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Robust data-driven approach for predicting the configurational energy of high entropy alloys

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Pith's one-line read A pair-interaction model fitted with Bayesian regression and BIC shell selection predicts the configurational energy of refractory high-entropy alloys with a held-out RMSE around 0.6 meV.

desk verdict Solid incremental methods paper for sparse-data HEAs configurational energy; accuracy holds on random configs but thermodynamic claims outrun the validation. read the letter →

arxiv 1908.03665 v1 pith:NHR3DDCZ submitted 2019-08-10 cond-mat.mtrl-sci physics.comp-phstat.ML

Jiaxin Zhang , Xianglin Liu , Sirui Bi , Junqi Yin , Guannan Zhang , Markus Eisenbach This is my paper · ORCID
classification cond-mat.mtrl-sciphysics.comp-phstat.ML
keywords highentropyalloysconfigurationalenergyeffectivepairinteractionmodelBayesianregularizedregressioninformationcriterionuncertaintyquantificationrefractoryfirst-principlescalculations
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 argues that a deliberately simple Hamiltonian—only pair interactions between atoms, truncated at a coordination shell chosen by Bayesian model selection—is enough to predict the configurational energy of refractory high-entropy alloys from sparse DFT data. The authors fit the effective pair interaction (EPI) model to randomly drawn configurations of NbMoTaW, NbMoTaWV, and NbMoTaWTi using Bayesian regularized regression, and report held-out testing RMSE values around 0.6 meV for all three alloys. They further show that choosing the number of shells with the Bayesian information criterion avoids both overfitting on small datasets and underfitting on larger ones, and that pooling configurations from several supercell sizes gives more stable predictions than training on any single small supercell. If correct, the payoff is a cheap substitute for direct DFT that can be fed into Monte Carlo simulations of order-disorder transitions.

What carries the argument

The load-bearing object is the effective pair interaction (EPI) model, an Ising-like Hamiltonian that maps a configuration to an energy through the probabilities $P^{X|Y}_m$ of finding element $X$ in the $m$-th coordination shell around element $Y$, for each independent pair $X\neq Y$. Three pieces carry the argument: Bayesian regularized regression with conjugate gamma priors on the noise and coefficient precisions, which supplies stable point estimates and uncertainty quantification for the pair coefficients; the BIC shell-selection criterion, which decides how many of the shells to keep; and ensemble sampling, which draws configurations from several supercell sizes so the training data include both short-range and long-range order.

What would settle it

Refit Eq. (8) with an additive supercell-size offset and with triplet correlation features on the same DFT data; if either change materially lowers the held-out RMSE or shifts the BIC-selected shell count for these alloys, the pair-only, size-independent assumption behind the 0.6 meV claim is falsified.

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Extended reading notes

Core claim

The central claim is that the configurational energy of a multicomponent alloy can be written, to good accuracy, as a sum of chemically distinct pair probabilities in the first few coordination shells, $E = N\sum_{X\neq Y,m} J^{X,Y}_m P^{X|Y}_m$, and that the coefficients $J^{X,Y}_m$ can be estimated reliably by Bayesian $\ell^2$-regularized regression even when the number of DFT configurations is small. To set model complexity, the paper minimizes the Bayesian information criterion expressed through the residual sum of squares, $\mathrm{BIC}_{\mathrm{RSS}} = n_d \log(\mathrm{RSS}/n_d) + k\log(n_d)$, and shows that the selected shell count grows sensibly with dataset size. With the BIC-selected shells and an ensemble sampling strategy that mixes supercells of 16–160 atoms, the fitted models reach testing RMSE about 0.6 meV on the three refractory alloys, and the uncertainty in the pair interactions drops sharply once a few hundred configurations are available.

Load-bearing premise

The model only works if the configurational energy is fully determined by two-body pair probabilities with coefficients that do not depend on supercell size, so significant triplet or many-body interactions, or a size-dependent offset in the DFT energies, would bias the fitted coefficients and the reported 0.6 meV accuracy.

Editorial extensions

If this is right

  • A Monte Carlo simulation of order-disorder transitions can replace direct DFT calls with the fitted EPI Hamiltonian, because the surrogate predicts large-supercell energies from small-supercell training data to within about 1 meV.
  • The BIC shell count supplies a data-size-dependent recipe—2–3 shells for small datasets, 5–6 for medium ones, 6–9 for large ones—so model complexity no longer has to be set arbitrarily.
  • Ensemble sampling across supercell sizes should be part of similar data-driven alloy models, since it lowers both the mean and the standard deviation of the prediction error compared with training on a single small supercell.
  • Increasing the number of training configurations from 100 to 400 reduces the variance of the fitted pair interactions by more than an order of magnitude, so the framework can tell users how much confidence to place in each energy estimate.
  • For NbMoTaWV and NbMoTaWTi the best model retains more coordination shells than for NbMoTaW, indicating that nearest-neighbor-only pair models would systematically underfit those alloys.

Reading between the lines

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

  • Because the EPI model is pair-only, a direct extension would be to add triplet correlation features and compare BIC; if triplets systematically lower held-out RMSE on these alloys, the 0.6 meV claim would need to be weakened.
  • The BIC-selected shell count can be read as a measured interaction range, which suggests a testable prediction: independent electronic-structure calculations should find longer-ranged or more frustrated effective interactions in NbMoTaWV and NbMoTaWTi than in NbMoTaW.
  • A stricter stress test than the paper reports is to train the model on one refractory alloy and predict another; success would indicate the pair coefficients capture transferable ordering physics, while failure would mean they encode chemistry-specific fits.
  • The paper stops short of propagating the Bayesian parameter uncertainties into Monte Carlo free energies; doing so would reveal whether a 0.6 meV energy error is small enough for accurate order-disorder transition temperatures.
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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

2 major / 5 minor

Summary. The paper proposes a Bayesian regularized regression framework, combined with an effective pair interaction (EPI) model and Bayesian information criterion (BIC) based feature selection, to predict the configurational energy of refractory high entropy alloys from sparse first-principles data. The method is demonstrated on NbMoTaW, NbMoTaWV, and NbMoTaWTi, using DFT energies from supercells of 16--128 or 20--160 atoms, with training data drawn from the three smaller supercells and testing on the largest supercell. The reported held-out test RMSE is around 0.6 meV for all three alloys. The paper also introduces an ensemble sampling strategy that combines configurations from different supercell sizes, analyzes the uncertainty and correlations of the fitted pair interaction parameters, and shows that BIC-based selection of the number of coordination shells reduces the risk of overfitting and underfitting when data are limited.

Significance. If the claims hold, the paper offers a practical recipe for constructing surrogate Hamiltonians for multicomponent alloys with quantified parameter uncertainty, which is valuable because conventional cluster expansion becomes combinatorially intractable for high entropy alloys. The work is concrete: the algorithm steps are clearly enumerated, the DFT data generation is described, and the held-out test evaluation gives a quantitative accuracy statement. The explicit use of BIC for shell truncation and the comparison of Bayesian regression against ordinary least squares are useful methodological contributions. The main limitation is that the validation is restricted to random configurations, so the stated suitability for Monte Carlo simulations of order-disorder transitions is not directly demonstrated.

major comments (2)
  1. [§2.2, Eq. (8) and §3.1, ensemble sampling] The regression model in Eq. (8) assumes that a single set of pair interaction coefficients J_m^{X,Y} describes the configurational energy across all supercell sizes, but the training data combine DFT energies from supercells of 16, 32, 64, and 128 atoms (or 20, 40, 80, and 160 atoms). If the per-atom DFT energies carry any supercell-size-dependent reference offset, for example from different Brillouin-zone sampling or from the definition of the configurational energy itself, then the fitted coefficients and the BIC-selected number of shells would be biased. The manuscript does not discuss this possibility or include a size-dependent offset term in the model. The authors should either add a supercell-size indicator or intercept in the regression, or demonstrate explicitly that no such offset is present for these materials and this DFT setup.
  2. [§3.1 and Step 6 (Section 2.5)] All training and testing configurations are described as randomly drawn, and the reported RMSE values therefore characterize prediction accuracy only for configurations near random disorder. The paper's stated purpose, however, is to feed the fitted Hamiltonian into Monte Carlo simulations for modeling thermodynamics and order-disorder transitions, where the sampled configurations develop short-range order and may include ordered states. The EPI model of Eq. (8) contains pair interactions only, and the paper does not validate the model on ordered or strongly short-range-ordered configurations. The central claim of robustness for thermodynamic applications is thus an extrapolation beyond the tested distribution. I recommend adding validation on ordered supercells or on configurations with strong SRO, or explicitly limiting the accuracy claim to random configurations.
minor comments (5)
  1. [§2.2, Eq. (9)] Equation (9) writes E = JP + ε with no constant term, while Eq. (5) contains a concentration-dependent constant J0 that is said to be discarded. For absolute DFT energies, the regression must include an intercept or the energies must be centered; the manuscript should state which convention is used.
  2. [§3.3, Figures 12--14] The text refers to 'RMSE results' for different shell numbers but does not explicitly state whether these RMSEs are computed on the held-out test supercell or on training data. Please clarify that the comparison in Figures 12--14 uses the same held-out test set as Table 1, and that BIC selection is performed using only training data.
  3. [Figure 8 caption] The caption of Figure 8 reads 'NbMoTaTi' but the text and Table 1 refer to NbMoTaWTi; please correct the caption.
  4. [§2.3, Eq. (14)] In Eq. (14), the notation N(E|JP, λ2) implies λ2 is the variance, but later in Eq. (16) λ2 is treated as a gamma-distributed precision parameter. Please make the variance/precision convention consistent.
  5. [§3.1, Table 1] The column headers 'TrainingεR (meV)' and 'TestingεR (meV)' are missing spaces; consider formatting as 'Training εR (meV)' for readability.

Circularity Check

0 steps flagged · score 1.0 of 10

No construction-level circularity: the reported predictions are held-out, and the self-citations are to methodology rather than to the claimed result.

full rationale

The central result, the configurational-energy surrogate with testing RMSE near 0.6 meV, is obtained by fitting the effective pair interaction model, Eq. (8), to DFT energies from smaller supercells and then evaluating on 200 held-out configurations from the largest supercell (Section 3.1, Table 1). This is a genuine out-of-sample test, not a re-statement of the training fit. The BIC feature selection in Section 2.4 also operates on the training data, and the subsequent comparisons among fixed shell numbers and the BIC-selected m are evaluated on the same held-out set, so the claimed advantage of feature selection is not forced by construction. The EPI model and several Bayesian/Latin-hypercube tools are drawn from the authors' prior work (refs [49]-[52], [54]), and the EPI form is introduced as an ansatz in Section 2.2; however, the paper does not rely on those citations to supply the tested predictions, and the cited methods have independent standing. The skeptical concern that validation uses only randomly drawn configurations while Monte Carlo use requires accuracy on ordered or short-range-ordered states is a generalizability and model-form risk, not a circularity of the derivation. No equation reduces to its own input, no fitted parameter is renamed as a prediction, and no load-bearing uniqueness claim is imported from the authors' own work. Thus the paper shows no significant circularity; at most there is a minor self-citation to the EPI modeling framework that is not load-bearing for the out-of-sample accuracy claim.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the assumed EPI linear model and standard Bayesian regression machinery. No new physical entities are introduced. The main free choices are the prior hyperparameters, the initial shell truncation, and the acceptance threshold.

free parameters (3)
  • Gamma prior hyperparameters alpha1, alpha2, beta1, beta2 = 1e-8 for all four
    Chosen as non-informative priors for the noise precision lambda2 and parameter precision xi in Eqs. (14)-(16). The reported results may depend on this choice, especially for very small datasets.
  • Coordination shell truncation m for the main EPI fit = 6 for the main results; up to 13 considered in BIC comparisons
    The paper initially fixes six shells for the principal fits (Section 3.1), then uses BIC to select 2 to 9 depending on data size. The upper limit of shells considered is a modeling choice.
  • RMSE acceptance threshold epsilon_bar = 1 meV
    Used in Step 5 of the algorithm as a stopping criterion for when additional DFT data are needed. It is an arbitrary but reasonable threshold.
assumptions (4)
  • domain assumption Configurational energy is a linear function of the pair probabilities P^{X|Y}_m (Eq. 8) with the same effective pair interactions across supercell sizes.
    This is the core EPI model introduced in Section 2.2. It neglects triplet and higher-order interactions and assumes transferability of pair coefficients across supercell sizes.
  • domain assumption DFT (LSMS) total energies are the ground truth and errors are i.i.d. Gaussian, epsilon ~ N(0, sigma^2).
    Used in the likelihood in Eq. (13) and in the BIC RSS expression in Eq. (20). If method errors are correlated or non-Gaussian, the uncertainty quantification would be optimistic.
  • standard math BIC with the Laplace approximation is an adequate approximation to the model evidence for selecting coordination shells.
    Standard result from Bayesian model selection, Eqs. (17)-(20). Assumes the posterior is well approximated by a Gaussian and that the sample size is large enough for the approximation.
  • standard math The gamma priors with alpha1=alpha2=beta1=beta2=1e-8 are non-informative and lead to a proper posterior.
    Standard choice in Bayesian ridge regression to induce weak regularization.

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Cite this review

Pith. "Pith review of Robust data-driven approach for predicting the configurational energy of high entropy alloys." pith.science (2026). https://pith.science/paper/NHR3DDCZ

@misc{pith2026190803665,
  author       = {Pith},
  title        = {Pith review of: Robust data-driven approach for predicting the configurational energy of high entropy alloys},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NHR3DDCZ}},
  note         = {Machine review of arXiv:1908.03665}
}
read the original abstract

High entropy alloys (HEAs) have been increasingly attractive as promising next-generation materials due to their various excellent properties. It's necessary to essentially characterize the degree of chemical ordering and identify order-disorder transitions through efficient simulation and modeling of thermodynamics. In this study, a robust data-driven framework based on Bayesian approaches is proposed and demonstrated on the accurate and efficient prediction of configurational energy of high entropy alloys. The proposed effective pair interaction (EPI) model with ensemble sampling is used to map the configuration and its corresponding energy. Given limited data calculated by first-principles calculations, Bayesian regularized regression not only offers an accurate and stable prediction but also effectively quantifies the uncertainties associated with EPI parameters. Compared with the arbitrary determination of model complexity, we further conduct a physical feature selection to identify the truncation of coordination shells in EPI model using Bayesian information criterion. The results achieve efficient and robust performance in predicting the configurational energy, particularly given small data. The developed methodology is applied to study a series of refractory HEAs, i.e. NbMoTaW, NbMoTaWV and NbMoTaWTi where it is demonstrated how dataset size affects the confidence we can place in statistical estimates of configurational energy when data are sparse.

Figures

Figures reproduced from arXiv: 1908.03665 by the authors.

Figure 1
Figure 1. Square lattice with effective pair interaction highlighted. (a) the nearest-neighbor pair is marked [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Flowchart of robust data-driven algorithm using Bayesian framework [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Bcc supercells of refractory HEAs. (a) NbMoTaW with 128 atoms, (b) NbMoTaWV with 160 [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Comparison of DFT calculated energy with predicted energy using Bayesian regularized regression [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: Testing performance comparison between ensemble sampling strategy and sampling drawn from [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: Effective pair interaction (EPI) bonds and their uncertainties that are quantified by the variance [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: Effective pair interaction (EPI) bonds and their uncertainties that are quantified by the variance [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: Effective pair interaction (EPI) bonds and their uncertainties that are quantified by the variance [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: Bayesian information criterion results for different number of shells in NbMoTaW given a specific [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]
Figure 10
Figure 10. Figure 10: Bayesian information criterion results for different number of shells in NbMoTaWV given a [PITH_FULL_IMAGE:figures/full_fig_p020_10.png]
Figure 11
Figure 11. Figure 11: Bayesian information criterion results for different number of shells in NbMoTaWTi given a [PITH_FULL_IMAGE:figures/full_fig_p021_11.png]
Figure 12
Figure 12. Figure 12: RMSE results of NbMoTaW with three selections of coordination shells number given different [PITH_FULL_IMAGE:figures/full_fig_p021_12.png]
Figure 13
Figure 13. Figure 13: RMSE results of NbMoTaWV with three selections of coordination shells number given different [PITH_FULL_IMAGE:figures/full_fig_p022_13.png]
Figure 14
Figure 14. Figure 14: RMSE results of NbMoTaWTi with three selections of coordination shells number given different [PITH_FULL_IMAGE:figures/full_fig_p022_14.png]

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Works this paper leans on

55 extracted references · 49 canonical work pages

  1. [1]

    Yeh, S.-K

    J.-W. Yeh, S.-K. Chen, S.-J. Lin, J.-Y. Gan, T.-S. Chin, T.-T. Shun, C.-H. Tsau, S.- Y. Chang, Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes, Advanced Engineering Materials 6 (2004) 299–303

    work page 2004

  2. [2]

    O. N. Senkov, G. Wilks, J. Scott, D. B. Miracle, Mechanical properties of nb25mo25ta25w25 and v20nb20mo20ta20w20 refractory high entropy alloys, Inter- metallics 19 (2011) 698–706

    work page 2011

  3. [3]

    Zhang, T

    Y. Zhang, T. T. Zuo, Z. Tang, M. C. Gao, K. A. Dahmen, P. K. Liaw, Z. P. Lu, Microstructures and properties of high-entropy alloys, Progress in Materials Science 61 (2014) 1–93

    work page 2014

  4. [4]

    Z. Li, K. G. Pradeep, Y. Deng, D. Raabe, C. C. Tasan, Metastable high-entropy dual- phase alloys overcome the strength–ductility trade-off, Nature 534 (2016) 227

    2016

  5. [5]

    Tsai, J.-W

    M.-H. Tsai, J.-W. Yeh, High-entropy alloys: a critical review, Materials Research Letters 2 (2014) 107–123

    2014

  6. [6]

    D. B. Miracle, O. N. Senkov, A critical review of high entropy alloys and related concepts, Acta Materialia 122 (2017) 448–511

    2017

  7. [7]

    M. C. Gao, J.-W. Yeh, P. K. Liaw, Y. Zhang, High-entropy alloys: fundamentals and applications, Springer, 2016

    work page 2016

  8. [8]

    Widom, W

    M. Widom, W. P. Huhn, S. Maiti, W. Steurer, Hybrid monte carlo/molecular dynam- ics simulation of a refractory metal high entropy alloy, Metallurgical and Materials Transactions A 45 (2014) 196–200

    work page 2014

Show all 55 references
  1. [9]

    B. S. Murty, J.-W. Yeh, S. Ranganathan, P. Bhattacharjee, High-entropy alloys, Else- vier, 2019. 24

    2019

  2. [10]

    Eisenbach, Z

    M. Eisenbach, Z. Pei, X. Liu, First-principles study of order-disorder transitions in multicomponent solid-solution alloys, Journal of Physics: Condensed Matter 31 (2019) 273002

    2019

  3. [11]

    Widom, Modeling the structure and thermodynamics of high-entropy alloys, Journal of Materials Research 33 (2018) 2881–2898

    M. Widom, Modeling the structure and thermodynamics of high-entropy alloys, Journal of Materials Research 33 (2018) 2881–2898

    2018

  4. [12]

    M. C. Gao, P. Gao, J. A. Hawk, L. Ouyang, D. E. Alman, M. Widom, Computational modeling of high-entropy alloys: Structures, thermodynamics and elasticity, Journal of Materials Research 32 (2017) 3627–3641

    2017

  5. [13]

    Ikeda, B

    Y. Ikeda, B. Grabowski, F. K¨ ormann, Ab initio phase stabilities and mechanical prop- erties of multicomponent alloys: A comprehensive review for high entropy alloys and compositionally complex alloys, Materials Characterization 147 (2019) 464–511

    2019

  6. [14]

    Y. Ye, Q. Wang, J. Lu, C. Liu, Y. Yang, High-entropy alloy: challenges and prospects, Materials Today 19 (2016) 349–362

    2016

  7. [15]

    D. Ma, B. Grabowski, F. K¨ ormann, J. Neugebauer, D. Raabe, Ab initio thermodynamics of the cocrfemnni high entropy alloy: Importance of entropy contributions beyond the configurational one, Acta Materialia 100 (2015) 90–97

    2015

  8. [16]

    Huang, A

    W. Huang, A. Urban, Z. Rong, Z. Ding, C. Luo, G. Ceder, Construction of ground-state preserving sparse lattice models for predictive materials simulations, npj Computational Materials 3 (2017) 30

    2017

  9. [17]

    S. N. Khan, M. Eisenbach, Density-functional monte-carlo simulation of cuzn order- disorder transition, Physical Review B 93 (2016) 024203

    2016

  10. [18]

    Kikuchi, A theory of cooperative phenomena, Physical review 81 (1951) 988

    R. Kikuchi, A theory of cooperative phenomena, Physical review 81 (1951) 988

    1951

  11. [19]

    J. M. Sanchez, F. Ducastelle, D. Gratias, Generalized cluster description of multi- component systems, Physica A: Statistical Mechanics and its Applications 128 (1984) 334–350

    1984

  12. [20]

    van de Walle, G

    A. van de Walle, G. Ceder, Automating first-principles phase diagram calculations, Journal of Phase Equilibria 23 (2002) 348

    2002

  13. [21]

    L. J. Nelson, G. L. Hart, F. Zhou, V. Ozoli¸ nˇ s, et al., Compressive sensing as a paradigm for building physics models, Physical Review B 87 (2013) 035125. 25

    2013

  14. [22]

    Mueller, G

    T. Mueller, G. Ceder, Bayesian approach to cluster expansions, Physical Review B 80 (2009) 024103

    2009

  15. [23]

    V. Blum, G. L. Hart, M. J. Walorski, A. Zunger, Using genetic algorithms to map first- principles results to model hamiltonians: Application to the generalized ising model for alloys, Physical Review B 72 (2005) 165113

    2005

  16. [24]

    G. L. Hart, V. Blum, M. J. Walorski, A. Zunger, Evolutionary approach for determining first-principles hamiltonians, Nature materials 4 (2005) 391

    2005

  17. [25]

    A. Seko, Y. Koyama, I. Tanaka, Cluster expansion method for multicomponent sys- tems based on optimal selection of structures for density-functional theory calculations, Physical Review B 80 (2009) 165122

    2009

  18. [26]

    A. R. Natarajan, A. Van der Ven, Machine-learning the configurational energy of multicomponent crystalline solids, npj Computational Materials 4 (2018) 56

    2018

  19. [27]

    J. H. Chang, D. Kleiven, M. Melander, J. Akola, J. M. Garcia-Lastra, T. Vegge, Clease: A versatile and user-friendly implementation of cluster expansion method, Journal of Physics: Condensed Matter 31 (2019) 325901

    2019

  20. [28]

    ˚Angqvist, W

    M. ˚Angqvist, W. A. Mu˜ noz, J. M. Rahm, E. Fransson, C. Durniak, P. Rozyczko, T. H. Rod, P. Erhart, Icet–a python library for constructing and sampling alloy cluster ex- pansions, Advanced Theory and Simulations (2019) 1900015

    2019

  21. [29]

    Jiang, B

    C. Jiang, B. P. Uberuaga, Efficient ab initio modeling of random multicomponent alloys, Physical review letters 116 (2016) 105501

    2016

  22. [30]

    M. I. Jordan, T. M. Mitchell, Machine learning: Trends, perspectives, and prospects, Science 349 (2015) 255–260

    2015

  23. [31]

    LeCun, Y

    Y. LeCun, Y. Bengio, G. Hinton, Deep learning, nature 521 (2015) 436

    2015

  24. [32]

    K. T. Butler, D. W. Davies, H. Cartwright, O. Isayev, A. Walsh, Machine learning for molecular and materials science, Nature 559 (2018) 547

    2018

  25. [33]

    Mueller, A

    T. Mueller, A. G. Kusne, R. Ramprasad, Machine learning in materials science: Recent progress and emerging applications, Reviews in Computational Chemistry 29 (2016) 186–273

    2016

  26. [34]

    Sanchez-Lengeling, A

    B. Sanchez-Lengeling, A. Aspuru-Guzik, Inverse molecular design using machine learn- ing: Generative models for matter engineering, Science 361 (2018) 360–365. 26

    2018

  27. [35]

    C. Kim, G. Pilania, R. Ramprasad, From organized high-throughput data to phe- nomenological theory using machine learning: the example of dielectric breakdown, Chemistry of Materials 28 (2016) 1304–1311

    2016

  28. [36]

    Raccuglia, K

    P. Raccuglia, K. C. Elbert, P. D. Adler, C. Falk, M. B. Wenny, A. Mollo, M. Zeller, S. A. Friedler, J. Schrier, A. J. Norquist, Machine-learning-assisted materials discovery using failed experiments, Nature 533 (2016) 73

    2016

  29. [37]

    Carrasquilla, R

    J. Carrasquilla, R. G. Melko, Machine learning phases of matter, Nature Physics 13 (2017) 431

    2017

  30. [38]

    Huang, P

    W. Huang, P. Martin, H. L. Zhuang, Machine-learning phase prediction of high-entropy alloys, Acta Materialia 169 (2019) 225–236

    2019

  31. [39]

    Kostiuchenko, F

    T. Kostiuchenko, F. K¨ ormann, J. Neugebauer, A. Shapeev, Impact of lattice relaxations on phase transitions in a high-entropy alloy studied by machine-learning potentials, npj Computational Materials 5 (2019) 55

    2019

  32. [40]

    Fujimura, A

    K. Fujimura, A. Seko, Y. Koyama, A. Kuwabara, I. Kishida, K. Shitara, C. A. Fisher, H. Moriwake, I. Tanaka, Accelerated materials design of lithium superionic conductors based on first-principles calculations and machine learning algorithms, Advanced Energy Materials 3 (2013) 980–985

    2013

  33. [41]

    Pilania, C

    G. Pilania, C. Wang, X. Jiang, S. Rajasekaran, R. Ramprasad, Accelerating materials property predictions using machine learning, Scientific reports 3 (2013) 2810

    2013

  34. [42]

    L. Ward, A. Agrawal, A. Choudhary, C. Wolverton, A general-purpose machine learning framework for predicting properties of inorganic materials, npj Computational Materials 2 (2016) 16028

    2016

  35. [43]

    Dragoni, T

    D. Dragoni, T. D. Daff, G. Cs´ anyi, N. Marzari, Achieving dft accuracy with a machine- learning interatomic potential: Thermomechanics and defects in bcc ferromagnetic iron, Physical Review Materials 2 (2018) 013808

    2018

  36. [44]

    Chmiela, A

    S. Chmiela, A. Tkatchenko, H. E. Sauceda, I. Poltavsky, K. T. Sch¨ utt, K.-R. M¨ uller, Machine learning of accurate energy-conserving molecular force fields, Science advances 3 (2017) e1603015

    2017

  37. [45]

    V. L. Deringer, G. Cs´ anyi, Machine learning based interatomic potential for amorphous carbon, Physical Review B 95 (2017) 094203. 27

    2017

  38. [46]

    Z. Li, J. R. Kermode, A. De Vita, Molecular dynamics with on-the-fly machine learning of quantum-mechanical forces, Physical review letters 114 (2015) 096405

    2015

  39. [47]

    Aldegunde, N

    M. Aldegunde, N. Zabaras, J. Kristensen, Quantifying uncertainties in first-principles alloy thermodynamics using cluster expansions, Journal of Computational Physics 323 (2016) 17–44

    2016

  40. [48]

    Kristensen, N

    J. Kristensen, N. J. Zabaras, Bayesian uncertainty quantification in the evaluation of alloy properties with the cluster expansion method, Computer Physics Communications 185 (2014) 2885–2892

    2014

  41. [49]

    Zhang, M

    J. Zhang, M. D. Shields, On the quantification and efficient propagation of imprecise probabilities resulting from small datasets, Mechanical Systems and Signal Processing 98 (2018) 465–483

    2018

  42. [50]

    X. Liu, J. Zhang, M. Eisenbach, Y. Wang, Machine learning modeling of high entropy alloy: the role of short-range order, arXiv preprint arXiv:1906.02889 (2019)

    2019 arXiv

  43. [51]

    Zhang, M

    J. Zhang, M. D. Shields, Efficient monte carlo resampling for probability measure changes from bayesian updating, Probabilistic Engineering Mechanics 55 (2019) 54–66

    2019

  44. [52]

    Zhang, M

    J. Zhang, M. D. Shields, The effect of prior probabilities on quantification and propa- gation of imprecise probabilities resulting from small datasets, Computer Methods in Applied Mechanics and Engineering 334 (2018) 483–506

    2018

  45. [53]

    Y. Wang, G. Stocks, W. Shelton, D. Nicholson, Z. Szotek, W. Temmerman, Order-n multiple scattering approach to electronic structure calculations, Physical review letters 75 (1995) 2867

    1995

  46. [54]

    M. D. Shields, J. Zhang, The generalization of latin hypercube sampling, Reliability Engineering & System Safety 148 (2016) 96–108

    2016

  47. [55]

    Mehta, M

    P. Mehta, M. Bukov, C.-H. Wang, A. G. Day, C. Richardson, C. K. Fisher, D. J. Schwab, A high-bias, low-variance introduction to machine learning for physicists, Physics Reports (2019). 28

    2019

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.