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REVIEW 3 major objections 6 minor 66 references

Universal crystal material property prediction via multi-view geometric fusion in graph transformers

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read MGT claims that fusing SE3-invariant and SO3-equivariant crystal graph views with a task-adaptive router and multi-task self-supervised pretraining reduces mean absolute error by up to 21% and boosts transfer learning by up to 58%.

desk verdict Useful incremental model with code and data, but the headline gains hinge on an unchecked OQMD/MP-JARVIS overlap and missing error bars. read the letter →

arxiv 2507.15303 v1 pith:V2C7F4MB submitted 2025-07-21 cs.LG cond-mat.mtrl-sci

Liang Zhang , Kong Chen , Yuen Wu This is my paper
classification cs.LGcond-mat.mtrl-sci
keywords crystalpropertypredictiongraphtransformerSE3invarianceSO3equivariancemixtureofexpertsself-supervisedpretrainingtransferlearningmaterialsdiscovery
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to establish that a crystal's two complementary geometric readings—one invariant under rotations and translations ($\mathrm{SE}(3)$) and one whose vector outputs rotate with the crystal ($\mathrm{SO}(3)$)—are better used together than separately. Its model, MGT, runs both views through graph transformer encoders, lets a lightweight mixture-of-experts router decide how much each view contributes per task, and pretrains the whole system with denoising and contrastive objectives. If the claim holds, one model can serve many crystal property predictions, including formation energy, band gaps, moduli, catalyst adsorption energy, and perovskite band gaps, with gains of up to about 21% on standard benchmarks and up to about 58% in transfer learning. The practical reason to care is that more accurate property prediction from structure alone shortens the expensive DFT-and-simulation loop in materials screening.

What carries the argument

The load-bearing device is the pair of complementary graph encoders plus the router. The $\mathrm{SE}(3)$ encoder's edge-wise and node-wise transformer layers process invariant scalars such as distances, angles, and lattice reference vectors; the $\mathrm{SO}(3)$ encoder uses spherical harmonics and tensor products to keep vector features equivariant under rotation; and the lightweight mixture-of-experts router, built on self-attention, computes per-task weights over the two embeddings. The pretraining objective combines denoising, which predicts Gaussian noise added to angle and edge features, with a temperature-scaled cross-entropy (NT-Xent) contrastive loss that aligns the $\mathrm{SE}(3)$ and $\mathrm{SO}(3)$ embeddings. This machinery forces the same crystal to be seen through two symmetry lenses at once and then lets the target task decide which lens matters more.

What would settle it

Run a structure-matching comparison between OQMD v1.5 and the Materials Project and JARVIS test splits (matching composition, space group, and relaxed geometry within a small tolerance), remove any matched structures, and rerun the eight reported benchmark comparisons; if the 3.3% to 20.8% MAE reductions shrink or vanish, the transfer claim fails.

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Extended reading notes

Core claim

The paper's central claim is that an architecture which fuses an $\mathrm{SE}(3)$-invariant crystal graph view with an $\mathrm{SO}(3)$-equivariant one, and adaptively reweights them per task, outperforms models that commit to a single geometric inductive bias. MGT encodes each view with a separate graph transformer: the $\mathrm{SE}(3)$ branch tracks distances, angles, and lattice basis vectors, while the $\mathrm{SO}(3)$ branch carries vector features through spherical-harmonic and tensor-product layers so that outputs rotate consistently. A self-attention-based mixture-of-experts router fuses the two embeddings, and multi-task self-supervised pretraining—denoising corrupted edge and angle features plus contrastive alignment of the two views—prepares the representation before fine-tuning. The reported evidence is that MGT beats CGCNN, ALIGNN, Matformer, PotNet, ComFormer, and ReGNet on eight of nine Materials Project and JARVIS tasks, with MAE reductions of 3.3% to 20.8%, and improves transfer-learning baselines by 15.4% to 57.8% on catalyst global-minimum adsorption energy and hybrid perovskite bandgap.

Load-bearing premise

The reported gains assume that pretraining on OQMD does not leak into the Materials Project and JARVIS evaluation sets, and the paper does not describe any deduplication or overlap check between the 587,483 pretraining structures and the downstream test structures, so if the same or nearly identical crystals appear in both, part of the improvement could come from memorization rather than transfer.

Editorial extensions

If this is right

  • MGT gives a single architecture that improves prediction accuracy across formation energy, band gap, total energy, bulk and shear moduli, and hull distance tasks, with MAE reductions of 3.3% to 20.8% over strong baselines.
  • Because the router assigns different $\mathrm{SE}(3)$/$\mathrm{SO}(3)$ weights for different tasks, the model adapts its symmetry inductive bias without retraining the encoders, and the reported contribution scores show this weighting is task-dependent.
  • The multi-task self-supervised pretraining on OQMD improves downstream accuracy beyond training from scratch, and the ablations indicate denoising and contrastive objectives are complementary.
  • In transfer learning, MGT improves global-minimum adsorption energy prediction on alloy, functional-group, and dense-catalyst datasets by 46.4%, 57.8%, and 15.4% over the prior baseline, and hybrid perovskite bandgap prediction by 25.7%.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the pretraining and downstream data overlap concern is resolved, the same dual-view pretraining recipe could be applied to other periodic systems such as metal-organic frameworks, molecular crystals, or surface slabs, where invariant scalars and equivariant vectors are both informative.
  • The router's task-dependent weighting suggests a broader design principle for property prediction: rather than committing a model family to one symmetry inductive bias, expose both views and let the target loss choose, which may matter most for datasets with mixed output types.
  • The paper's reported with/without-pretraining gap for formation energy is small (MAE 0.0165 versus 0.0174), so much of the advantage may already come from the architectural fusion; a direct test would be whether the router alone, without self-supervised pretraining, matches the full model on the transfer tasks.
  • Because the MoE module sharpens clustering of materials in latent space, the framework could also be useful for structure-property clustering and outlier detection, not just property regression.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The manuscript proposes MGT, a dual-encoder graph transformer that combines an SE3-invariant encoder (edge-wise and node-wise transformers using distances, angles, and lattice vectors) with an SO3-equivariant encoder (spherical harmonics and tensor product layers), fused by a self-attention-based mixture-of-experts router. The model is pretrained on OQMD v1.5 with denoising and contrastive objectives, then fine-tuned on Materials Project and JARVIS property tasks and on catalyst GMAE and HOIP bandgap transfer tasks. The headline claims are MAE reductions of 3.3-20.8% on eight of nine downstream tasks and 15.4-57.8% on transfer tasks, supported by ablations and t-SNE interpretability analyses.

Significance. If the results are reproducible, MGT would be a useful contribution: it is one of the first crystal property predictors to explicitly fuse SE3-invariant and SO3-equivariant geometric views with an adaptive router, and the public code and data releases lower the barrier to verification. The multi-task pretraining design is sensible, and the ablation study is informative. However, the quantitative claims are empirical and depend on clean dataset separation and statistically stable evaluation; those points are currently not established.

major comments (3)
  1. [Methods, Dataset] The pretraining corpus OQMD v1.5 (587,483 structures) is described, and the downstream corpora are MP (2018.6.1) and JARVIS, but the manuscript never checks for structural or compositional overlap between OQMD and the MP/JARVIS test splits. Because OQMD, MP, and JARVIS are overlapping DFT databases, and because the pretraining objectives in Eqs. (11)-(13) are geometric denoising and cross-view contrastive alignment, contamination by test structures could directly inflate the reported 3.3-20.8% MAE improvements and the 15.4-57.8% transfer gains. The authors should report overlap statistics (e.g., exact and near-duplicate matches using structure matching on composition, lattice, and coordinates), and either exclude overlapping structures from pretraining or rerun the fine-tuning comparison on a contamination-free subset. This is a load-bearing check for the central claim that SSL pretraining on OQMD transfers to MP/JARVIS.
  2. [Performance evaluation] The results in Supplementary Tables 1-2 and the transfer tables are single-run MAE/R2 values without repeated seeds or error bars, although the improvements are sometimes modest (3.3%). Single-run comparisons with model selection can be within run-to-run noise, especially for small datasets such as OCD-GMAE (973 structures) and HOIP (1346 structures). The authors should report mean plus/minus standard deviation over at least 5 random seeds and, ideally, paired significance tests, and they should explicitly identify which of the nine downstream tasks is the one where MGT does not outperform the baselines. Without this, the claim of eight of nine and the headline reduction percentages are not statistically grounded.
  3. [Results and discussion, Performance evaluation] The text states that MGT outperforms baselines in eight downstream tasks but never names the ninth task or discusses why it fails there. This missing information matters because the paper's central claim is about universal prediction, and the exceptional case could reveal a systematic limitation of the SE3/SO3 fusion or the MoE router. Please add a table row or paragraph that explicitly reports the one task where MGT does not lead, with the corresponding MAE comparison.
minor comments (6)
  1. [Equations (4) and (6)] The attention weighting is written as sigma(BNorm(QK^T/sqrt(d))) summed over neighbors; this is not softmax attention as commonly used in transformers, so the notation should be clarified and the normalization over neighbors should be justified.
  2. [Methods, Dataset] There is a typo 'JARIVS' in the Dataset paragraph; it should be 'JARVIS'. Also, Extended Data Fig. 2 uses 'Material Project' instead of 'Materials Project'.
  3. [Extended Data Fig. 1] The caption of Extended Data Fig. 1d says 'Materials Project dataset' while the main text says 'Bandgap (OPT) prediction task for JARVIS dataset'; one of these is inconsistent and should be corrected.
  4. [Preliminaries, Eq. (1)] The phrase 'give M' should be 'given M', and the symbol A^N is not defined; please define the alphabet of atomic species used for A.
  5. [Equations (11) and (12)] The denoising losses are written as sums over batch size m, but the noise is applied to angle features in the SE3 graph and edge features in the SO3 graph; please clarify whether the sum is over all angle/edge features in each graph or over graph-level embeddings.
  6. [Abstract and Results] The abstract says MAE is reduced by up to 21% while the Results section reports 3.3-20.8%; these numbers should be aligned for consistency.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper's claims are empirical benchmark results on external datasets and held-out splits, with no fitted parameter renamed as a prediction and no load-bearing self-citation chain.

full rationale

Each load-bearing claim in the paper is an empirical benchmark result rather than a derivation from a fitted parameter. MGT is pretrained on OQMD and then fine-tuned and evaluated on held-out splits of MP and JARVIS (Methods, Dataset), with downstream losses defined in Eq. 15 and pretraining losses in Eqs. 11-14. The MoE router (Eq. 10) is trained as part of supervised fine-tuning, and its learned contribution scores are reported as post-hoc analysis (Extended Data Fig. 1), not used as predictions that define the performance metric. The geometric-completeness assertion that SE3/SO3 graph features can uniquely determine a crystal structure is imported from an external prior work (ref. 14, Yan et al.), not from the present authors, so no self-citation chain forces the architecture choice. Ablations compare model variants on the same held-out splits, which is standard empirical validation. No equation in the paper defines a target quantity in terms of the quantity it claims to predict, and no fitted value is renamed as a 'prediction.' The possible OQMD/MP test-set overlap is a data-leakage/correctness concern, not a circularity of the derivation chain; it does not make any result equivalent to its input by construction.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced. The MGT framework is an architectural method that combines existing geometric representations and learning techniques. The ledger focuses on hand-chosen hyperparameters and standard domain assumptions that the central claim depends on, particularly the completeness of the graph representations and the reliability of DFT labels.

free parameters (4)
  • loss balancing coefficients λ1, λ2, λ3 = λ1=1.0, λ2=0.5, λ3=0.5
    Chosen by hand to weight contrastive and denoising losses in the pretraining objective (Eq. 14). No sensitivity analysis is reported, so the impact of these values on the final results is unknown.
  • denoising noise rate = 0.15
    Set to 0.15 to control the perturbation magnitude in denoising pretraining. This value is chosen without reported tuning and could affect how well the model learns robust features.
  • initial learning rates = 1e-5 for pretraining, 5e-4 for downstream, 6e-3 for transfer learning
    Selected per training phase. No learning rate sweep is described, so these values are additional hand-chosen hyperparameters that could influence the reported improvements.
  • temperature τ in NT-Xent loss = not specified
    Present in Eq. 13 but no value is reported in the manuscript, leaving a reproducibility gap in the contrastive learning setup.
assumptions (4)
  • domain assumption SE3 invariant and SO3 equivariant crystal graphs are geometrically complete and uniquely determine a crystal structure.
    Invoked in the Preliminaries, relying on prior work (ComFormer, ref 14) for completeness. The paper does not re-derive or justify this for the specific datasets used, but treats it as a given foundation.
  • domain assumption DFT-computed properties (formation energy, bandgap, etc.) in OQMD, MP, JARVIS, and transfer datasets are accurate ground truth for the target properties.
    All labels are taken from DFT databases without error analysis. The method's performance is measured against these labels, and any systematic errors in DFT would propagate to the evaluation.
  • domain assumption The local graph construction with a cutoff radius r preserves sufficient geometric information for accurate property prediction.
    The model only sees edges within cutoff r, following prior work. The paper does not demonstrate sufficiency of the chosen cutoff on these datasets, but it is a standard practice in this field.
  • standard math Standard mathematical building blocks (spherical harmonics, tensor products, self-attention) behave as defined.
    Used in the SO3 encoder and MoE router (Methods, Eqs. 8-10). These are well-established tools from the literature, so they are treated as unproven background.

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Cite this review

Pith. "Pith review of Universal crystal material property prediction via multi-view geometric fusion in graph transformers." pith.science (2026). https://pith.science/paper/V2C7F4MB

@misc{pith2026250715303,
  author       = {Pith},
  title        = {Pith review of: Universal crystal material property prediction via multi-view geometric fusion in graph transformers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V2C7F4MB}},
  note         = {Machine review of arXiv:2507.15303}
}
read the original abstract

Accurately and comprehensively representing crystal structures is critical for advancing machine learning in large-scale crystal materials simulations, however, effectively capturing and leveraging the intricate geometric and topological characteristics of crystal structures remains a core, long-standing challenge for most existing methods in crystal property prediction. Here, we propose MGT, a multi-view graph transformer framework that synergistically fuses SE3 invariant and SO3 equivariant graph representations, which respectively captures rotation-translation invariance and rotation equivariance in crystal geometries. To strategically incorporate these complementary geometric representations, we employ a lightweight mixture of experts router in MGT to adaptively adjust the weight assigned to SE3 and SO3 embeddings based on the specific target task. Compared with previous state-of-the-art models, MGT reduces the mean absolute error by up to 21% on crystal property prediction tasks through multi-task self-supervised pretraining. Ablation experiments and interpretable investigations confirm the effectiveness of each technique implemented in our framework. Additionally, in transfer learning scenarios including crystal catalyst adsorption energy and hybrid perovskite bandgap prediction, MGT achieves performance improvements of up to 58% over existing baselines, demonstrating domain-agnostic scalability across diverse application domains. As evidenced by the above series of studies, we believe that MGT can serve as useful model for crystal material property prediction, providing a valuable tool for the discovery of novel materials.

Figures

Figures reproduced from arXiv: 2507.15303 by the authors.

Figure 1
Figure 1. Schematic diagram of MGT framework workflow. a, database preparation, which are pretraining database and fine-tuning database, respectively. b, SE3 invariant features include the edge length ‖𝑥𝑗 ′ − 𝑥𝑖‖ 2 and the angle 𝜃𝑗 ′ 𝑖,𝑖𝑖𝑘 , 𝑘 ∈ {1, 2, 3} . SO3 equivariant features include the edge length ‖𝑥𝑗 ′ − 𝑥𝑖‖ 2 and the equivariant vectors 𝑥𝑗 ′ − 𝑥𝑖 . c, For pretraining, using multi-objective SSL strategy that simultan… view at source ↗
Figure 2
Figure 2. MGT architecture, including multiple different modules. a, Edge-wise transformer. b, Node-wise transformer. c, Equivariant node update module. d, Mix of experts (MoE), using self￾attention mechanism [PITH_FULL_IMAGE:figures/full_fig_p024_2.png] view at source ↗
Figure 6
Figure 6. Performance comparison of MGT on Alloy-GMAE, FG-GMAE, OCD-GMAE and HOIP datasets with MAE, RMSE, and R2 . a, Actual and predicted results of Alloy-GMAE prediction task. b, Actual and predicted results of FG-GMAE prediction task. c, Actual and predicted results of OCD￾GMAE prediction task. d, Actual and predicted results of HOIP bandgap prediction task [PITH_FULL_IMAGE:figures/full_fig_p028_6.png] view at source ↗

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Reference graph

Works this paper leans on

66 extracted references · 54 canonical work pages

  1. [1]

    Application of a quartz -crystal microbalance to measure ionic fluxes in microporous carbons for energy storage

    Levi, Mikhael D., et al. Application of a quartz -crystal microbalance to measure ionic fluxes in microporous carbons for energy storage. Nat. Mater. 8, 872-875 (2009)

    work page 2009

  2. [2]

    Structural control over single -crystalline oxides for heterogeneous catalysis

    Kim, Seok-Jin, et al. Structural control over single -crystalline oxides for heterogeneous catalysis. Nat. Rev. Chem. 1-18 (2025)

    work page 2025

  3. [3]

    Xiang, L. et al. Synergistic Machine Learning Accelerated Discovery of Nanoporous Inorganic Crystals as Non‐Absorbable Oral Drugs. Adv. Mater. 36, 2404688 (2024)

    work page 2024

  4. [4]

    Smoleński, T. et al. Signatures of Wigner crystal of electrons in a monolayer semiconductor. Nature 595, 53–57 (2021)

    2021

  5. [5]

    D., Xia, Y

    Griesemer, S. D., Xia, Y . & Wolverton, C. Accelerating the prediction of stable materials with machine learning. Nat Comput Sci 3, 934–945 (2023)

    work page 2023

  6. [6]

    Gusev, V . V . et al. Optimality guarantees for crystal structure prediction. Nature 619, 68–72 (2023)

    work page 2023

  7. [7]

    Deng, B. et al. CHGNet as a pretrained universal neural network potential for charge -informed atomistic modelling. Nat Mach Intell 5, 1031–1041 (2023)

    work page 2023

  8. [8]

    & Ceder, G

    Reed, J. & Ceder, G. Role of Electronic Structure in the Susceptibility of Metastable Transition - Metal Oxide Structures to Transformation. Chem. Rev. 104, 4513–4534 (2004)

    work page 2004

Show all 66 references
  1. [9]

    Sibanda, D., Oyinbo, S. T. & Jen, T. -C. A review of atomic layer deposition modelling and simulation methodologies: Density functional theory and molecular dynamics. NANOTECHNOL. REV . 11, 1332–1363 (2022)

    2022

  2. [10]

    & Grossman, J

    Xie, T. & Grossman, J. C. Crystal Graph Convolutional Neural Networks for an Accurate and Interpretable Prediction of Material Properties. Phys. Rev. Lett. 120, 145301 (2018)

    2018

  3. [11]

    Yan, K., Liu, Y ., Lin, Y . & Ji, S. Periodic Graph Transformers for Crystal Material Property Prediction. Adv. Neural. Inf. Process. Syst. 35, 15066–15080 (2022)

    2022

  4. [12]

    Lin, Y . et al. Efficient Approximations of Complete Interatomic Potentials for Crystal Property Prediction. In International Conference on Machine Learning, 21260-21287 (2023)

    2023

  5. [13]

    & Yang, B

    Huang, J., Xing, Q., Ji, J. & Yang, B. PerCNet: Periodic complete representation for crystal graphs. Neural Networks 181, 106841 (2025)

    2025

  6. [14]

    Complete and efficient graph transformers for crystal material property prediction

    Yan, K, et al. Complete and efficient graph transformers for crystal material property prediction. In International Conference on Learning Representations, (2024). 19

    2024

  7. [15]

    Batzner, S. et al. E(3) -equivariant graph neural networks for data -efficient and accurate interatomic potentials. Nat Commun 13, 2453 (2022)

    2022

  8. [16]

    & Smidt, T

    Liao, Y .-L. & Smidt, T. Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs. In International Conference on Learning Representations, (2022)

    2022

  9. [17]

    Equiformerv2: Improved equivariant transformer for scaling to higher -degree representations

    Liao, Y.-L., et al. Equiformerv2: Improved equivariant transformer for scaling to higher -degree representations. In International Conference on Learning Representations, (2024)

    2024

  10. [18]

    & Zou, Q

    Jiang, X., Tan, L. & Zou, Q. DGCL: dual-graph neural networks contrastive learning for molecular property prediction. Briefings in Bioinformatics 25, bbae474 (2024)

    2024

  11. [19]

    N., et al

    Rizve, M . N., et al. Exploring complementary strengths of invariant and equivariant representations for few -shot learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 10836–10846 (CVPR, 2021)

    2021

  12. [20]

    Liu, Y . et al. RoBERTa: A Robustly Optimized BERT Pretraining Approach. Preprint at https://arxiv.org/abs/1907.11692 (2019)

    2019 arXiv

  13. [21]

    Ding, N. et al. Parameter -efficient fine-tuning of large -scale pre-trained language models. Nat Mach Intell 5, 220–235 (2023)

    2023

  14. [22]

    & Zisserman, A

    Doersch, C. & Zisserman, A. Multi -task Self-Supervised Visual Learning. In Proceedings of the IEEE international conference on computer vision, 2051-2060 (ICCV , 2017)

    2017

  15. [23]

    & Lukkien, J

    Saeed, A., Ozcelebi, T. & Lukkien, J. Multi -task Self-Supervised Learning for Human Activity Detection. Proc. ACM Interact. Mob. Wearable Ubiquitous Technol. 3, 1–30 (2019)

    2019

  16. [24]

    I., & Jacobs, R

    Jordan, M. I., & Jacobs, R. A. Hierarchical mixtures of experts and the EM algorithm. Neural computation 6, 181-214 (1994)

    1994

  17. [25]

    Deepseek-v3 technical report

    Liu, A., et al. Deepseek-v3 technical report. Preprint at https://arxiv.org/abs/2412.19437 (2024)

    2024 arXiv

  18. [26]

    & Schwaller, P

    Chen, J., Huang, X., Hua, C., He, Y . & Schwaller, P. A multi-modal transformer for predicting global minimum adsorption energy. Nat Commun 16, 3232 (2025)

    2025

  19. [27]

    D., Krishnan, S

    Kim, C., Huan, T. D., Krishnan, S. & Ramprasad, R. A hybrid organic-inorganic perovskite dataset. Sci Data 4, 170057 (2017)

    2017

  20. [28]

    & Hinton, G

    Van der Maaten, L. & Hinton, G. Visualizing data using t -SNE. J. Mach. Learn. Res. 9, 2579– 2605 (2008)

    2008

  21. [29]

    Crystal diffusion variational autoencoder for periodic material generation

    Xie, T., et al. Crystal diffusion variational autoencoder for periodic material generation. Preprint 20 at https://arxiv.org/abs/2110.06197 (2021)

    2021 arXiv

  22. [30]

    Fang, X. et al. Geometry-enhanced molecular representation learning for property prediction. Nat Mach Intell 4, 127–134 (2022)

    2022

  23. [31]

    Rong, Y . et al. Self-supervised graph transformer on large -scale molecular data. Adv. Neural Inf. Process. Syst. 33, 12559–12571 (2020)

    2020

  24. [32]

    Hu, W. et al. Strategies for pre-training graph neural networks. In 8th International Conference on Learning Representations (ICLR, 2020)

    2020

  25. [33]

    & Manzagol, P

    Vincent, P., Larochelle, H., Bengio, Y . & Manzagol, P. -A. Extracting and composing robust features with denoising autoencoders. In ICML '08: Proc. of the 25th International Conference on Machine Learning 1096–1103 (ACM, 2008)

    2008

  26. [34]

    & Barati Farimani, A

    Wang, Y ., Wang, J., Cao, Z. & Barati Farimani, A. Molecular contrastive learning of representations via graph neural networks. Nat Mach Intell 4, 279–287 (2022)

    2022

  27. [35]

    & Ong, S

    Chen, C., Ye, W., Zuo, Y ., Zheng, C. & Ong, S. P. Graph Networks as a Universal Machine Learning Framework for Molecules and Crystals. Chem. Mater. 31, 3564–3572 (2019)

    2019

  28. [36]

    Choudhary, K. et al. The joint automated repository for various integrated simulations (JARVIS) for data-driven materials design. npj Comput Mater 6, 173 (2020)

    2020

  29. [37]

    & DeCost, B

    Choudhary, K. & DeCost, B. Atomistic Line Graph Neural Network for improved materials property predictions. npj Comput Mater 7, 185 (2021)

    2021

  30. [38]

    & Gao, P

    Nie, J., Xiao, P., Ji, K. & Gao, P. ReGNet: Reciprocal Space -Aware Long-Range Modeling and Multi-Property Prediction for Crystals. Preprint at https://arxiv.org/abs/2502.02748 (2025)

    2025 arXiv

  31. [39]

    & Müller, K.-R

    Montavon, G., Samek, W. & Müller, K.-R. Methods for interpreting and understanding deep neural networks. Digital Signal Processing 73, 1–15 (2018)

    2018

  32. [40]

    Weiss, K., Khoshgoftaar, T. M. & Wang, D. A survey of transfer learning. J Big Data 3, 9 (2016)

    2016

  33. [41]

    Dai, W., Yang, Q., Xue, G.-R. & Yu, Y . Boosting for transfer learning. In ICML '07: Proc. of the 24th International Conference on Machine Learning 193–200. (ACM, 2008)

    2008

  34. [42]

    T., Frost, J

    Butler, K. T., Frost, J. M., Skelton, J. M., Svane, K. L. & Walsh, A. Computational materials design of crystalline solids. Chem. Soc. Rev. 45, 6138–6146 (2016)

    2016

  35. [43]

    Chen, C. et al. Accelerating Computational Materials Discovery with Machine Learning and Cloud High-Performance Computing: from Large -Scale Screening to Experimental Validation. J. 21 Am. Chem. Soc. 146, 20009–20018 (2024)

    2024

  36. [44]

    Lin, D. -Z. et al. A high -throughput experimentation platform for data -driven discovery in electrochemistry. Sci. Adv. 11, eadu4391 (2025)

    2025

  37. [45]

    Szymanski, N. J. et al. An autonomous laboratory for the accelerated synthesis of novel materials. Nature 624, 86–91 (2023)

    2023

  38. [46]

    Gainza, P. et al. De novo design of protein interactions with learned surface fingerprints. Nature 617, 176–184 (2023)

    2023

  39. [47]

    & You, F

    Wang, Z. & You, F. Leveraging generative models with periodicity-aware, invertible and invariant representations for crystalline materials design. Nat Comput Sci, 1-12, (2025)

    2025

  40. [48]

    Jiao, R. et al. Crystal structure prediction by joint equivariant diffusion. Adv. Neural Inf. Process. Syst. 36, 17464-17497 (2023)

    2023

  41. [49]

    E., Kirklin, S., Aykol, M., Meredig, B

    Saal, J. E., Kirklin, S., Aykol, M., Meredig, B. & Wolverton, C. Materials Design and Discovery with High -Throughput Density Functional Theory: The Open Quantum Materials Database (OQMD). JOM 65, 1501–1509 (2013)

    2013

  42. [50]

    M., Butler, K

    Antunes, L. M., Butler, K. T. & Grau-Crespo, R. Crystal structure generation with autoregressive large language modeling. Nat Commun 15, 10570 (2024)

    2024

  43. [51]

    T., Boes, J

    Mamun, O., Winther, K. T., Boes, J. R. & Bligaard, T. High -throughput calculations of catalytic properties of bimetallic alloy surfaces. Sci Data 6, 76 (2019)

    2019

  44. [52]

    Pablo-García, S. et al. Fast evaluation of the adsorption energy of organic molecules on metals via graph neural networks. Nat Comput Sci 3, 433–442 (2023)

    2023

  45. [53]

    Lan, J. et al. AdsorbML: a leap in efficiency for adsorption energy calculations using generalizable machine learning potentials. npj Comput Mater 9, 172 (2023)

    2023

  46. [54]

    Chanussot, L. et al. Open Catalyst 2020 (OC20) Dataset and Community Challenges. ACS Catal. 11, 6059–6072 (2021)

    2021

  47. [55]

    Acosta, F. M. A. Radial basis function and related models: An overview. Signal Processing 45, 37–58 (1995)

    1995

  48. [56]

    Thomas, N. et al. Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds. Preprint at https://arxiv.org/abs/1802.08219 (2018)

    2018 arXiv

  49. [57]

    & Smidt, T

    Geiger, M. & Smidt, T. e3nn: Euclidean Neural Networks. Preprint at 22 https://arxiv.org/abs/2207.09453 (2022)

    2022 arXiv

  50. [58]

    Vaswani, A. et al. Attention is all you need. Adv. Neural Inf. Process. Syst. 30, 5998–6008 (2017)

    2017

  51. [59]

    Improved deep metric learning with multi -class n-pair loss objective

    Sohn, K. Improved deep metric learning with multi -class n-pair loss objective. Adv. Neural Inf. Process. Syst. 29 (2016)

    2016

  52. [60]

    & Orabona, F

    Zhuang, Z., Liu, M., Cutkosky, A. & Orabona, F. Understanding AdamW through Proximal Methods and Scale-Freeness. Preprint at https://arxiv.org/abs/2202.00089 (2022)

    2022 arXiv

  53. [61]

    Paszke, A. et al. PyTorch: An Imperative Style, High -Performance Deep Learning Library. Adv. Neural Inf. Process. Syst. 32, 8024–8035 (2019)

    2019

  54. [62]

    & Lenssen, J

    Fey, M. & Lenssen, J. E. Fast Graph Representation Learning with PyTorch Geometric. Preprint at http://arxiv.org/abs/1903.02428 (2019)

    2019 arXiv

  55. [63]

    Barroso-Luque, L. et al. Open Materials 2024 (OMat24) Inorganic Materials Dataset and Models. Preprint at https://arxiv.org/abs/2410.12771 (2024)

    2024 arXiv

  56. [64]

    Hjorth Larsen, A. et al. The atomic simulation environment —a Python library for working with atoms. J. Phys.: Condens. Matter 29, 273002 (2017)

    2017

  57. [65]

    Ong, S. P. et al. Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis. Computational Materials Science 68, 314–319 (2013)

    2013

  58. [66]

    Cui, T. et al. Geometry-enhanced pretraining on interatomic potentials. Nat Mach Intell 6, 428– 436 (2024). 23 Fig. 1. Schematic diagram of MGT framework workflow. a, database preparation, which are pretraining database and fine-tuning database, respectively. b, SE3 invariant ...

    2024

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.