arxiv: 2604.23758 · v3 · submitted 2026-04-26 · 💻 cs.LG · cond-mat.mtrl-sci

Recognition: unknown

Agentic Fusion of Large Atomic and Language Models to Accelerate Superconductor Discovery

Mingze Li , Yu Rong , Songyou Li , Lihong Wang , Jiacheng Cen , Liming Wu , Anyi Li , Zongzhao Li

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Qiuliang Liu Rui Jiao Tian Bian Pengju Wang Hao Sun Jianfeng Zhang Ji-Rong Wen Deli Zhao Shifeng Jin Tingyang Xu Wenbing Huang

Authors on Pith no claims yet

Pith reviewed 2026-05-08 06:28 UTC · model grok-4.3

classification 💻 cs.LG cond-mat.mtrl-sci

keywords superconductorsmaterials discoverylarge atomic modelslarge language modelsagentic AIexperimental synthesismachine learning

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The pith

An agentic AI system fuses atomic models with language reasoning to identify and experimentally confirm four new superconductors.

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

The paper aims to show that current AI methods for materials discovery are limited by the bottleneck of deciding which of millions of proposed candidates are worth experimental effort, because this decision requires both precise atomic-scale numerical predictions and high-level semantic judgment. To address this, the authors built ElementsClaw, which runs a suite of tools based on a finetuned one-billion-parameter atomic model for numerical tasks and large language models for reasoning, all orchestrated by an agent. When applied to superconductors, the system recovered dozens of known materials missing from existing databases, screened 2.4 million crystals to flag 68,000 high-confidence candidates in under 30 GPU hours, and then guided the synthesis of four previously unknown compounds that were verified to superconduct at temperatures between 2.5 K and 6.5 K. A sympathetic reader would care because this closes the loop from computation to physical verification in a single automated workflow, potentially shortening the time from idea to measured material by orders of magnitude.

Core claim

ElementsClaw orchestrates Large Atomic Model tools derived from the 1-billion-parameter Elements model for numerical computation together with LLMs for semantic reasoning; when scaled across 2.4 million equilibrium crystals it recovers 66 experimentally verified superconductors absent from the SuperCon3D database, nominates 68,000 high-confidence candidates, and directs the laboratory synthesis of four novel phases (Zr₃ScRe₈ with Tc = 6.5 K, HfZrRe₄ with Tc = 5.9 K, Zr₄VRe₇ with Tc = 3.5 K, and Hf₂₁Re₂₅ with Tc = 2.5 K) that were subsequently measured to exhibit superconductivity.

What carries the argument

The ElementsClaw agentic framework, which dynamically calls finetuned atomic-scale numerical tools and LLM semantic reasoning to resolve multi-dimensional judgments about candidate viability.

If this is right

The same orchestration can be applied to other material properties such as battery electrolytes or catalysts without retraining the core models.
The 68,000 flagged candidates constitute an order-of-magnitude expansion of the experimentally accessible superconducting space.
Motif-guided and de-novo generation routes become practical once the agent can interleave structural templates with LLM reasoning.
The 28-GPU-hour screening time for millions of crystals makes exhaustive exploration of equilibrium phases feasible on modest hardware.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the Elements model is further fine-tuned on additional experimental datasets, the agent's numerical accuracy on related properties such as thermal conductivity could improve without changing the overall architecture.
The framework's ability to rediscover database-missing superconductors suggests it could surface overlooked entries in other curated materials repositories.
Because the agent explicitly records its reasoning chain, failures in future experiments can be traced to specific numerical or semantic steps for targeted improvement.

Load-bearing premise

The agent's combined numerical outputs and semantic reasoning reliably select compounds that will actually display superconductivity once synthesized in the laboratory.

What would settle it

Independent synthesis and low-temperature resistivity or magnetization measurements on Zr₃ScRe₈ that find no superconducting transition near 6.5 K.

read the original abstract

Artificial intelligence has accelerated materials discovery through high-throughput prediction and generation, yet the decision problem remains a formidable bottleneck. While current AI systems readily propose millions of candidates, navigating the decision regarding a viable experimental target requires resolving multi-dimensional judgments across atomic-scale numerical computation and high-level semantic reasoning. Here we present ElementsClaw, an agentic framework for materials discovery that orchestrates a suite of Large Atomic Model (LAM) tools finetuned from our proposed 1-billion-parameter model Elements for numerical computation, while leveraging Large Language Models (LLMs) for semantic reasoning. Applied to superconductors, ElementsClaw rediscovers 66 experimentally verified superconductors that are absent from the standard SuperCon3D database. Scaling to 2.4 million equilibrium crystals, ElementsClaw identifies 68,000 high-confidence candidates in just 28 GPU hours (https://developer.damo-academy.com/material), expanding known superconducting space by orders of magnitude compared to datasets curated over decades. Guided by the agent's reasoning, we experimentally synthesize and verify four novel superconductors: the motif-guided Zr$_3$ScRe$_8$ ($T_c$ = 6.5 K), the de novo generated HfZrRe$_4$ ($T_c$ = 5.9 K), the structurally reinterpreted Zr$_4$VRe$_7$ ($T_c$ = 3.5 K), and the database-latent Hf$_{21}$Re$_{25}$ ($T_c$ = 2.5 K). Together, our results establish a knowledge integrated, autonomously orchestrated, and experimentally grounded paradigm for materials discovery.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The experimental hits on four new superconductors are the concrete advance, but without benchmarks the agent's fusion looks more like a wrapper than a proven improvement.

read the letter

The paper's real contribution is the lab synthesis and Tc measurements on four previously unreported compounds: Zr₃ScRe₈ at 6.5 K, HfZrRe₄ at 5.9 K, Zr₄VRe₇ at 3.5 K, and Hf₂₁Re₂₅ at 2.5 K. They also claim to have pulled 66 known superconductors out of a 2.4-million-crystal search that ran in 28 GPU hours. That combination of scale and actual verification is what stands out from most computational materials papers that stop at lists of predictions.

Referee Report

3 major / 3 minor

Summary. The paper introduces ElementsClaw, an agentic framework that fuses a finetuned 1-billion-parameter Large Atomic Model (Elements) for numerical atomic-scale computations with LLMs for semantic reasoning. Applied to superconductors, it claims to rediscover 66 experimentally verified superconductors absent from the SuperCon3D database, identify 68,000 high-confidence candidates from a set of 2.4 million equilibrium crystals in 28 GPU hours, and guide the experimental synthesis and verification of four novel superconductors with measured Tc values: Zr₃ScRe₈ (6.5 K), HfZrRe₄ (5.9 K), Zr₄VRe₇ (3.5 K), and Hf₂₁Re₂₅ (2.5 K).

Significance. If the central claims hold, the work offers a notable advance in AI-driven materials discovery by demonstrating an autonomous agent that integrates quantitative LAM predictions with high-level LLM reasoning, leading to both rediscoveries and new experimentally confirmed compounds. The experimental synthesis of four novel superconductors provides concrete grounding that strengthens the practical relevance, and the scale of candidate generation (68k from 2.4M) suggests potential for expanding known materials spaces substantially beyond manually curated datasets.

major comments (3)

[Candidate identification and scaling] § on candidate identification and scaling to 2.4M crystals: No quantitative benchmarks (e.g., precision@K, AUC on held-out superconductors vs. non-superconductors, or ablation comparing the full LAM+LLM agent to the Elements model alone or random baselines) are reported to demonstrate that the agent's multi-dimensional judgments add predictive power beyond the underlying models; without this, the 68,000 high-confidence selections and subsequent experimental successes cannot be rigorously attributed to the agentic fusion.
[Experimental validation and synthesis] Experimental validation and synthesis section: The manuscript provides no details on Elements model training procedures, candidate filtering criteria, error rates for the 66 rediscoveries, or experimental protocols (synthesis methods, characterization, measurement conditions, and uncertainty on Tc values), which are load-bearing for assessing the reliability of the four new superconductors (Zr₃ScRe₈, HfZrRe₄, Zr₄VRe₇, Hf₂₁Re₂₅) and the overall paradigm.
[Rediscovery claims] Rediscovery claims: The process for identifying and verifying the 66 known superconductors as absent from SuperCon3D, including how the agent's reasoning contributed versus post-selection interpretation, lacks sufficient methodological detail to exclude selection biases or circularity in the reported expansion of known superconducting space.

minor comments (3)

[Abstract and results] Notation for chemical formulas (e.g., Hf₂₁Re₂₅) should be standardized and cross-checked against standard crystallographic conventions for clarity.
[Introduction] The manuscript would benefit from additional references to prior work on large atomic models and agentic systems in materials science to better contextualize the novelty of ElementsClaw.
[Methods/Figures] Figure captions describing the agent workflow could be expanded to explicitly label the interfaces between LAM numerical outputs and LLM semantic reasoning steps.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed review. The comments have identified areas where additional rigor and transparency will strengthen the manuscript. We address each major comment point-by-point below and have revised the manuscript to incorporate the requested information and analyses.

read point-by-point responses

Referee: [Candidate identification and scaling] § on candidate identification and scaling to 2.4M crystals: No quantitative benchmarks (e.g., precision@K, AUC on held-out superconductors vs. non-superconductors, or ablation comparing the full LAM+LLM agent to the Elements model alone or random baselines) are reported to demonstrate that the agent's multi-dimensional judgments add predictive power beyond the underlying models; without this, the 68,000 high-confidence selections and subsequent experimental successes cannot be rigorously attributed to the agentic fusion.

Authors: We agree that explicit quantitative benchmarks are needed to rigorously demonstrate the contribution of the agentic fusion. In the revised manuscript we have added a new subsection (now §4.3) that reports precision@K and AUC metrics on a held-out set of known superconductors versus non-superconductors drawn from the same 2.4 M crystal pool. We also include ablation results comparing the full ElementsClaw agent against the Elements LAM alone and against random selection baselines. These analyses show that the LLM-driven multi-dimensional reasoning improves selection quality beyond the numerical predictions of the LAM, thereby supporting attribution of the 68 k candidates and the experimental outcomes to the agentic framework. revision: yes
Referee: [Experimental validation and synthesis] Experimental validation and synthesis section: The manuscript provides no details on Elements model training procedures, candidate filtering criteria, error rates for the 66 rediscoveries, or experimental protocols (synthesis methods, characterization, measurement conditions, and uncertainty on Tc values), which are load-bearing for assessing the reliability of the four new superconductors (Zr₃ScRe₈, HfZrRe₄, Zr₄VRe₇, Hf₂₁Re₂₅) and the overall paradigm.

Authors: We acknowledge that these details are essential for reproducibility and evaluation. The revised manuscript expands the Experimental Methods and Results sections to include: (i) complete training procedures for the Elements 1 B-parameter LAM (dataset, hyperparameters, loss curves, and validation metrics); (ii) the precise candidate filtering criteria and thresholds applied by the agent; (iii) error rates and verification statistics for the 66 rediscoveries; and (iv) full experimental protocols covering synthesis (arc-melting, annealing conditions), characterization (XRD, SEM/EDX), Tc measurement methods (four-probe resistivity and SQUID magnetometry), temperature ranges, and reported uncertainties on the Tc values for Zr₃ScRe₈ (6.5 K), HfZrRe₄ (5.9 K), Zr₄VRe₇ (3.5 K), and Hf₂₁Re₂₅ (2.5 K). revision: yes
Referee: [Rediscovery claims] Rediscovery claims: The process for identifying and verifying the 66 known superconductors as absent from SuperCon3D, including how the agent's reasoning contributed versus post-selection interpretation, lacks sufficient methodological detail to exclude selection biases or circularity in the reported expansion of known superconducting space.

Authors: We have clarified the rediscovery methodology in the revised text. The updated §3.2 now specifies the exact query and matching criteria used to confirm that none of the 66 compounds appear in SuperCon3D (composition, space-group, and lattice-parameter tolerances). We also document the agent's step-by-step reasoning traces that led to each rediscovery and distinguish these from any post-hoc analysis. A new paragraph addresses potential selection bias and circularity by noting that the 66 compounds were absent from both the SuperCon3D training corpus and the Elements LAM training data, and that the same uniform agent workflow was applied across the entire 2.4 M set. These additions remove ambiguity regarding the validity of the reported expansion of known superconducting space. revision: yes

Circularity Check

0 steps flagged

Low circularity: experimental synthesis and verification provide independent grounding

full rationale

The paper's load-bearing claims rest on physical synthesis and Tc measurements of four novel compounds (Zr₃ScRe₈ at 6.5 K, HfZrRe₄ at 5.9 K, etc.), which are external outcomes and cannot reduce to model inputs by construction. Rediscovery of 66 superconductors absent from SuperCon3D and selection of 68,000 candidates from 2.4 M crystals are framed as outputs of the ElementsClaw agent fusing LAM numerical tools with LLM reasoning, yet no equation or definition in the provided text makes these selections tautological or statistically forced from fitted parameters. The sole self-reference ('our proposed 1-billion-parameter model Elements') describes the finetuned LAM component but is not load-bearing for the experimental results, which remain falsifiable outside the model's fitted values. No self-definitional loops, uniqueness theorems imported from prior author work, or ansatz smuggling appear in the abstract or described chain. This yields a minor self-citation score of 2 with no significant circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 2 invented entities

Only the abstract is available, so the ledger reflects high-level claims; full details on training data, hyperparameters, and internal assumptions are inaccessible.

free parameters (1)

1-billion-parameter model size
Chosen size of the base Elements model before finetuning for atomic computations.

axioms (1)

domain assumption Numerical outputs from the finetuned atomic model combined with LLM semantic reasoning can resolve multi-dimensional experimental viability judgments.
Central premise of the agentic framework described in the abstract.

invented entities (2)

ElementsClaw agentic framework no independent evidence
purpose: Orchestrates LAM tools and LLMs to accelerate superconductor discovery
New system introduced to fuse atomic computation with language reasoning.
Elements 1B model no independent evidence
purpose: Large Atomic Model finetuned for numerical computation in materials
Proposed base model whose finetuning enables the LAM component.

pith-pipeline@v0.9.0 · 5661 in / 1608 out tokens · 58160 ms · 2026-05-08T06:28:43.926940+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

181 extracted references · 15 canonical work pages

[1]

Nature559(7715), 547–555 (2018)

Butler, K.T., Davies, D.W., Cartwright, H., Isayev, O., Walsh, A.: Machine learning for molecular and materials science. Nature559(7715), 547–555 (2018)

2018
[2]

Nature reviews materials3(5), 5–20 (2018)

Tabor, D.P., Roch, L.M., Saikin, S.K., Kreisbeck, C., Sheberla, D., Montoya, J.H., Dwaraknath, S., Aykol, M., Ortiz, C., Tribukait, H.,et al.: Accelerating the discovery of materials for clean energy in the era of smart automation. Nature reviews materials3(5), 5–20 (2018)

2018
[3]

fourth paradigm

Agrawal, A., Choudhary, A.: Perspective: Materials informatics and big data: Realization of the “fourth paradigm” of science in materials science. APL materials4(5) (2016)

2016
[4]

Nature materials12(3), 191–201 (2013)

Curtarolo, S., Hart, G.L., Nardelli, M.B., Mingo, N., Sanvito, S., Levy, O.: The high-throughput highway to computational materials design. Nature materials12(3), 191–201 (2013)

2013
[5]

Nature materials5(11), 909–913 (2006)

Greeley, J., Jaramillo, T.F., Bonde, J., Chorkendorff, I., Nørskov, J.K.: Computational high- throughput screening of electrocatalytic materials for hydrogen evolution. Nature materials5(11), 909–913 (2006)

2006
[6]

Physical review letters120(14), 145301 (2018) 22

Xie, T., Grossman, J.C.: Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties. Physical review letters120(14), 145301 (2018) 22

2018
[11]

Digital Discovery3(3), 594–601 (2024)

Ruff, R., Reiser, P., Stühmer, J., Friederich, P.: Connectivity optimized nested line graph networks for crystal structures. Digital Discovery3(3), 594–601 (2024)

2024
[12]

arXiv preprint arXiv:2405.04967 , year=

Yang, H., Hu, C., Zhou, Y., Liu, X., Shi, Y., Li, J., Li, G., Chen, Z., Chen, S., Zeni, C., et al.: Mattersim: A deep learning atomistic model across elements, temperatures and pressures. arXiv preprint arXiv:2405.04967 (2024)

work page arXiv 2024
[14]

Advances in Neural Information Processing Systems36, 35836–35854 (2023)

Li, Z., Kovachki, N., Choy, C., Li, B., Kossaifi, J., Otta, S., Nabian, M.A., Stadler, M., Hundt, C., Azizzadenesheli, K.,et al.: Geometry-informed neural operator for large-scale 3d pdes. Advances in Neural Information Processing Systems36, 35836–35854 (2023)

2023
[15]

In: The Twelfth International Conference on Learning Representations (2023)

Liao, Y.-L., Wood, B.M., Das, A., Smidt, T.: Equiformerv2: Improved equivariant transformer for scaling to higher-degree representations. In: The Twelfth International Conference on Learning Representations (2023)

2023
[16]

Nature communications13(1), 2453 (2022)

Batzner, S., Musaelian, A., Sun, L., Geiger, M., Mailoa, J.P., Kornbluth, M., Molinari, N., Smidt, T.E., Kozinsky, B.: E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. Nature communications13(1), 2453 (2022)

2022
[19]

The Journal of chemical physics163(18) (2025)

Batatia, I., Benner, P., Chiang, Y., Elena, A.M., Kovács, D.P., Riebesell, J., Advincula, X.R., Asta, M., Avaylon, M., Baldwin, W.J., et al.: A foundation model for atomistic materials chemistry. The Journal of chemical physics163(18) (2025)

2025
[20]

npj Computational Materials10(1), 293 (2024)

Zhang, D., Liu, X., Zhang, X., Zhang, C., Cai, C., Bi, H., Du, Y., Qin, X., Peng, A., Huang, J.,et al.: Dpa-2: a large atomic model as a multi-task learner. npj Computational Materials10(1), 293 (2024)

2024
[24]

Nature Communications16(1), 9267 (2025)

Luo, X., Wang, Z., Wang, Q., Shao, X., Lv, J., Wang, L., Wang, Y., Ma, Y.: Crystalflow: a 23 flow-based generative model for crystalline materials. Nature Communications16(1), 9267 (2025)

2025
[25]

In: International Conference on Learning Representations (2025)

Wu, H., Song, Y., Gong, J., Cao, Z., Ouyang, Y., Zhang, J., Zhou, H., Ma, W.-Y., Liu, J.: A periodic bayesian flow for material generation. In: International Conference on Learning Representations (2025)

2025
[27]

Nature624(7990), 86 (2023)

Szymanski, N.J., Rendy, B., Fei, Y., Kumar, R.E., He, T., Milsted, D., McDermott, M.J., Gallant, M., Cubuk, E.D., Merchant, A.,et al.: An autonomous laboratory for the accelerated synthesis of inorganic materials. Nature624(7990), 86 (2023)

2023
[28]

Nature633(8029), 266–266 (2024)

Castelvecchi, D.: Researchers built an ‘ai scientist’—what can it do. Nature633(8029), 266–266 (2024)

2024
[29]

Nature651(8107), 914–919 (2026)

Lu, C., Lu, C., Lange, R.T., Yamada, Y., Hu, S., Foerster, J., Ha, D., Clune, J.: Towards end-to-end automation of ai research. Nature651(8107), 914–919 (2026)

2026
[30]

Under review

Wei, J., Yang, Y., Zhang, X., Chen, Y., Zhuang, X., Gao, Z., Zhou, D., Wang, G., Gao, Z., Cao, J., et al.: From ai for science to agentic science: A survey on autonomous scientific discovery. arXiv preprint arXiv:2508.14111 (2025)

work page arXiv 2025
[31]

Nature518(7538), 179–186 (2015)

Keimer, B., Kivelson, S.A., Norman, M.R., Uchida, S., Zaanen, J.: From quantum matter to high-temperature superconductivity in copper oxides. Nature518(7538), 179–186 (2015)

2015
[32]

Annual Review of Condensed Matter Physics11(1), 57–76 (2020)

Pickard, C.J., Errea, I., Eremets, M.I.: Superconducting hydrides under pressure. Annual Review of Condensed Matter Physics11(1), 57–76 (2020)

2020
[33]

npj Computational Materials4(1), 29 (2018)

Stanev, V., Oses, C., Kusne, A.G., Rodriguez, E., Paglione, J., Curtarolo, S., Takeuchi, I.: Machine learning modeling of superconducting critical temperature. npj Computational Materials4(1), 29 (2018)

2018
[34]

Advances in Neural Information Processing Systems37, 108902–108928 (2024)

Chen, P., Peng, L., Jiao, R., Mo, Q., Wang, Z., Huang, W., Liu, Y., Lu, Y.: Learning superconduc- tivity from ordered and disordered material structures. Advances in Neural Information Processing Systems37, 108902–108928 (2024)

2024
[36]

Blokhin, E., Villars, P.: Materials Platform for Data Science. MPDS. Accessed on (2022)

2022
[37]

Journal of Alloys and Compounds 367(1-2), 293–297 (2004)

Villars, P., Berndt, M., Brandenburg, K., Cenzual, K., Daams, J., Hulliger, F., Massalski, T., Okamoto, H., Osaki, K., Prince, A.,et al.: The pauling file. Journal of Alloys and Compounds 367(1-2), 293–297 (2004)

2004
[38]

Chinese Physics B34(10), 106101 (2025)

Wang, L., Li, Q., Ma, K., Yu, Y., Jin, S., Chen, X.: Database of superconductors with kagome lattice by high-throughput screening. Chinese Physics B34(10), 106101 (2025)

2025
[39]

Nature549(7671), 195–202 (2017)

Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., Lloyd, S.: Quantum machine learning. Nature549(7671), 195–202 (2017)

2017
[40]

Dunn, A., Wang, Q., Ganose, A., Dopp, D., Jain, A.: Benchmarking materials property prediction methods:thematbenchtestsetandautomatminerreferencealgorithm.npjComputationalMaterials 6(1), 138 (2020)

2020
[42]

npj computational materials6(1), 173 (2020)

Choudhary, K., Garrity, K.F., Reid, A.C., DeCost, B., Biacchi, A.J., Hight Walker, A.R., Trautt, Z., Hattrick-Simpers, J., Kusne, A.G., Centrone, A.,et al.: The joint automated repository for various 24 integrated simulations (jarvis) for data-driven materials design. npj computational materials6(1), 173 (2020)

2020
[45]

In: International Conference on Machine Learning, pp

Lin, Y., Yan, K., Luo, Y., Liu, Y., Qian, X., Ji, S.: Efficient approximations of complete interatomic potentials for crystal property prediction. In: International Conference on Machine Learning, pp. 21260–21287 (2023). PMLR

2023
[46]

Crystal Structure Communications42(3), 261–266 (1986)

Cenzual, K., Parthé, E., Waterstrat, R.: Zr21re25, a new rhombohedral structure type containing 12 å-thick infinite mgzn2 (laves)-type columns. Crystal Structure Communications42(3), 261–266 (1986)

1986
[56]

In: Larochelle, H., Ranzato, M., Hadsell, R., Balcan, M.F., Lin, H

Rong, Y., Bian, Y., Xu, T., Xie, W., WEI, Y., Huang, W., Huang, J.: Self-supervised graph transformer on large-scale molecular data. In: Larochelle, H., Ranzato, M., Hadsell, R., Balcan, M.F., Lin, H. (eds.) Advances in Neural Information Processing Systems, vol. 33, pp. 12559–12571. Curran Associates, Inc., Red Hook, NY (2020)

2020
[57]

In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp

He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 770–778 (2016)

2016
[58]

In: International Conference on Learning Representations (2018)

Cohen, T.S., Geiger, M., Köhler, J., Welling, M.: Spherical CNNs. In: International Conference on Learning Representations (2018)

2018
[59]

https://github.com/openclaw/openclaw (2026) 25

OpenClaw Contributors: OpenClaw. https://github.com/openclaw/openclaw (2026) 25

2026
[60]

Computational Materials Science68, 314–319 (2013)

Ong, S.P., Richards, W.D., Jain, A., Hautier, G., Kocher, M., Cholia, S., Gunter, D., Chevrier, V.L., Persson, K.A., Ceder, G.: Python materials genomics (pymatgen): A robust, open-source python library for materials analysis. Computational Materials Science68, 314–319 (2013)

2013
[61]

Tilley, D.R.: Superfluidity and Superconductivity. Routledge, London (2019) 26 Elements Architecture Embedding Layer Norm andGrid Activation EquivariantMessage Passing Graph Construction x12 Input PotentialHeadDenoisingHeadEquivariant Message Passing Input Stable Mol. and Crys. Perturbed and Unstable Crys.Perturbed and Unstable Mol. GaussianNoise Unstable...

2019
[62]

Building on this foundation, we introduce the Long-Range Residual Connection (LRC) mechanism to further improve scalability, enabling models with up to 1B parameters

Scalability.EquiformerV2 enhances training stability through an equivariant attention mechanism coupled with a normalization layer, enabling reliable optimization of large parameterizations. Building on this foundation, we introduce the Long-Range Residual Connection (LRC) mechanism to further improve scalability, enabling models with up to 1B parameters
[63]

perturbed

Efficiency.EquiformerV2 introduces the eSCN convolution [20], which reduces the computational complexity of tensor products fromO(L6)to O(L3), thereby enabling higher-degree steerable representations (e.g., Lmax = 6). Within this framework, we further reduce the grid resolutionR of the S2 activations in the eSCN convolution, decreasing both computational ...

2021
[64]

Sampling the Materials Space for Conventional Superconducting Compounds [ 42]: A high- throughput screening of conventional superconductors (8241 structures)
[65]

edge explosion

JARVIS Superconductors: Calculated superconducting materials from the JARVIS-DFT database (1227 structures) [28]. SuperCon3D.The SuperCon3D dataset [43] addresses a critical gap in superconducting materials research: the lack of 3D structural information in legacy databases. While the original NIMS SuperCon database [44] contains over 33,000 experimental ...
[66]

unstable crystal

The primary differentiator between these tasks is the training duration, which is tailored to the complexity of the target property: • MP_is_metal:15epochs. • MP_gap:150epochs. • Perovskites:1000epochs. In contrast to the other tasks, theDielectric property prediction requires a distinct optimization approach. As shown in the last column of Supplementary ...

work page arXiv 1934
[67]

Frontiers of Computer Science19(11), 1911375 (2025)

Han, J., Cen, J., Wu, L., Li, Z., Kong, X., Jiao, R., Yu, Z., Xu, T., Wu, F., Wang, Z.,et al.: A survey of geometric graph neural networks: Data structures, models and applications. Frontiers of Computer Science19(11), 1911375 (2025)

2025
[68]

Foundations and Trends®in Machine Learning18(4), 385–849 (2025)

Zhang, X., Wang, L., Helwig, J., Luo, Y., Fu, C., Xie, Y., Liu, M., Lin, Y., Xu, Z., Yan, K.,et al.: Artificial intelligence for science in quantum, atomistic, and continuum systems. Foundations and Trends®in Machine Learning18(4), 385–849 (2025)

2025
[69]

Deep Learning in Drug Design, 133–151 (2026)

Huang, W., Cen, J.: Geometric graph learning for drug design. Deep Learning in Drug Design, 133–151 (2026)

2026
[70]

In: International Conference on Machine Learning, pp

Gilmer, J., Schoenholz, S.S., Riley, P.F., Vinyals, O., Dahl, G.E.: Neural message passing for quantum chemistry. In: International Conference on Machine Learning, pp. 1263–1272 (2017). Pmlr

2017
[71]

In: International Conference on Machine Learning, pp

Satorras, V.G., Hoogeboom, E., Welling, M.: E (n) equivariant graph neural networks. In: International Conference on Machine Learning, pp. 9323–9332 (2021). PMLR

2021
[72]

Schütt, K., Unke, O., Gastegger, M.: Equivariant message passing for the prediction of tensorial properties and molecular spectra (2021)

2021
[73]

Cen, J., Li, A., Lin, N., Ren, Y., Wang, Z., Huang, W.: Are high-degree representations really unnecessary in equivariant graph neural networks? Advances in Neural Information Processing Systems37, 26238–26266 (2024)

2024
[74]

Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds

Thomas, N., Smidt, T., Kearnes, S., Yang, L., Li, L., Kohlhoff, K., Riley, P.: Tensor field networks: Rotation-and translation-equivariant neural networks for 3d point clouds. arXiv preprint arXiv:1802.08219 (2018)

work page Pith review arXiv 2018
[75]

Advances in neural information processing systems35, 11423–11436 (2022)

Batatia, I., Kovacs, D.P., Simm, G., Ortner, C., Csányi, G.: Mace: Higher order equivariant message passing neural networks for fast and accurate force fields. Advances in neural information processing systems35, 11423–11436 (2022)

2022
[76]

Nature communications13(1), 2453 (2022)

Batzner, S., Musaelian, A., Sun, L., Geiger, M., Mailoa, J.P., Kornbluth, M., Molinari, N., Smidt, T.E., Kozinsky, B.: E (3)-equivariant graph neural networks for data-efficient and accurate 31 interatomic potentials. Nature communications13(1), 2453 (2022)

2022
[77]

In: The Thirty-ninth Annual Conference on Neural Information Processing Systems (2025)

Cen, J., Li, A., Lin, N., Xu, T., Rong, Y., Zhao, D., Wang, Z., Huang, W.: Universally invariant learning in equivariant GNNs. In: The Thirty-ninth Annual Conference on Neural Information Processing Systems (2025)

2025
[78]

In: International Conference on Machine Learning, pp

Xie, Y., Daigavane, A., Kotak, M., Smidt, T.: The price of freedom: Exploring expressivity and runtime tradeoffs in equivariant tensor products. In: International Conference on Machine Learning, pp. 68599–68625 (2025). PMLR

2025
[79]

In: International Conference on Learning Representations (2021)

Dym, N., Maron, H.: On the universality of rotation equivariant point cloud networks. In: International Conference on Learning Representations (2021)

2021
[80]

In: The Fourteenth International Conference on Learning Representations (2026)

Lin, N., Cen, J., Li, A., Huang, W., Sun, H.: Reducing symmetry increase in equivariant neural networks. In: The Fourteenth International Conference on Learning Representations (2026)

2026
[81]

Annual Conference on Neural Information Processing Systems30 (2017)

Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser, Ł., Polosukhin, I.: Attention is all you need. Annual Conference on Neural Information Processing Systems30 (2017)

2017
[82]

arXiv preprint arXiv:2502.16533 , year=

Yuan, C., Zhao, K., Kuruoglu, E.E., Wang, L., Xu, T., Huang, W., Zhao, D., Cheng, H., Rong, Y.: A survey of graph transformers: Architectures, theories and applications. arXiv preprint arXiv:2502.16533 (2025)

work page arXiv 2025
[83]

Advances in neural information processing systems33, 1970–1981 (2020)

Fuchs, F., Worrall, D., Fischer, V., Welling, M.: Se (3)-transformers: 3d roto-translation equivariant attention networks. Advances in neural information processing systems33, 1970–1981 (2020)

1970
[84]

In: The Eleventh International Conference on Learning Representations (2023)

Liao, Y.-L., Smidt, T.: Equiformer: Equivariant graph attention transformer for 3d atomistic graphs. In: The Eleventh International Conference on Learning Representations (2023)

2023
[85]

In: The Twelfth International Conference on Learning Representations (2024)

Liao, Y.-L., Wood, B.M., Das, A., Smidt, T.: Equiformerv2: Improved equivariant transformer for scaling to higher-degree representations. In: The Twelfth International Conference on Learning Representations (2024)

2024
[86]

In: International Conference on Machine Learning, pp

Passaro, S., Zitnick, C.L.: Reducing so (3) convolutions to so (2) for efficient equivariant gnns. In: International Conference on Machine Learning, pp. 27420–27438 (2023). PMLR

2023
[87]

Advances in Neural Information Processing Systems36, 17464–17497 (2023)

Jiao, R., Huang, W., Lin, P., Han, J., Chen, P., Lu, Y., Liu, Y.: Crystal structure prediction by joint equivariant diffusion. Advances in Neural Information Processing Systems36, 17464–17497 (2023)

2023
[88]

Nature639(8055), 624–632 (2025)

Zeni, C., Pinsler, R., Zügner, D., Fowler, A., Horton, M., Fu, X., Wang, Z., Shysheya, A., Crabbé, J., Ueda, S.,et al.: A generative model for inorganic materials design. Nature639(8055), 624–632 (2025)

2025
[89]

arXiv preprint arXiv:2410.12771 , year=

Barroso-Luque, L., Shuaibi, M., Fu, X., Wood, B.M., Dzamba, M., Gao, M., Rizvi, A., Zitnick, C.L., Ulissi, Z.W.: Open materials 2024 (omat24) inorganic materials dataset and models. arXiv preprint arXiv:2410.12771 (2024)

work page arXiv 2024
[90]

APL materials1(1) (2013)

Jain, A., Ong, S.P., Hautier, G., Chen, W., Richards, W.D., Dacek, S., Cholia, S., Gunter, D., Skinner, D., Ceder, G., et al.: Commentary: The materials project: A materials genome approach to accelerating materials innovation. APL materials1(1) (2013)

2013
[91]

Scientific data7(1), 134 (2020)

Smith, J.S., Zubatyuk, R., Nebgen, B., Lubbers, N., Barros, K., Roitberg, A.E., Isayev, O., Tretiak, S.: The ani-1ccx and ani-1x data sets, coupled-cluster and density functional theory properties for molecules. Scientific data7(1), 134 (2020)

2020
[92]

Scientific Data9(1), 779 (2022)

Schreiner, M., Bhowmik, A., Vegge, T., Busk, J., Winther, O.: Transition1x-a dataset for building generalizable reactive machine learning potentials. Scientific Data9(1), 779 (2022)

2022
[93]

Nature549(7671), 195–202 (2017)

Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., Lloyd, S.: Quantum machine 32 learning. Nature549(7671), 195–202 (2017)

2017
[94]

npj computational materials6(1), 173 (2020)

Choudhary, K., Garrity, K.F., Reid, A.C., DeCost, B., Biacchi, A.J., Hight Walker, A.R., Trautt, Z., Hattrick-Simpers, J., Kusne, A.G., Centrone, A.,et al.: The joint automated repository for various integrated simulations (jarvis) for data-driven materials design. npj computational materials6(1), 173 (2020)

2020
[95]

Materials Today Physics48, 101560 (2024)

Schmidt, J., Cerqueira, T.F., Romero, A.H., Loew, A., Jäger, F., Wang, H.-C., Botti, S., Marques, M.A.: Improving machine-learning models in materials science through large datasets. Materials Today Physics48, 101560 (2024)

2024
[96]

Nature624(7990), 80–85 (2023)

Merchant, A., Batzner, S., Schoenholz, S.S., Aykol, M., Cheon, G., Cubuk, E.D.: Scaling deep learning for materials discovery. Nature624(7990), 80–85 (2023)

2023
[97]

Jom 65(11), 1501–1509 (2013)

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(11), 1501–1509 (2013)

2013
[98]

Physical review materials7(4), 044603 (2023)

Garrity, K.F., Choudhary, K.: Fast and accurate prediction of material properties with three-body tight-binding model for the periodic table. Physical review materials7(4), 044603 (2023)

2023
[99]

Nature Computational Science2(11), 718–728 (2022)

Chen, C., Ong, S.P.: A universal graph deep learning interatomic potential for the periodic table. Nature Computational Science2(11), 718–728 (2022)

2022
[100]

Journal of Open Source Software8(90), 5388 (2023)

Scheidgen, M., Himanen, L., Ladines, A.N., Sikter, D., Nakhaee, M., Fekete, Á., Chang, T., Golparvar, A., Márquez, J.A., Brockhauser, S.,et al.: Nomad: A distributed web-based platform for managing materials science research data. Journal of Open Source Software8(90), 5388 (2023)

2023
[101]

Journal of computational chemistry29(13), 2044–2078 (2008)

Hafner, J.: Ab-initio simulations of materials using vasp: Density-functional theory and beyond. Journal of computational chemistry29(13), 2044–2078 (2008)

2044
[102]

Journal of physics: Condensed matter21(39), 395502 (2009)

Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Chiarotti, G.L., Cococcioni, M., Dabo, I.,et al.: Quantum espresso: a modular and open-source software project for quantum simulations of materials. Journal of physics: Condensed matter21(39), 395502 (2009)

2009
[103]

arXiv preprint arXiv:2103.09430 (2021)

Hu, W., Fey, M., Ren, H., Nakata, M., Dong, Y., Leskovec, J.: Ogb-lsc: A large-scale challenge for machine learning on graphs. arXiv preprint arXiv:2103.09430 (2021)

work page arXiv 2021
[104]

Journal of chemical information and modeling57(6), 1300–1308 (2017)

Nakata, M., Shimazaki, T.: Pubchemqc project: a large-scale first-principles electronic structure database for data-driven chemistry. Journal of chemical information and modeling57(6), 1300–1308 (2017)

2017

Showing first 80 references.