI3	3.5	-0.553	yes	yes	–

Outputs

• property_prediction: benchmarks/runs/perov5/meidnet-2k/property_prediction
• inverse_design: benchmarks/runs/perov5/meidnet-2k/inverse_design

Reproduce

python scripts/benchmarks.py run perov5 --method meidnet-2k

Computed on Intel64 Family 6 Model 197 Stepping 2, GenuineIntel (16 threads), CPU only; generating the candidates took 39 min.