LeMat-Traj: Unified Atomistic Trajectory Dataset

• LeMat-Traj is a harmonized dataset that aggregates over 120 million DFT relaxation trajectories into a standardized, OPTIMADE-compatible format.
• It employs an ingestion pipeline (Fetch → Transform → Validate → Harmonize → Push) using tools like Pymatgen and Matminer to ensure data consistency and provenance.
• MLIP training experiments demonstrate over a 36% force MAE reduction when fine-tuning on LeMat-Traj, underscoring its practical impact.

LeMat-Traj is a curated dataset of materials trajectories for atomistic modeling that aggregates large-scale geometry-optimization trajectories from the Materials Project, Alexandria, and OQMD into a unified, OPTIMADE-compatible schema. It was introduced to address the fragmented availability and inconsistent formatting of quantum mechanical trajectory datasets derived from Density Functional Theory, with explicit harmonization across the widely used DFT functionals PBE, PBESol, SCAN, and r2SCAN. The release comprises over 120 million atomic configurations, standardizes structural and target units, preserves provenance, and is paired with the modular open-source library LeMaterial-Fetcher for reproducible large-scale data ingestion, validation, harmonization, and publication (Ramlaoui et al., 28 Aug 2025).

1. Scope and motivation

LeMat-Traj targets a central bottleneck in training accurate, transferable machine learning interatomic potentials: the fragmentation of Density Functional Theory trajectory data across repositories that vary in file formats, metadata completeness, DFT settings, and access methods (Ramlaoui et al., 28 Aug 2025). The motivating premise is that MLIPs benefit from both broad exploration of the potential energy surface and dense, clean sampling near equilibrium. In the formulation used for LeMat-Traj, high-force states from active learning or molecular dynamics complement geometry-optimization trajectories that densely sample low-force regions near minima.

The dataset directly addresses several interoperability problems. Major repositories often remain siloed, use distinct formats, and report heterogeneous metadata such as functionals, k-points, and pseudopotentials. This makes it costly to combine otherwise compatible data and can bias models toward the subset that a research group is able to preprocess. LeMat-Traj responds by adopting a common schema across sources, standardizing structural and target units, harmonizing and tagging by functional, validating physical and schema consistency, and publishing the result in a format that is lightweight to consume at scale while preserving provenance.

A plausible implication is that LeMat-Traj is designed not only as a static corpus, but also as infrastructure for reducing repeated data-engineering overhead in MLIP development. That interpretation is supported by the joint presentation of the dataset and its companion curation framework, LeMaterial-Fetcher.

2. Aggregation, scale, and schema

LeMat-Traj aggregates relaxation trajectories from the Materials Project, Alexandria, and OQMD. The dataset comprises “over 120 million” configurations, with an exact total of 121,825,393 atomic configurations (Ramlaoui et al., 28 Aug 2025).

Functional	Source	Trajectories / Configurations
PBE	Materials Project	195,721 / 3,649,785
PBE	Alexandria	3,414,074 / 110,804,226
PBE	OQMD	135,966 / 264,782
PBESol	Materials Project	39,981 / 309,873
PBESol	Alexandria	252,791 / 6,099,623
SCAN	Materials Project	7,756 / 180,528
r2SCAN	Materials Project	37,888 / 516,576

The schema follows the OPTIMADE specification and adapts it to trajectories by making each entry a single configuration with energy and forces, associated to a trajectory via identifiers. Full relaxation paths are reconstructed by grouping by the trajectory identifier. Two trajectory-specific fields are emphasized: Relaxation Step, the integer index of the frame within an optimization path, and Relaxation Number, the identifier for multiple relaxations of the same starting structure.

Structural fields remain consistent with OPTIMADE, including atomic numbers or species, positions, lattice or cell, and periodic boundary conditions. Targets and metadata include per-frame total energy and per-atom forces, with stress available where reported. Functional labels are preserved per trajectory or frame, and provenance includes source database, task identifiers, and calculation lineage enabling filtering by origin. Additional metadata such as k-point meshes, pseudopotentials, and calculator settings can be incorporated when available, although the present release does not guarantee completeness of these fields across all entries.

3. Curation pipeline and quality controls

LeMaterial-Fetcher implements the pipeline used to build LeMat-Traj through the sequence Fetch → Transform → Validate → Harmonize → Push (Ramlaoui et al., 28 Aug 2025). In the fetch stage, the framework interfaces with source APIs or database dumps, including Materials Project tasks, Alexandria exports, and OQMD MySQL tables. In the transform stage, it converts structures and targets into a common schema, standardizing units and extracting available DFT metadata, leveraging Pymatgen and Matminer for robust structure handling. The validate stage enforces physical plausibility and schema conformity. The harmonize stage aligns key calculation parameters as tags and splits, enforces pseudopotential compatibility across sources with a documented Yb exception, and groups frames into trajectories with explicit indices. The push stage publishes the curated dataset to Hugging Face Datasets with versioning and provenance tracking.

Deduplication and pseudopotential compatibility follow the procedure in Siron et al. (LeMat-Bulk) for aggregating and de-duplicating quantum materials databases. A specific exception is documented for Ytterbium: Yb-containing samples are taken from Materials Project rather than Alexandria due to pseudopotential incompatibility. Source-specific mapping rules are also explicit. Materials Project ingestion iterates over all non-deprecated tasks and collects all associated relaxation trajectories that pass filters; Alexandria contributes all samples except Yb-containing entries; OQMD traversal gathers relaxation, coarse, and fine relaxation stages and uses input or output structures per stage when targets are present in required format.

The quality filters are restrictive enough to remove clearly problematic frames while retaining informative imperfect relaxations. Configurations missing energy or forces are discarded. Trajectories are removed when the energy change between the penultimate and final step exceeds $2\times10^{-2}$ eV, a convergence criterion adapted from MPtrj. Trajectories are also excluded when the final-step maximum atomic force norm exceeds $0.2$ eV/Å. Entries failing OPTIMADE schema validation are removed. Units used in the analyses and filters are eV for energy, eV/Å for forces, and meV/Å$^3$ for stress.

The pipeline is described as parallel and memory-efficient. It successfully used up to 128 cores and 256 GB RAM, and building the 120M-row release and uploading to Hugging Face took about 16 hours on a consumer-grade 12-worker setup based on an AMD Ryzen 5600G.

4. Coverage of structures, forces, and trajectories

The current release includes only relaxation trajectories and equilibrium single-point structures; MD, AIMD, and NEB are not included (Ramlaoui et al., 28 Aug 2025). Within that scope, the dataset spans both relaxed low-energy states and high-energy, high-force structures. Early relaxation steps exhibit mean $\Delta E \approx 0.05$ eV/atom with variance greater than 1 eV/atom, and mean maximum force around $0.3$–$0.4$ eV/Å with variance extending beyond 1 eV/Å. Near convergence, mean maximum forces are around $0.01$–$0.02$ eV/Å, with significant density below $10^{-3}$ eV/Å. The PBE split spans maximum atomic force norms from approximately $10^{-7}$ to $0.2$0 eV/Å.

The low-force regime is enriched by the inclusion of equilibrium OQMD structures with near-zero forces. At the same time, Materials Project contributes higher-force examples on average, with mean maximum force around 593 meV/Å versus around 110 meV/Å in the rest, which strengthens robustness against underestimation of forces. This suggests that the dataset is intentionally balanced across different stages of the relaxation process rather than restricted to converged minima.

Trajectory lengths show a broad distribution with a long tail. Many trajectories exceed 100 frames and some exceed 1000 frames. Compared to MPtrj, which is described as mostly shorter than 50 frames, and MatPES, which is broader than MPtrj but has fewer very long trajectories, LeMat-Traj provides denser coverage along long relaxation paths.

Chemical and structural diversity are also emphasized. In the PBE split, elemental frequency spans nearly the entire periodic table; oxides dominate, and actinides are underrepresented. Alexandria provides about 92% of the PBE volume, while Materials Project and OQMD improve diversity, including oxides, battery materials, and broader force coverage. The dataset contains more than 200 unique space groups across all seven crystal systems with strict symmetry tolerance $0.2$1. Notably, 98% of trajectories retain the same space group label between first and last step, indicating symmetry conservation during relaxation.

5. Role in MLIP training and empirical results

The training experiments reported for LeMat-Traj use the MACE architecture, with particular emphasis on the hypothesis that near-equilibrium dense sampling complements high-force pretraining (Ramlaoui et al., 28 Aug 2025). The principal baseline is MACE pretrained on OMat24, followed by fine-tuning on LeMat-Traj. Additional models are trained from scratch on individual functional splits and fine-tuned from MACE-MPA-0 to assess cross-functional transfer.

For practical training, subsets are split at the trajectory level to avoid leakage and are stratified by element presence and balanced across sources. For PBE and PBESol, the paper uses 10% Materials Project, 10% OQMD, and 80% Alexandria when available, with 80/20 train/test splits. Training on a single A100-40GB GPU uses a constant learning rate of $0.2$2 and batch size 128. The two-stage schedule from scratch uses Stage 1 weights $0.2$3 and Stage 2 weights $0.2$4, while fine-tuning uses $0.2$5.

On the held-out LeMat-Traj PBE 10K test set, the reported results are:

• OMat24 pretraining only: Energy MAE 59.5 meV; Force MAE 42.7 meV/Å; Force cosine 0.29.
• LeMat-Traj only: Energy MAE 25.3 meV; Force MAE 50.8 meV/Å; Force cosine 0.23.
• OMat24 + fine-tune on LeMat-Traj: Energy MAE 18.8 meV; Force MAE 27.2 meV/Å; Force cosine 0.30.

The paper identifies this as “over 36%” reduction in force MAE on relaxation tasks relative to the OMat24 pretrained baseline, since $0.2$6.

Downstream evaluation on a Matbench Discovery subset also favors the LeMat-Traj regimen. The reported metrics are:

• MACE (OMat24): F1 0.575; MAE 87.8 meV; RMSE 172.8 meV.
• MACE (MPtrj): F1 0.694; MAE 47.2 meV; RMSE 83.9 meV.
• MACE (LeMat-Traj Full): F1 0.768; MAE 37.2 meV; RMSE 69.0 meV.
• MACE (OMat24 + ft LeMat-Traj): F1 0.772; MAE 33.4 meV; RMSE 67.8 meV.

Cross-functional transfer is presented as an additional use case. On PBESol, MACE-MPA-0 reports energy 370.9 meV/atom, force 101 meV/Å, stress 14.7 meV/Å$0.2$7, cosine 0.13; MACE-PBESol trained from scratch reports 51.2, 33, 2.1, and 0.04; MACE-MPA-0-PBESol-ft reports 18.0, 27, 1.6, and 0.19. On r2SCAN, MACE-MPA-0 reports energy 9204.9 meV/atom, force 111 meV/Å, cosine 0.15; MACE-r2SCAN from scratch reports 141.7, 36, and 0.09; MACE-MPA-0-r2SCAN-ft reports 96.3, 28, and 0.22. In the paper’s interpretation, pretraining on one functional and fine-tuning on another reduces data requirements and improves convergence, supporting multi-fidelity transfer across functionals.

6. Limitations, access, and terminological ambiguity

The current release has several explicit limitations. It focuses on geometry optimization trajectories and equilibrium structures and does not include MD trajectories. The PBE split is dominated by Alexandria, around 92% of the volume, which can introduce source-specific biases. Combining sources with different k-point grids, pseudopotentials, and other calculator settings may introduce noise. Although LeMaterial-Fetcher preserves provenance and enforces pseudopotential compatibility, a deeper quantitative study of cross-database parameter heterogeneity is identified as future work (Ramlaoui et al., 28 Aug 2025).

Access and licensing are integral to the project definition. The dataset is publicly available at https://huggingface.co/datasets/LeMaterial/LeMat-Traj under CC-BY 4.0. The code for LeMaterial-Fetcher is available at https://github.com/LeMaterial/lematerial-fetcher under Apache 2.0. Smaller-scale subsets for experiments and stratified splits are available at https://huggingface.co/datasets/LeMaterial/LeMat-Traj-subset. Provenance is preserved so that filtering by source, functional, and calculation lineage remains possible.

The label “LeMat-Traj” is not unique across the literature. In a separate combinatorics context, it refers to the trajectory statistic $0.2$8 on ordered pairs of Dyck paths in “Meanders and Dyck-Path Billiards,” where the statistic counts the number of billiard trajectories in the grid polygon enclosed by $0.2$9 and $^3$0 and is shown to coincide with the component statistic of meanders (Eu et al., 23 Sep 2025). In another unrelated synopsis based on the Legendre transform applied to ellipses for charged-particle track reconstruction, “LeMat-Traj” is used as a label for a common-tangent detection pipeline in $^3$1 space, built around the support function

$^3$2

That usage derives from “Track reconstruction through the application of the Legendre Transform on ellipses” (Alexopoulos et al., 2016). This suggests that the term is context-sensitive and should be disambiguated by domain.

In materials informatics, however, LeMat-Traj denotes a large, harmonized, provenance-aware trajectory dataset for atomistic modeling, together with a reproducible ingestion and curation framework. Within that domain, its defining contribution is to combine scale, standardized representation, functional-aware partitioning, and explicit trajectory indexing in a form intended for transferable MLIP training and systematic future expansion (Ramlaoui et al., 28 Aug 2025).