eSEN-30M-OAM: Universal Pretrained MLIP

• eSEN-30M-OAM is a universal pretrained machine-learning interatomic potential designed for geometry optimization, formation energy evaluation, and high-throughput materials screening.
• It employs a crystal-graph neural network with 10 layers and a frozen representation backbone that facilitates efficient transfer learning for diverse material properties.
• Benchmarking on Heusler alloys and zeolite frameworks demonstrates its smooth energy landscape, high precision in thermodynamic filtering, and competitive RMSE metrics.

Searching arXiv for the original eSEN paper and supporting benchmark papers. eSEN-30M-OAM is a general-purpose, pretrained machine-learning interatomic potential (MLIP) based on the eSEN architecture and used as a universal geometry-and-energy engine in contemporary materials-screening workflows. In the current literature, it is presented not as a Heusler-specific or zeolite-specific model, but as a broadly pretrained potential spanning chemically diverse materials spaces and capable of replacing density functional theory (DFT) for structural relaxation and relative thermodynamic screening in high-throughput settings (Xiao et al., 28 Aug 2025). Subsequent benchmarking on zeolite structures likewise treats eSEN-30M-OAM as a pretrained universal MLIP used without further training and reports it as the most consistent performer among the tested universal MLIPs across pure-silica and guest-containing zeolite systems (Ito et al., 9 Sep 2025).

1. Identity, naming, and domain of use

Within the Heusler-alloy study, the model is introduced simply as “eSEN-30M-OAM” and described as a general-purpose, pretrained interatomic potential. Its operational role is sharply defined: it replaces DFT for structure optimization, formation-energy evaluation, and convex-hull screening, while separate transfer-learned regressors derived from its backbone handle magnetic and other target-property predictions (Xiao et al., 28 Aug 2025). In the zeolite benchmark, the same model is abbreviated as eSEN and referred to as “the eSEN model from OMat24”; the supplementary information states that the model used there is eSEN-30M-OAM, trained on OMat24 and fine-tuned by using the dataset from MPtrj and Alexandria (Ito et al., 9 Sep 2025).

The name should not be overinterpreted beyond what the cited papers state. The Heusler paper notes that the “30M” in the name likely refers to scale, but does not explicitly decode it, and neither the Heusler nor the zeolite paper explains the suffix “OAM” (Xiao et al., 28 Aug 2025). A common misconception is to associate that suffix with orbital angular momentum in optics or wireless communications. That association is not supported by the materials papers. Indeed, a paper on disordered statistical q-plates explicitly states that the label “eSEN-30M-OAM” does not appear there and that any connection would be interpretive only (Moriya, 4 Sep 2025). Likewise, OAM-based integrated sensing and communication concerns vortex electromagnetic waves rather than interatomic potentials (Liang et al., 2024).

This naming ambiguity has not affected how the model is used in materials informatics. Across the cited benchmark papers, eSEN-30M-OAM consistently denotes a pretrained universal MLIP for atomistic modeling rather than an optics or communications construct.

2. Architecture and pretrained representation

The Heusler benchmark provides partial but technically informative architecture details. From that paper alone, eSEN can be identified as a crystal-graph / message-passing neural-network MLIP with an embedding layer and 10 layers total. The transfer-learning discussion states that “the eSEN model consists of 10 layers” and that the embedding layer plus the first several message-passing layers can be frozen while the remaining layers are adapted to downstream tasks (Xiao et al., 28 Aug 2025).

The pretraining corpus is described as broad and chemically diverse. The Heusler paper states that the pretrained eSEN base draws on OMat, MPtrj, and sAlexandria, and emphasizes that the model is intended as a foundation-style universal materials potential rather than a Heusler-specialized potential (Xiao et al., 28 Aug 2025). The zeolite benchmark uses closely aligned language, stating that the model from OMat24 used in that study is eSEN-30M-OAM and that it is trained on OMat24 and fine-tuned by using the dataset from MPtrj and Alexandria (Ito et al., 9 Sep 2025). Taken together, these descriptions place eSEN-30M-OAM in the class of broadly pretrained universal MLIPs rather than narrow domain-specific force fields.

The cited papers are also explicit about what the base model does not encode. The Heusler study states that eSEN performs strongly on magnetic systems despite not explicitly incorporating magnetic moments into its architecture or training (Xiao et al., 28 Aug 2025). No evidence is given that the base MLIP directly encodes spin, oxidation states, or orbital occupations. This suggests that its utility in magnetic materials screening arises from learned structural and chemical representations rather than from explicit magnetic-state variables.

3. Geometry-and-energy engine in Heusler high-throughput screening

In the Heusler-alloy benchmark, eSEN-30M-OAM is the front end of an ML-accelerated high-throughput workflow for magnetic materials discovery. The workflow begins with candidate generation for conventional quaternary and all-$d$ Heusler compositions. For each composition, an initial lattice constant is estimated from known $X_2YZ$ Heuslers in the DXMag database sharing two elemental species; a cubic conventional cell is then built; multiple strained starting structures are generated; those structures are converted to primitive cells; and the resulting inputs are relaxed with eSEN-30M-OAM (Xiao et al., 28 Aug 2025).

The production workflow uses a multi-start relaxation scheme rather than a single relaxation. The Methods section states that $a,b,c$ were uniformly scaled by $\pm 10\%$ or $\pm 30\%$, and alternatively $c$ alone was scaled by $\pm 10\%$ or $\pm 30\%$. In the MLIP benchmark, the starting-structure set is even larger: uniform scaling of all three axes by $\pm10\%$ and $\pm30\%$, plus $X_2YZ$0-only distortions by $X_2YZ$1. The relaxed structure with the lowest eSEN energy is taken as the predicted ground state (Xiao et al., 28 Aug 2025).

After relaxation, eSEN is used to compute the energies needed for thermodynamic screening. Using the eSEN energies of the candidate phase, the elemental reference phases, and the relevant competing phases, the workflow computes formation energy $X_2YZ$2 and distance to the convex hull $X_2YZ$3. These are filtered using the thresholds

$X_2YZ$4

The same relaxed structures also determine whether a phase is sufficiently tetragonal for magnetocrystalline anisotropy screening through the criterion

$X_2YZ$5

Thus eSEN serves simultaneously as a structure relaxer, thermodynamic evaluator, and tetragonal–cubic phase discriminator (Xiao et al., 28 Aug 2025).

The relaxation protocol in that study uses ASE with the FIRE optimizer, with symmetry constraints enforced throughout the relaxation process. The paper does not provide a force convergence threshold, stress threshold, or maximum number of steps. It also does not report wall-clock inference time or FLOP counts, so the efficiency claims are workflow-level rather than kernel-level (Xiao et al., 28 Aug 2025).

4. Heusler benchmark performance and screening fidelity

The Heusler paper benchmarks eSEN-30M-OAM against ALIGNN-FF, CHGNet, SevenNet-l3i5, SevenNet-MF-ompa, HIENet, MatterSim-v1, eqV2-S-OAM, eqV2-M-OAM, and eqV2-L-OAM. The central comparative claim is that eSEN and the eqV2 family both perform strongly for structural and energetic prediction, but eSEN yields a smoother energy landscape and fewer local-minimum traps, making global-minimum searches more efficient (Xiao et al., 28 Aug 2025).

In a structure-optimization benchmark over 10,000 conventional ternary Heuslers randomly selected from DXMag ground states, eSEN and the eqV2 models are the best performers at the 5% relative-error threshold for lattice constants and $X_2YZ$6, with eSEN slightly better at the stricter 1% threshold. For formation energies and hull distances, eSEN and the eqV2 variants show the highest accuracy at the 0.05 eV/atom threshold, while eSEN shows “a slight drop in accuracy” at the 0.01 eV/atom threshold (Xiao et al., 28 Aug 2025).

For the cubic Heusler subset, the paper reports explicit regression metrics:

Quantity	eSEN	ALIGNN-FF
$X_2YZ$7	0.994	0.128
$X_2YZ$8	0.023 $X_2YZ$9	0.330 $a,b,c$0
$a,b,c$1	0.995	0.453
$a,b,c$2	0.029 eV/atom	0.310 eV/atom
$a,b,c$3	0.980	0.330

These results are accompanied by an important qualification: total energies from MLIPs are reported to be systematically lower than DFT values, but the Heusler paper argues that because the same offset appears in elemental and competing phases, the relative thermodynamic quantities $a,b,c$4 and $a,b,c$5 remain accurate (Xiao et al., 28 Aug 2025).

The most practically consequential evidence comes from end-to-end screening. The workflow screened 131,544 conventional quaternary and 104,139 all-$a,b,c$6 Heuslers. It identified 366 quaternary and 924 all-$a,b,c$7 candidates before DFT validation, although the Discussion later mentions 334 conventional quaternary and 924 all-$a,b,c$8 compounds; the paper therefore contains an internal inconsistency on the quaternary count (Xiao et al., 28 Aug 2025). For the ML-selected candidates, DFT validation showed that all selected compounds remained tetragonal, giving the eSEN-based tetragonality criterion 100% precision on that selected set. The DFT confirmation rates for the thermodynamic filters were:

Filter validated by DFT	Conventional quaternary	All-$a,b,c$9
$\pm 10\%$0	99.1%	97.8%
$\pm 10\%$1	96.4%	98.8%

The multi-start global-minimum benchmark also quantifies the smoother-landscape claim. In that benchmark, eqV2-L-OAM gives 91,585 local minima versus 32,606 for eSEN, which the authors interpret as evidence that eSEN’s smoother energy surface requires fewer initial structures to reach the global minimum (Xiao et al., 28 Aug 2025).

5. Relation to eSEM and frozen transfer learning

A central feature of the Heusler workflow is the division of labor between eSEN and eSEM. The abstract states that structure optimization and evaluation of formation energy and distance to hull convex were performed using eSEN-30M-OAM, whereas local magnetic moments, phonon stability, magnetic stability, and $\pm 10\%$2 were predicted by eSEM models (Xiao et al., 28 Aug 2025). In operational terms, eSEN first relaxes structures and computes energies; only then are transfer-learned regressors applied to the eSEN-relaxed geometries to predict

$\pm 10\%$3

The transfer-learning setup uses the eSEN backbone as a frozen base. The paper states that the embedding layer and first seven layers are frozen, while the final three layers and output head are trainable. The authors denote the best-performing configuration as TL-MLIP-7 and report that it gives the best performance for $\pm 10\%$4, $\pm 10\%$5, magnetocrystalline anisotropy energy, and local magnetic moments (Xiao et al., 28 Aug 2025). This supports a broader interpretation of eSEN not merely as an energy model, but as a reusable learned representation of local chemistry and structure.

The same section clarifies a frequent misunderstanding: eSEN itself is not the magnetic-property predictor in the screening stage. The magnetic pre-screening criterion

$\pm 10\%$6

is applied by the eSEM local-moment regressor on eSEN-relaxed structures, not by the base MLIP. Likewise, the downstream filters

$\pm 10\%$7

belong to the eSEM stage rather than the eSEN stage (Xiao et al., 28 Aug 2025).

The hybrid-workflow experiments isolate the contribution of the base MLIP. Using ALIGNN-FF + ALIGNN regressors, only 25.2% of the reduced candidate set were DFT-confirmed as strong-MAE compounds. A hybrid with eSEN structure optimization + ALIGNN property models reached 54.0%, whereas the reverse hybrid with ALIGNN-FF structure optimization + eSEN property models reached 31.3%. The fully eSEN-based workflow achieved 82.0% DFT-confirmed strong-MAE precision for conventional quaternaries (Xiao et al., 28 Aug 2025). This suggests that the quality of eSEN-relaxed structures is a dominant contributor to downstream screening accuracy.

6. Cross-domain generalization: zeolite benchmarking

The zeolite benchmark evaluates eSEN-30M-OAM in a chemically narrower but structurally diverse setting comprising pure silica frameworks, 347 copper-introduced CHA-type aluminosilicate structures, and 1,190 ERI-type aluminosilicates containing potassium and the OSDA hexane-1,6-bis(trimethylazanium) (Ito et al., 9 Sep 2025). In that paper, eSEN is one of the benchmarked pretrained universal MLIPs, alongside CHGNet, ORB-v3, MatterSim, PFP-v7, and EquiformerV2-lE4-lF100-S2EFS-OC22, and is compared with universal analytic IPs and tailor-made zeolite force fields (Ito et al., 9 Sep 2025).

For pure silica geometry, the paper does not reproduce a single scalar error value for eSEN in the main text excerpt, but it places eSEN in the cluster of MLIPs that provide DFT-like results and explicitly shows that DFT with PBE+D3, SLC, and eSEN produce reasonable RTE-type zeolite structures, whereas GFN-FF does not. According to a structure-matching algorithm implemented in pymatgen, the relaxed RTE structures obtained using SLC, PBE+D3, and eSEN are considered equivalent (Ito et al., 9 Sep 2025).

The energy benchmarks are more quantitative. For silica polymorph relative energies referenced to $\pm 10\%$8-quartz, eSEN achieves RMSE = 1.55 kJ mol$\pm 10\%$9 against experiment, which is the best value among the universal MLIPs and second only to DFT itself (Ito et al., 9 Sep 2025). For a much broader pure-silica topology set referenced to DFT(PBE+D3), eSEN achieves RMSE = 0.44 kJ mol$\pm 30\%$0, the lowest value of all tested models (Ito et al., 9 Sep 2025).

For the guest-containing zeolite sets, the benchmark is performed on single-point energies of DFT-relaxed structures. Here again eSEN ranks first among the tested MLIPs:

Benchmark	eSEN RMSE	Unit
Silica relative energies vs experiment	1.55	kJ mol$\pm 30\%$1
Broad pure-silica relative energies vs DFT	0.44	kJ mol$\pm 30\%$2
Cu/CHA relative energies vs DFT	0.14	kJ mol$\pm 30\%$3 atom$\pm 30\%$4
K-OSDA/ERI relative energies vs DFT	0.02	kJ mol$\pm 30\%$5 atom$\pm 30\%$6

The paper’s conclusion is correspondingly strong but specific: among the universal MLIPs tested, the eSEN-30M-OAM model shows the most consistent performance across all zeolite structures studied (Ito et al., 9 Sep 2025). This extends the Heusler paper’s claim of cross-domain generalization into a second materials class with markedly different chemistry and structural motifs.

7. Scope, limitations, and current interpretation

The cited papers define a relatively clear operating envelope for eSEN-30M-OAM. Its demonstrated strengths are geometry optimization, relative chemical stability, cross-domain transfer without domain-specific retraining, and use as a pretrained backbone for downstream regressors (Xiao et al., 28 Aug 2025). At the same time, the Heusler study is explicit that eSEN should not be interpreted as a spin-lattice Hamiltonian or a direct model of magnetic energetics. Its success on magnetic Heuslers occurs despite not explicitly incorporating magnetic moments into its architecture or training, which is both a strength in generalization and a limitation in physical scope (Xiao et al., 28 Aug 2025).

Several caveats recur across the benchmark literature. First, the Heusler study reports a systematic offset in absolute total energies relative to DFT and therefore positions eSEN as more trustworthy for relative thermodynamics such as $\pm 30\%$7 and $\pm 30\%$8 than for absolute total energies (Xiao et al., 28 Aug 2025). Second, the cited papers do not provide calibrated uncertainty estimates, so there is no explicit uncertainty-aware screening framework. Third, the Heusler paper demonstrates eSEN mainly through static relaxation and phase-stability screening, not through long molecular dynamics, finite-temperature lattice dynamics, or stress-sensitive elastic-property prediction (Xiao et al., 28 Aug 2025). Fourth, the zeolite guest-containing benchmarks validate eSEN primarily on single-point energetics of DFT-relaxed structures, not on exhaustive MLIP-driven relaxation of all guest-loaded systems (Ito et al., 9 Sep 2025).

A further limitation is documentary rather than algorithmic. The Heusler paper identifies the original architecture paper as Fu et al. (2025), but does not reproduce the full descriptor definitions or hyperparameter specification. The same paper notes that the meaning of “OAM” is not explained there, and the broader literature includes unrelated uses of “OAM” in optics and communications (Xiao et al., 28 Aug 2025). As a result, the present understanding of eSEN-30M-OAM in the benchmark literature is functional rather than philological: it is a newly available, state-of-the-art, broadly pretrained universal MLIP that can act both as a direct interatomic potential for structural optimization and thermodynamic screening and as a frozen representation backbone for transfer learning to harder materials properties (Xiao et al., 28 Aug 2025).

In that sense, eSEN-30M-OAM occupies a specific place in current materials informatics. It is not presented as an all-purpose surrogate for every quantum-mechanical observable, but as a highly effective replacement for DFT in the repetitive front-end tasks of high-throughput materials discovery, with strong evidence for fidelity on Heusler alloys and zeolite structures and with a documented pathway from universal pretraining to property-specific transfer learning (Xiao et al., 28 Aug 2025).