MEIDNet (first early-fusion model)

The earliest ablation of the paper, without property-aware decoding.

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 normalised encoder outputs, before the projection heads
Checkpoint	dual_autoencoder_clip_earlyfusion.pth · sha256 59fc26f97d04…
Links	paper · code · weights

Property prediction

metric	value	definition
MAE ΔH	0.522 eV/atom	mean absolute error of the formation enthalpy (heat_all)
RMSE ΔH	0.698 eV/atom	root-mean-square error of the formation enthalpy
R² ΔH	0.119	coefficient of determination of the formation enthalpy (0 = no better than the mean)
MAE gap	13.469 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	11.998 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	13.492 eV	root-mean-square error of the direct band gap
R² gap	-632.529	coefficient of determination of the direct band gap; not informative here, because the gap is zero for most materials
MAE ΔH ≠ 0	0.522 eV/atom	mean absolute error of the formation enthalpy on materials where it is not zero
n	3,785	test materials evaluated

MEIDNet (first early-fusion model): formation enthalpy, predicted vs. DFT

MEIDNet (first early-fusion model): direct band gap, predicted vs. DFT

Representation

metric	value	definition
R@1	0.028	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	0.131	the same within the five nearest profiles
cos	0.655	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	0.051 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	0.064 eV	direct-band-gap error of the same probe
L2	0.822	mean L2 distance between the two latents of the same material (unit latents)
cos, encoder outputs	0.655	the matched cosine between the normalised encoder outputs, before the projection heads
cos, projection heads	-0.979	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	0.648	stable, unique and novel candidates divided by the budget of 54; a candidate that was not delivered counts as a failure
Stable	0.944	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	0.704	fraction of delivered candidates whose composition is not in the data set (training, validation and test splits)
ΔHf	-1.29 eV/atom	median MACE-MP-0 formation energy of the delivered candidates
DFT hit	0.188	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	16	candidates with a known DFT band gap (the denominator of DFT hit)
Delivered	54	candidates delivered out of the budget of 54
Valid	1.000	fraction of the budget that passes every rule of the family
SUN count	35	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	CaZrO3	1.5	-3.347	yes	no	6.70
oxide_T1_2	NaTaO3	1.5	-2.902	yes	no	5.30
oxide_T1_3	CaTiO3	1.5	-3.364	yes	no	4.70
oxide_T1_4	SrZrO3	1.5	-3.478	yes	no	6.60
oxide_T1_5	SrGeO3	1.5	-2.485	yes	no	1.70
oxide_T1_6	BaTiO3	1.5	-3.364	yes	no	4.00
oxide_T2_1	LaScO3	2.5	-3.629	yes	no	6.40
oxide_T2_2	BaMnO3	2.5	-1.919	yes	no	0.00
oxide_T2_3	CaGeO3	2.5	-2.460	yes	no	2.70
oxide_T2_4	SmCoO3	2.5	-1.977	yes	yes	–
oxide_T2_5	SrHfO3	2.5	-3.645	yes	no	7.20
oxide_T2_6	SrMnO3	2.5	-1.992	yes	no	0.00
oxide_T3_1	SmMnO3	3.5	-2.318	yes	yes	–
oxide_T3_2	LaMnO3	3.5	-2.467	yes	no	0.00
oxide_T3_3	KTaO3	3.5	-2.930	yes	no	5.00
oxide_T3_4	LaCoO3	3.5	-2.084	yes	no	0.00
oxide_T3_5	CaHfO3	3.5	-3.529	yes	no	7.30
oxide_T3_6	CsTaO3	3.5	-2.671	yes	no	3.50
chalcogenide_T1_1	SmScSe3	1.5	-1.801	yes	yes	–
chalcogenide_T1_2	LaMnSe3	1.5	-1.510	yes	yes	–
chalcogenide_T1_3	NaTaSe3	1.5	-1.125	yes	yes	–
chalcogenide_T1_4	SrHfSe3	1.5	-1.938	yes	yes	–
chalcogenide_T1_5	SrZrSe3	1.5	3.303	no	yes	–
chalcogenide_T1_6	CaTiSe3	1.5	130210516176.396	no	yes	–
chalcogenide_T2_1	CaZrSe3	2.5	-1.736	yes	yes	–
chalcogenide_T2_2	SmMnSe3	2.5	-1.258	yes	yes	–
chalcogenide_T2_3	LaScSe3	2.5	-2.041	yes	yes	–
chalcogenide_T2_4	RbTaSe3	2.5	-1.273	yes	yes	–
chalcogenide_T2_5	KTaSe3	2.5	-1.263	yes	yes	–
chalcogenide_T2_6	CaSnSe3	2.5	-1.012	yes	yes	–
chalcogenide_T3_1	CaHfSe3	3.5	-1.737	yes	yes	–
chalcogenide_T3_2	TmMnSe3	3.5	-1.060	yes	yes	–
chalcogenide_T3_3	BaHfSe3	3.5	-2.068	yes	yes	–
chalcogenide_T3_4	YbFeSe3	3.5	-1.180	yes	yes	–
chalcogenide_T3_5	SrSnSe3	3.5	5.797	no	yes	–
chalcogenide_T3_6	TmCoSe3	3.5	-0.922	yes	yes	–
halide_T1_1	NaCuI3	1.5	-0.724	yes	yes	–
halide_T1_2	NaNiI3	1.5	-0.723	yes	yes	–
halide_T1_3	NaMnI3	1.5	-0.900	yes	yes	–
halide_T1_4	KMnI3	1.5	-1.083	yes	yes	–
halide_T1_5	NaZnI3	1.5	-0.928	yes	yes	–
halide_T1_6	RbMnI3	1.5	-1.123	yes	yes	–
halide_T2_1	KCuI3	2.5	-0.892	yes	yes	–
halide_T2_2	NaCoI3	2.5	-0.586	yes	yes	–
halide_T2_3	NaSnI3	2.5	-0.936	yes	yes	–
halide_T2_4	KPbI3	2.5	-1.186	yes	yes	–
halide_T2_5	CsMnI3	2.5	-1.160	yes	yes	–
halide_T2_6	KNiI3	2.5	-0.883	yes	yes	–
halide_T3_1	CsZnI3	3.5	-1.165	yes	yes	–
halide_T3_2	KZnI3	3.5	-1.102	yes	yes	–
halide_T3_3	CsPbI3	3.5	-1.302	yes	yes	–
halide_T3_4	NaFeI3	3.5	-0.553	yes	yes	–
halide_T3_5	KFeI3	3.5	-0.737	yes	yes	–
halide_T3_6	RbZnI3	3.5	-1.136	yes	yes	–

Outputs

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

Reproduce

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

Computed on Intel64 Family 6 Model 197 Stepping 2, GenuineIntel (16 threads), CPU only; generating the candidates took 37 min.