Pith. sign in

REVIEW 3 major objections 5 minor 3 cited by

Enhancing Materials Discovery with Valence Constrained Design in Generative Modeling

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read CrysVCD claims that generating a charge-balanced chemical formula before generating the crystal structure produces chemically valid crystals, and that fine-tuning on machine-learned stability scores raises thermodynamically stable output…

desk verdict A smart modular two-stage generative model with a real evaluation weakness: stability claims rest on a closed-loop surrogate. read the letter →

arxiv 2507.19799 v1 pith:K7KVV7TC submitted 2025-07-26 cond-mat.mtrl-sci cs.LG

Mouyang Cheng , Weiliang Luo , Hao Tang , Bowen Yu , Yongqiang Cheng , Weiwei Xie , Ju Li , Heather J. Kulik
show 1 more author
Mingda Li
This is my paper
classification cond-mat.mtrl-scics.LG
keywords valencebalancecomposition-firstgenerationcrystaldiffusionmodelthermodynamicstabilityphononconditionalthermalconductivitydielectricconstant
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

This paper proposes CrysVCD, a generative model for crystals that refuses to let the network guess charge balance. Instead, a transformer first writes a chemical formula as a sequence of element-oxidation-state tokens whose charges sum to zero, and a diffusion model then builds the atomic structure for that formula. The claim is that putting the valence constraint before structure generation removes a large class of chemically invalid outputs and makes stability screening far cheaper, since checking a formula's total charge is nearly instantaneous compared with denoising a structure. When the model is fine-tuned on stability scores from a machine-learned interatomic potential, the paper reports 85% of generated crystals are thermodynamically stable and 68% are phonon-stable, and it demonstrates targeted generation of a high-thermal-conductivity semiconductor and a high-dielectric compound. A sympathetic reader would take the central insight to be that chemical rules can be made part of the generative grammar rather than a post-hoc filter.

What carries the argument

The load-bearing object is the valence-constrained elemental language model in Stage I. It tokenizes a formula as valence-labeled element-count pairs $(a^v, c)$, embeds each token by the electronic shell occupancies of that ion following the Aufbau principle, and trains an autoregressive transformer to predict the next token as a joint logit over element-valence and count. A filter enforces charge neutrality $\sum c_i v_i = 0$ before any structure is generated, so every final crystal is valence-balanced by construction. Stage II is an E(3)-equivariant diffusion model performing crystal structure prediction conditioned on the formula, with property embeddings added at both stages and classifier-free guidance at weight $w=2$ for conditional generation.

What would settle it

Take a few hundred CrysVCD-generated structures that the MLIP labels stable and recompute their energy above hull and phonon imaginary frequencies with density functional theory; if the stable fraction falls well below 85% thermodynamic or 68% phonon stability, the headline stability numbers are artifacts of the surrogate evaluator.

Watch

Extended reading notes

Core claim

The central discovery is that decomposing crystal generation into composition first, structure second, with an explicit charge-neutrality constraint, produces chemically valid crystals and improves downstream stability. The composition generator treats each atom in a specific oxidation state, e.g. Fe$^{2+}$ or O$^{2-}$, as a token and autoregressively builds the formula under the constraint that the sum of charge times atom count equals zero, $\sum c_i v_i = 0$; mixed-valence cases such as Fe$_3$O$_4$ are handled by allowing multiple valence tokens for one element. The structure generator then performs crystal structure prediction conditioned on that formula, so the only structures ever denoised are ones whose chemistry is already valid. Fine-tuning the pair on energy-above-hull and phonon-stability labels from a machine-learned interatomic potential shifts the generated distribution toward stable materials, raising the phonon-stable fraction from 49% to 68% and reaching over 85% thermodynamic stability; the same conditioning machinery steers generation toward high thermal conductivity (a GeC candidate with 183 W $m^{{-1}}$ $K^{{-1}}$) and high dielectric constant (CoSnO$_2$, with surrogate-predicted $\varepsilon \approx 62$ and a DFT-verified component of 70.5).

Load-bearing premise

The 85% and 68% stability rates assume the machine-learned interatomic potential's energy-above-hull and phonon predictions are accurate enough to serve both as fine-tuning labels and as the evaluation metric; only a handful of functional candidates are checked with density functional theory.

Editorial extensions

If this is right

  • Every crystal CrysVCD outputs is charge-balanced by construction, so valence screening no longer needs a post-hoc search over oxidation-state assignments; the paper reports the composition step checks total valence orders of magnitude faster than the diffusion step.
  • Fine-tuning on stability labels from a machine-learned interatomic potential shifts the generated distribution toward lower energy above hull and fewer imaginary phonon modes, raising phonon-stable output from 49% to 68%.
  • The same property-conditioning mechanism can target functional targets beyond stability: high thermal conductivity and high dielectric constant, yielding candidates (hexagonal GeC, CoSnO$_2$) that are absent from the training data.
  • Because Stage II only needs a formula-conditioned structure generator, the valence-constrained composition model can be bolted onto other generative backbones rather than only the diffusion model demonstrated here.

Reading between the lines

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

  • If the machine-learned potential is biased toward its own training distribution, the 85% and 68% stability rates would likely drop under full DFT re-evaluation; the paper's own DFT checks cover only a few selected functional candidates, not a statistical sample of the stability claims.
  • The composition-first idea transfers naturally to other hard chemical constraints, such as electronegativity ordering, magnetic valence, or site-occupancy rules, where the same tokenization-plus-filter trick could prune invalid candidates before expensive structure generation.
  • The concurrent learning loop of generate, evaluate with a fast surrogate, and fine-tune on the resulting labels is a general recipe for scarce property data; its ceiling for dielectric design is set by surrogate accuracy, so the high-kappa candidates should be read as surrogate-guided hypotheses until experimental or higher-level validation.
  • A direct test of the plugin claim would be to swap the Stage II diffusion model for a different structure predictor and measure whether the valence-constrained compositions still lower the energy-above-hull distribution relative to unconstrained generation; the paper shows this effect for one backbone only.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper introduces CrysVCD, a two-stage generative model for crystal structures. Stage I uses a transformer-based elemental language model to autoregressively generate valence-balanced chemical compositions, with token embeddings initialized from electronic configurations; Stage II uses a DiffCSP-style diffusion model to generate crystal structures conditioned on the composition. The authors show that valence-constrained generation lowers the energy-above-hull distribution relative to plain DiffCSP, and that a concurrent learning loop, in which unconditional generations are labeled by stability metrics from the MatterSim machine-learning interatomic potential and then used to fine-tune a conditional model, raises the fraction of generated crystals classified as thermodynamically stable (roughly 85% with Ehull < 0.1 eV) and as phonon-stable (68%). They also demonstrate conditional generation of high-thermal-conductivity materials (e.g., hexagonal GeC with DF T-verified kph = 183 W/m/K) and high-dielectric-constant materials (e.g., CoSnO2 with εDFT,zz = 70.5). The framework is proposed as a modular plug-in that can be integrated into existing generative pipelines.

Significance. If the stability statistics are robust under independent evaluation, this is a useful contribution: the two-stage design explicitly enforces charge neutrality before structure generation, the embeddings encode periodic chemical trends, and the closed-loop fine-tuning scheme is a practical way to steer generation toward stability. The authors also commit to releasing code and data, and they provide DFT-level verification for specific functional candidates (GeC, CoSnO2). The principal uncertainty is that the headline 85% and 68% stability rates are measured with MatterSim, the same surrogate that provides the fine-tuning labels, and the provided surrogate validation (SI Fig. S10) is on in-distribution MP-20 compounds rather than on the generated crystals. The paper itself shows in SI §3.3 that surrogate error grows on a biased high-κ subset (κRMSE 0.86 vs 0.58), so an independent DFT cross-check of the generated crystals is needed to support the central quantitative claims.

major comments (3)
  1. [Stability guided generation and fine-tuning; MLIP and DFT calculations] The reported 85% thermodynamic and 68% phonon stability rates are computed with MatterSim (MatterSim-v1.0.0-1M for Ehull and MatterSim-v1.0.0-5M for phonons), which is the same MLIP that provides the positive/negative labels used to fine-tune the conditional model. This closed loop means the rates partly measure how well the model satisfies the surrogate's preferences, not necessarily how stable the crystals are at the DFT level. The SI validation (Fig. S10) only benchmarks MatterSim on MP-20 entries that are already DFT-stable and likely part of MatterSim's training distribution; it does not validate on generated hypothetical crystals. To make the headline claim load-bearing, the authors should re-evaluate a random sample (e.g., 100–200) of the generated crystals with DFT (PBE) for both Ehull and phonon stability, and report the resulting stability percentages together with a MatterSim-vs-DFT comparison for those structures.
  2. [Abstract and Results (Stability guided generation and fine-tuning)] The abstract states that fine-tuned CrysVCD achieves "85% thermodynamic stability," whereas the Results text states that the model "achieves > 85% stability rate" and does not give an exact percentage or the number of crystals evaluated. Please reconcile these numbers, specify the denominator and the exact Ehull threshold used (the text mentions 0.1 eV, while Fig. 3b refers to thresholds of 0 and -0.05 eV), and state the number of generated crystals over which the 85% and 68% rates are computed.
  3. [Generating high-performance functional materials with CrysVCD (Fig. 4d-f)] The high-κ dielectric generation uses the same GNNOPT surrogate both to fine-tune the conditional model and to screen/evaluate the generated candidates, with DFT verification reported for only one material (CoSnO2). For the claim that the ε distribution shifts toward values above 50, the authors should report how many generated candidates were DFT-verified, or at least list the DFT-computed ε for a handful of top-ranked candidates, so that the reader can gauge the surrogate bias on out-of-distribution generated structures.
minor comments (5)
  1. [Abstract] The abstract contains apparent typos: "Y et" and "V ery" should read "Yet" and "Very," respectively.
  2. [Results, Stability guided generation and fine-tuning] The text contains the typo "CrysCVD" (first paragraph of the benchmarking discussion) where the model name should be "CrysVCD."
  3. [Fig. 3(b) caption] The caption mentions fine-tuning with Ehull thresholds of 0 and -0.05 eV, but these threshold values are not defined or explained in the main text; please clarify what these thresholds mean for the fine-tuning procedure.
  4. [Methods, Chemical formula generation] The comproportionation constraint states that no element may simultaneously exhibit both positive and negative oxidation states; consider clarifying that this applies to different atoms of the same element within one structure, which appears to be the intended meaning.
  5. [Results, Model architecture and Methods] The statement that "all generated crystals are guaranteed to be valence-balanced by construction" should specify that the charge-balance filter is applied to ionic compounds (as described in Methods), while alloys are balanced by construction through zero-valence tokens; this nuance is present but could be stated more explicitly where the claim is made.

Circularity Check

2 steps flagged · score 6.0 of 10

Stability and high-kappa claims are evaluated with the same surrogate models that provide fine-tuning labels; headline rates measure fit to MatterSim/GNNOPT, not independent DFT stability.

  1. fitted input called prediction [Results, 'Stability guided generation and fine-tuning in CrysVCD' (Fig. 3); Methods, 'MLIP and DFT calculations']
    "To further evaluate the stability of the generated crystals, we use MatterSim to evaluate the Ehull and phonon frequencies, and use these labels to fine-tune the CrysVCD model. ... The portion of phonon-stable configurations (without any imaginary frequency) in the generated crystals increases from 49% (unconditional) to 68% (fine-tuned)."

    The same MatterSim oracle supplies both the fine-tuning labels and the reported stability evaluation. The abstract's '85% thermodynamic stability and 68% phonon stability' therefore describes how well the model reproduces MatterSim preferences, not DFT-level stability. No independent DFT check is reported for the generated crystals underlying those percentages; the only MLIP validation in SI §3.2 is on MP-20 entries already known DFT-stable, and SI §3.3 shows surrogate error can grow out-of-distribution (kappa-RMSE 0.86 vs 0.58). The headline rates are thus fitted-input predictions: the evaluation metric coincides with the training label source.

  2. fitted input called prediction [Results, 'Generating high-performance functional materials with CrysVCD'; SI §3.4]
    "This dataset is used for both fine-tuning the CrysVCD model for conditional generation and training the surrogate model for predicting the dielectric constant. ... Once trained, the GNNOPT model is integrated into the conditional generation loop of fine-tuned CrysVCD to rapidly evaluate and guide the selection of candidate materials with high epsilon."

    The dielectric surrogate is both the optimization target during fine-tuning and the evaluator of generated candidates (epsilon_theta = 62.2 for CoSnO2). Thus the reported shift toward epsilon > 50 (Fig. 4e) is largely a measure of fitting the surrogate; only one candidate has a partial DFT check (epsilon_DFT,zz = 70.5). The surrogate is trained on the same MP-20 entries used to condition the model, so the generation-evaluation loop shares its error model.

full rationale

CrysVCD is a two-stage generator with a valence-constrained composition transformer and a DiffCSP-style structure diffusion model. The valence-balance constraint is enforced by construction and is not circular. The stability fine-tuning labels come from MatterSim evaluations, and the reported stability percentages are computed with the same MatterSim models. This makes the 85%/68% headline a partially closed-loop result: fine-tuning optimizes MatterSim Ehull/phonon scores and evaluation reads out those same scores. The paper's only MLIP validation is on in-distribution MP-20 structures (SI Fig. S10), and SI §3.3 shows error degradation on a biased subset, so the surrogate is not established for generated out-of-distribution structures. Therefore the thermodynamic and phonon stability rates are not independent predictions. The dielectric study is similar: GNNOPT provides both the fine-tuning signal and the evaluation, with only one DFT-verified candidate. Thermal conductivity examples are less circular because the highlighted GeC is verified with DFT phonon band structure and kappa_ph, although screening uses MatterSim. No load-bearing self-citation or imported uniqueness claim was found. Score 6 reflects that some headline 'predictions' reduce to the surrogate label source, while the method, the valence constraint, and the specific DFT-verified candidates retain independent content.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The method imports standard chemical rules, a manually constructed oxidation state table, and pretrained surrogate models. The most significant imported assumption is that MatterSim and the dielectric surrogate are accurate enough to both label training data and evaluate final results.

free parameters (1)
  • classifier-free guidance weight w = 2
    In the Methods section, the guidance weight w = 2 is chosen by hand to scale the property-conditioned distribution. The reported stability and property distributions depend on this choice.
assumptions (4)
  • domain assumption Formal oxidation state balance is a necessary condition for valid ionic crystals.
    Stage I filters generated compositions by requiring charge neutrality sum c_i v_i = 0. This is a standard chemical rule, but it is only a necessary condition and does not guarantee thermodynamic or phonon stability.
  • domain assumption The manually compiled oxidation state list V and the valence decomposition algorithm correctly assign oxidation states for MP-20 compounds.
    The Methods section relies on a hand-built set of non-zero oxidation states and a breadth-first search with comproportionation constraints to label 97.6% of the dataset. Errors in this list would propagate into the generated formulas.
  • domain assumption MatterSim MLIP predictions of energy above hull and phonon imaginary frequencies are accurate enough to serve as training labels and evaluation metrics.
    The full-stability pipeline in the Results and Methods uses MatterSim-v1.0.0-1M for Ehull and MatterSim-v1.0.0-5M for phonons, with DFT applied only to selected functional candidates. This surrogate accuracy is load-bearing for the headline 85% and 68% stability numbers.
  • domain assumption The e3nn surrogate model trained on 944 dielectric entries predicts static dielectric constants accurately enough to guide conditional generation.
    In the high-kappa section, the surrogate model both selects candidates and is used to estimate epsilon for generated materials, with only one DFT verification for CoSnO2.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Enhancing Materials Discovery with Valence Constrained Design in Generative Modeling." pith.science (2026). https://pith.science/paper/K7KVV7TC

@misc{pith2026250719799,
  author       = {Pith},
  title        = {Pith review of: Enhancing Materials Discovery with Valence Constrained Design in Generative Modeling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K7KVV7TC}},
  note         = {Machine review of arXiv:2507.19799}
}
abstract

Diffusion-based deep generative models have emerged as powerful tools for inverse materials design. Yet, many existing approaches overlook essential chemical constraints such as oxidation state balance, which can lead to chemically invalid structures. Here we introduce CrysVCD (Crystal generator with Valence-Constrained Design), a modular framework that integrates chemical rules directly into the generative process. CrysVCD first employs a transformer-based elemental language model to generate valence-balanced compositions, followed by a diffusion model to generate crystal structures. The valence constraint enables orders-of-magnitude more efficient chemical valence checking, compared to pure data-driven approaches with post-screening. When fine-tuned on stability metrics, CrysVCD achieves 85% thermodynamic stability and 68% phonon stability. Moreover, CrysVCD supports conditional generation of functional materials, enabling discovery of candidates such as high thermal conductivity semiconductors and high-$\kappa$ dielectric compounds. Designed as a general-purpose plugin, CrysVCD can be integrated into diverse generative pipeline to promote chemical validity, offering a reliable, scientifically grounded path for materials discovery.

Figures

Figures reproduced from arXiv: 2507.19799 by the authors.

Figure 1
Figure 1. Overview of CrysVCD. Rather than performing pure data-driven denoising diffusion generation, CrysVCD introduces a two-step, property-guided pipeline that incorporates physical and chemical constraints. A property-conditioned elemental language model first generates a composition with balanced chemical valence (e.g., ZrO2), which is then refined by a geometric diffusion model under classifier-free guidance, which int… view at source ↗
Figure 2
Figure 2. Strategies of CrysVCD architecture and training. (a) Tokenizer for the elemental language model as Stage I of CrysVCD. Chemical formulas are first parsed into valence-specific elemental tokens with electronic configurations of oxidation states. These tokenized vectors are then passed into the geometric diffusion model (Stage II) for the structure generation of CrysVCD. (b) Concurrent learning scheme of CrysVCD for o… view at source ↗
Figure 3
Figure 3. Thermodynamic and phonon stability of generated crystals by CrysVCD. (a) Examples of generated crystals from CrysVCD, including alloys (binary and ternary) and ionic compounds with oxidation states (ternary and quaternary) from left to right. (b) Normalized probability distribution of the energy above hull (Ehull) of crystal structures generated by different versions of CrysVCD and the previous generative model Diff… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Generation of high-performance functional materials with CrysVCD. (a) Workflow of first-principles calculations to generate a thermal conductivity dataset considering phonon anharmonicity. (b) Probability distribution of the thermal conductivity of materials generated …

Discussion (0). Sign in to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Chemical filters for ultra-high-throughput materials screening and generation

    cond-mat.mtrl-sci 2026-07 conditional novelty 6.0 of 10

    A configurable oxidation-state filter (SMACT-based) lets users tune strictness and doubles as an RL reward, improving chemical realism of generated crystals.

  2. Charting the emergent low-dimensional manifold of quantum materials

    cond-mat.supr-con 2026-06 unverdicted novelty 6.0 of 10

    Unsupervised manifold learning on ICSD data reveals a low-dimensional embedding that segregates superconductors and predicts critical temperatures across families.

  3. Inverse Design of Inorganic Compounds with Generative AI

    physics.chem-ph 2026-04 unverdicted novelty 2.0 of 10

    A review of generative AI for inverse design of inorganic compounds, analyzing adaptations for their complexity in composition, geometry, symmetry, and electronic structure, with discussion of future benchmarks and sy...

Reference graph

Works this paper leans on

46 extracted references · 32 canonical work pages · cited by 3 Pith papers

  1. [1]

    author Olson, G. B. journal title Computational design of hierarchically structured materials . Science volume 277 , pages 1237--1242 ( year 1997 )

    work page 1997

  2. [2]

    author Olson, G. B. journal title Designing a new material world . Science volume 288 , pages 993--998 ( year 2000 )

    work page 2000

  3. [3]

    author Oganov, A. R. , author Pickard, C. J. , author Zhu, Q. & author Needs, R. J. journal title Structure prediction drives materials discovery . Nature Reviews Materials volume 4 , pages 331--348 ( year 2019 )

    work page 2019

  4. [4]

    journal title Inverse design in search of materials with target functionalities

    author Zunger, A. journal title Inverse design in search of materials with target functionalities . Nature Reviews Chemistry volume 2 , pages 0121 ( year 2018 )

    work page 2018

  5. [5]

    author Han, X.-Q. et al. journal title AI -driven inverse design of materials: Past, present and future . Chinese Physics Letters ( year 2024 )

    work page 2024

  6. [6]

    author Cheng, M. et al. journal title AI -driven materials design: a mini-review . arXiv preprint arXiv:2502.02905 ( year 2025 )

    arXiv 2025

  7. [7]

    , author Fu, X

    author Xie, T. , author Fu, X. , author Ganea, O.-E. , author Barzilay, R. & author Jaakkola, T. journal title Crystal diffusion variational autoencoder for periodic material generation . arXiv preprint arXiv:2110.06197 ( year 2021 )

    arXiv

  8. [8]

    author Jiao, R. et al. journal title Crystal structure prediction by joint equivariant diffusion . Advances in Neural Information Processing Systems volume 36 , pages 17464--17497 ( year 2023 )

    work page 2023

Show all 46 references
  1. [9]

    author Zeni, C. et al. journal title A generative model for inorganic materials design . Nature pages 1--3 ( year 2025 )

    2025

  2. [10]

    author Gruver, N. et al. journal title Fine-tuned language models generate stable inorganic materials as text . arXiv preprint arXiv:2402.04379 ( year 2024 )

    2024 arXiv

  3. [11]

    author Antunes, L. M. , author Butler, K. T. & author Grau-Crespo, R. journal title Crystal structure generation with autoregressive large language modeling . Nature Communications volume 15 , pages 10570 ( year 2024 )

    2024

  4. [12]

    author Yang, S. et al. journal title Generative hierarchical materials search . Advances in Neural Information Processing Systems volume 37 , pages 38799--38819 ( year 2025 )

    2025

  5. [13]

    & author Salimans, T

    author Ho, J. & author Salimans, T. journal title Classifier-free diffusion guidance . arXiv preprint arXiv:2207.12598 ( year 2022 )

    2022 arXiv

  6. [14]

    & author Nichol, A

    author Dhariwal, P. & author Nichol, A. journal title Diffusion models beat gans on image synthesis . Advances in neural information processing systems volume 34 , pages 8780--8794 ( year 2021 )

    2021

  7. [15]

    author Karras, T. et al. journal title Guiding a diffusion model with a bad version of itself . Advances in Neural Information Processing Systems volume 37 , pages 52996--53021 ( year 2024 )

    2024

  8. [16]

    & author Grossman, J

    author Xie, T. & author Grossman, J. C. journal title Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties . Physical review letters volume 120 , pages 145301 ( year 2018 )

    2018

  9. [17]

    author Reiser, P. et al. journal title Graph neural networks for materials science and chemistry . Communications Materials volume 3 , pages 93 ( year 2022 )

    2022

  10. [18]

    , author Jain, A

    author Ho, J. , author Jain, A. & author Abbeel, P. journal title Denoising diffusion probabilistic models . Advances in neural information processing systems volume 33 , pages 6840--6851 ( year 2020 )

    2020

  11. [19]

    author Unke, O. T. et al. journal title SpookyNet : Learning force fields with electronic degrees of freedom and nonlocal effects . Nature communications volume 12 , pages 7273 ( year 2021 )

    2021

  12. [20]

    , author Hao, M

    author Zheng, Q. , author Hao, M. , author Miao, R. , author Schaadt, J. & author Dames, C. journal title Advances in thermal conductivity for energy applications: a review . Progress in Energy volume 3 , pages 012002 ( year 2021 )

    2021

  13. [21]

    author Plata, J. J. et al. journal title An efficient and accurate framework for calculating lattice thermal conductivity of solids: AFLOW—AAPL automatic anharmonic phonon library . npj Computational Materials volume 3 , pages 45 ( year 2017 )

    2017

  14. [22]

    , author Ahlawat, P

    author P \'o ta, B. , author Ahlawat, P. , author Cs \'a nyi, G. & author Simoncelli, M. journal title Thermal conductivity predictions with foundation atomistic models . arXiv preprint arXiv:2408.00755 ( year 2024 )

    2024 arXiv

  15. [23]

    author Li, J. et al. journal title Probing the limit of heat transfer in inorganic crystals with deep learning . arXiv preprint arXiv:2503.11568 ( year 2025 )

    2025 arXiv

  16. [24]

    author Guo, L. et al. journal title Generative deep learning for predicting ultrahigh lattice thermal conductivity materials . npj Computational Materials volume 11 , pages 97 ( year 2025 )

    2025

  17. [25]

    , author Chaput, L

    author Togo, A. , author Chaput, L. & author Tanaka, I. journal title Distributions of phonon lifetimes in B rillouin zones . Physical review B volume 91 , pages 094306 ( year 2015 )

    2015

  18. [26]

    & author Smidt, T

    author Geiger, M. & author Smidt, T. journal title e3nn: Euclidean neural networks . arXiv preprint arXiv:2207.09453 ( year 2022 )

    2022 arXiv

  19. [27]

    author Hung, N. T. , author Okabe, R. , author Chotrattanapituk, A. & author Li, M. journal title Universal ensemble-embedding graph neural network for direct prediction of optical spectra from crystal structures . Advanced Materials volume 36 , pages 2409175 ( year 2024 )

    2024

  20. [28]

    author Ma, A. et al. journal title Topogivity: A machine-learned chemical rule for discovering topological materials . Nano Letters volume 23 , pages 772--778 ( year 2023 )

    2023

  21. [29]

    & author Solja c i \'c , M

    author Ma, A. & author Solja c i \'c , M. journal title Learning simple heuristic rules for classifying materials based on chemical composition . arXiv preprint arXiv:2505.02361 ( year 2025 )

    2025

  22. [30]

    author Jain, A. et al. journal title Commentary: The M aterials P roject: A materials genome approach to accelerating materials innovation . APL materials volume 1 ( year 2013 )

    2013

  23. [31]

    author Radford, A. et al. journal title Language models are unsupervised multitask learners . OpenAI blog volume 1 , pages 9 ( year 2019 )

    2019

  24. [32]

    author Wolf, T. et al. journal title Huggingface's transformers: State-of-the-art natural language processing . arXiv preprint arXiv:1910.03771 ( year 2019 )

    1910 arXiv

  25. [33]

    author Vaswani, A. et al. journal title Attention is all you need . Advances in neural information processing systems volume 30 ( year 2017 )

    2017

  26. [34]

    author Ong, S. P. et al. journal title Python M aterials G enomics (pymatgen): A robust, open-source python library for materials analysis . Computational Materials Science volume 68 , pages 314--319 ( year 2013 )

    2013

  27. [35]

    journal title Convergence properties of the BFGS algoritm

    author Dai, Y.-H. journal title Convergence properties of the BFGS algoritm . SIAM Journal on Optimization volume 13 , pages 693--701 ( year 2002 )

    2002

  28. [36]

    author Larsen, A. H. et al. journal title The atomic simulation environment—a P ython library for working with atoms . Journal of Physics: Condensed Matter volume 29 , pages 273002 ( year 2017 )

    2017

  29. [37]

    , author Chaput, L

    author Togo, A. , author Chaput, L. , author Tadano, T. & author Tanaka, I. journal title Implementation strategies in phonopy and phono3py . J. Phys. Condens. Matter volume 35 , pages 353001 , 10.1088/1361-648X/acd831 ( year 2023 )

    doi

  30. [38]

    journal title First-principles phonon calculations with phonopy and phono3py

    author Togo, A. journal title First-principles phonon calculations with phonopy and phono3py . J. Phys. Soc. Jpn. volume 92 , pages 012001 , 10.7566/JPSJ.92.012001 ( year 2023 )

    2023 doi

  31. [39]

    & author Furthm \"u ller, J

    author Kresse, G. & author Furthm \"u ller, J. journal title Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set . Physical review B volume 54 , pages 11169 ( year 1996 )

    1996

  32. [40]

    author Bl \"o chl, P. E. journal title Projector augmented-wave method . Physical review B volume 50 , pages 17953 ( year 1994 )

    1994

  33. [41]

    & author Joubert, D

    author Kresse, G. & author Joubert, D. journal title From ultrasoft pseudopotentials to the projector augmented-wave method . Physical review b volume 59 , pages 1758 ( year 1999 )

    1999

  34. [42]

    author Perdew, J. P. , author Burke, K. & author Ernzerhof, M. journal title Generalized gradient approximation made simple . Physical review letters volume 77 , pages 3865 ( year 1996 )

    1996

  35. [43]

    , author Xu, N

    author Wang, V. , author Xu, N. , author Liu, J.-C. , author Tang, G. & author Geng, W.-T. journal title VASPKIT : A user-friendly interface facilitating high-throughput computing and analysis using VASP code . Computer Physics Communications volume 267 , pages 108033 ( year 2021 )

    2021

  36. [44]

    , " * write output.state after.block = add.period write newline

    ENTRY address archive author booktitle chapter edition editor eprint howpublished institution journal key month note number organization pages publisher school series title type url doi volume year label INTEGERS output.state before.all mid.sentence after.sentence after.block ...

  37. [45]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

  38. [46]

    author Riebesell, J. et al. journal title Matbench D iscovery--a framework to evaluate machine learning crystal stability predictions . arXiv preprint arXiv:2308.14920 ( year 2023 )

    2023 arXiv

Pith tools

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