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arxiv: 2604.10157 · v1 · submitted 2026-04-11 · ❄️ cond-mat.mtrl-sci · cs.LG· physics.comp-ph

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Accelerated Dopant Screening in Oxide Semiconductors via Multi-Fidelity Contextual Bandits and a Three-Tier DFT Validation Funnel

Abhinaba Basu
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Pith reviewed 2026-05-10 15:40 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cs.LGphysics.comp-ph
keywords dopant screeningmulti-fidelitycontextual banditsDFToxide semiconductorsband gapZnOco-doping
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The pith

Multi-fidelity contextual bandits screen 529 oxide dopant candidates using 19 percent of the DFT budget and always find the optimum.

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

The authors present a screening method for dopants in oxide semiconductors that combines surrogate models at different accuracy levels with a staged DFT validation process. This allows exploration of large combinatorial spaces of dopants and co-dopants that would otherwise require prohibitive computation. Applied to ZnO and other hosts, it highlights copper co-doped systems as effective for tuning band gaps into the visible range. The strategy cuts computational effort substantially while maintaining high reliability in locating top performers.

Core claim

The central discovery is that a multi-fidelity strategy built around contextual bandits and a three-tier validation funnel (PBE, PBE+U, ionic relaxation) can replace 81 percent of direct DFT evaluations in a 529-candidate ZnO co-doping screen, lowering the cost from 440 to 62 CPU-hours, and locate the global optimum in 100 percent of 50 trials.

What carries the argument

Multi-fidelity contextual bandits, which use predictions from models trained on cheaper calculations to decide which candidates merit expensive higher-fidelity DFT runs, form the selection mechanism that drives the efficient search.

Load-bearing premise

Lower-fidelity surrogate models trained on initial DFT data will not miss dopant candidates that only become superior after applying higher-fidelity corrections or ionic relaxation.

What would settle it

A full enumeration of the 529 candidates using the complete three-tier DFT funnel would show if the bandit method overlooked any candidate with a better visible-light band gap than the reported optimum.

Figures

Figures reproduced from arXiv: 2604.10157 by Abhinaba Basu.

Figure 1
Figure 1. Figure 1: Three-tier DFT screening funnel. Tier 1 uses MF-OFUL-guided PBE-SCF for fast initial ranking (245 calculations, 93.9% convergence). Simple flagging criteria—d-electron count > 0 and ionic radius mismatch > 20%—route candidates to Tier 2 (PBE+U) or Tier 3 (ionic relaxation). The two higher tiers catch orthogonal failure modes: d-electron delocalization (V, Cu, Fe dopants) and geometric distortion (In at the… view at source ↗
Figure 2
Figure 2. Figure 2: Simple regret comparison across methods. Mean ± s.d. over 6 hosts × 10 seeds on 1,000-candidate synthetic benchmarks at 8% budget. MF-OFUL achieves 10× lower simple regret than all other methods. Brackets show Wilcoxon p-values. MF-BO-EI (n = 18) uses identical fidelity-switching logic as MF-OFUL but never triggers its surrogate because EI selects high-GP-uncertainty candidates that always exceed the fidel… view at source ↗
Figure 3
Figure 3. Figure 3: PBE versus PBE+U bandgaps for transition metal dopants. Grouped bar chart showing qualitative reclassifications. Arrows indicate direction and magnitude of shift. Red dashed line: metallic threshold (0.5 eV). Three of five doped systems cross the metallic threshold upon applying the Hubbard U correction, demonstrating that PBE-SCF alone is insufficient for transition metal dopant screening. 3d states creat… view at source ↗
Figure 4
Figure 4. Figure 4: HSE06 hybrid functional validation. (a) PBE versus HSE06 bandgaps for 5 systems. PBE misclassifies V-doped ZnO as near-metallic (0.15 eV → 3.87 eV at HSE06) and ZnO:Cu as wide-gap (3.21 eV → 0.09 eV). (b) PBE+U versus HSE06 shows substantially improved agreement for d-electron systems, with mean absolute deviation of 0.15 eV. The dashed line indicates perfect agreement; the shaded band marks the metallic t… view at source ↗
Figure 5
Figure 5. Figure 5: Empirical Lyapunov diagnostics. (a) Lyapunov function decomposition: total L(t) (black), information deficit Φ(t) (blue, saturates), and bias potential µ · B(t) (red, grows linearly but bounded). (b) UCB width evolution: OFUL (blue, 80 steps) versus MF-OFUL (red, ∼548 steps). Triangles mark MF-OFUL’s DFT steps. Shaded bands: ±1 s.d. across 5 seeds. The information deficit saturates while the bias potential… view at source ↗
Figure 6
Figure 6. Figure 6: Collaborative filtering biplot of the host–dopant interaction matrix. SVD decomposition of the (5×16) reward matrix into two latent dimensions. Hosts (stars) cluster by crystal chemistry: MgO–ZnO (Group-II oxides) and TiO2–SnO2 (rutile-type Group-IV oxides), with SrTiO3 as an outlier. Dopants separate into sp-electron (triangles: Al, Ga, In, Sc, Y) and d-electron (squares: V, Cr, Mn, Fe, Co, Ni, Cu) groups… view at source ↗
Figure 7
Figure 7. Figure 7: Bandgap landscape of the 529-candidate ZnO co-doping campaign. Each point represents a DFT-evaluated candidate, sorted by bandgap and colored by reward (green: near 2.0 eV target; red: far from target). Cu-containing systems (diamonds) cluster near the target window (green band), while most other combinations produce wide-gap or near-metallic outcomes. Key Cu co-doped candidates are annotated. type accepto… view at source ↗
Figure 8
Figure 8. Figure 8: Simple regret versus DFT budget on real QE data. Mean ± s.d. over 10 seeds on the 223-candidate cross-host QE oracle (5 oxide hosts). MF-OFUL achieves SR = 0.000 at 12% budget (annotated), finding the global optimum in every run. The surrogate activation threshold creates a sharp transition between 8% (no surrogate) and 12% (full activation), while DFT-only methods improve gradually. but a system: the comb… view at source ↗
read the original abstract

Band gap engineering of oxide semiconductors through doping is critical for photocatalysis and optoelectronics, yet the combinatorial space of dopant elements, substitution sites, and co-doping combinations far exceeds typical density functional theory (DFT) budgets. We screen doped candidates across five oxide hosts (ZnO, TiO2, SrTiO3, SnO2, MgO), culminating in a 529-candidate ZnO co-doping campaign, and identify Cu-containing co-doped ZnO systems as consistently achieving visible-light-range band gaps (1.0-1.8 eV), with Y2Cu2 co-doped ZnO as the optimal candidate (1.84 eV). A three-tier validation funnel (PBE, PBE+U, ionic relaxation) reveals that no single level of theory suffices: V-doped ZnO shifts from near-metallic to wide-gap upon Hubbard U correction, while Cu-doped SrTiO3 enters the visible-light window only after correcting for d-electron localization. To make this screening tractable, we introduce a multi-fidelity screening strategy that replaces 81% of DFT evaluations with computationally inexpensive surrogate predictions, reducing a 529-candidate closed-loop Quantum ESPRESSO campaign from an estimated 440 to 62 CPU-hours while finding the global optimum in 100% of 50 independent trials (p = 5.0e-8 versus random screening, Wilcoxon signed-rank). Cross-host analysis of the dopant-host interaction matrix reveals that dopant performance is governed by just two latent chemical dimensions, enabling prediction of rankings in unseen hosts. All 583 DFT calculations, screening code, and stability proofs are released as an open benchmark.

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.

Referee Report

1 major / 2 minor

Summary. The manuscript introduces a multi-fidelity contextual bandit algorithm integrated with a three-tier DFT validation funnel (PBE, PBE+U, ionic relaxation) to efficiently screen dopant combinations in oxide semiconductors. For a 529-candidate ZnO co-doping campaign, the approach replaces 81% of expensive DFT calculations with surrogate predictions, reducing estimated CPU time from 440 to 62 hours, while identifying Cu-containing co-doped ZnO systems, particularly Y2Cu2 co-doped ZnO with a band gap of 1.84 eV, as optimal for visible-light absorption. The method recovers the global optimum in all 50 independent trials with statistical significance (p=5e-8 vs random), and cross-host analysis suggests dopant performance is captured by two latent chemical dimensions. All data and code are openly released.

Significance. If the surrogate models maintain sufficient correlation with high-fidelity outcomes, this work could substantially accelerate dopant screening in oxide semiconductors by demonstrating a scalable way to substitute most DFT evaluations with inexpensive predictions. The open release of all 583 DFT calculations, screening code, and stability proofs is a clear strength supporting reproducibility. The explicit demonstration that single-tier DFT is insufficient (via ranking shifts such as V-doped ZnO becoming wide-gap only after +U correction) provides useful guidance for the field.

major comments (1)
  1. [Bandit performance evaluation] Bandit performance and surrogate validation sections: The 100% global-optimum recovery rate across 50 trials is reported against random screening, but surrogate accuracy on unseen high-fidelity points is validated only indirectly through overall campaign success. Given the documented changes in candidate rankings across the three tiers (e.g., V-doped ZnO and Cu-doped SrTiO3), an explicit metric such as Spearman rank correlation between surrogate predictions and final PBE+U+relaxed band gaps on a held-out subset would directly test the risk that lower-fidelity surrogates systematically deprioritize candidates whose advantage appears only at higher fidelity.
minor comments (2)
  1. [Cross-host analysis] The cross-host analysis claims that dopant performance is governed by two latent chemical dimensions, but the extraction method (e.g., dimensionality reduction on the interaction matrix) and the precise definition of these dimensions should be stated explicitly with supporting equations or figures.
  2. [Results] Figure captions and axis labels in the results section on CPU-hour estimates should clarify whether the 440-to-62 hour reduction includes only the surrogate-replaced evaluations or also the cost of training the contextual bandit models.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive review and the recommendation of minor revision. The suggestion to strengthen surrogate validation is well-taken, and we address it directly below.

read point-by-point responses

  1. Referee: Bandit performance evaluation] Bandit performance and surrogate validation sections: The 100% global-optimum recovery rate across 50 trials is reported against random screening, but surrogate accuracy on unseen high-fidelity points is validated only indirectly through overall campaign success. Given the documented changes in candidate rankings across the three tiers (e.g., V-doped ZnO and Cu-doped SrTiO3), an explicit metric such as Spearman rank correlation between surrogate predictions and final PBE+U+relaxed band gaps on a held-out subset would directly test the risk that lower-fidelity surrogates systematically deprioritize candidates whose advantage appears only at higher fidelity.

    Authors: We agree that an explicit rank-correlation metric on held-out high-fidelity data would provide a more direct test of surrogate reliability, particularly given the observed ranking shifts across DFT tiers. While the 100% global-optimum recovery and p=5e-8 significance versus random screening already demonstrate that the multi-fidelity policy does not systematically miss superior candidates, we will add the requested analysis in revision. Specifically, we will reserve a random 20% held-out subset of the 529 ZnO co-dopants, compute Spearman rank correlation between the contextual-bandit surrogate predictions (at the time of selection) and the final PBE+U+relaxed band gaps, and report both the coefficient and its significance. The corresponding scatter plot will be included in the supplementary information. This addition directly addresses the concern about potential deprioritization of candidates whose advantage emerges only at higher fidelity. revision: yes

Circularity Check

0 steps flagged

No significant circularity; validation uses independent high-fidelity DFT

full rationale

The paper's efficiency claims (81% surrogate replacement, CPU-hour reduction, 100% optimum recovery) rest on explicit three-tier DFT validation runs and held-out lower-fidelity training data for the contextual bandit. The two latent chemical dimensions are extracted from cross-host analysis and tested on unseen hosts rather than being fitted to the final high-fidelity outcomes. No self-definitional equations, fitted-input predictions, or load-bearing self-citations reduce the reported results to their inputs by construction. The p-value is versus random screening on the same validated set, preserving independent content.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard DFT approximations (PBE, Hubbard U corrections) and the assumption that surrogate models trained on lower-fidelity data preserve ranking order at higher fidelity; no new entities are postulated.

axioms (1)
  • domain assumption PBE+U corrections and ionic relaxation are required to obtain reliable band gaps for transition-metal dopants
    Explicitly demonstrated by V-doped ZnO and Cu-doped SrTiO3 examples in the abstract

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Reference graph

Works this paper leans on

43 extracted references · 26 canonical work pages

  1. [1]

    Transparent conducting oxide semiconductors for transparent electrodes.Semi- cond

    Minami, T. Transparent conducting oxide semiconductors for transparent electrodes.Semi- cond. Sci. Technol.20, S35 (2005). URLhttps://doi.org/10.1088/0268-1242/20/4/ 004

    work page doi:10.1088/0268-1242/20/4/ 2005

  2. [2]

    & Kumagai, Y

    Oba, F. & Kumagai, Y. Design and exploration of semiconductors from first princi- ples.Appl. Phys. Express11, 060101 (2018). URLhttps://doi.org/10.7567/APEX. 11.060101

    work page doi:10.7567/apex 2018

  3. [3]

    C., Jain, A., Mueller, T

    Hautier, G., Fischer, C. C., Jain, A., Mueller, T. & Ceder, G. Finding nature’s missing ternary oxide compounds using machine learning and density functional theory.Chem. Mater.22, 3762–3767 (2010). URLhttps://doi.org/10.1021/cm100795d

    work page doi:10.1021/cm100795d 2010

  4. [4]

    Xue, D.et al.Accelerated search for materials with targeted properties by adaptive design. Nat. Commun.7, 11241 (2016). URLhttps://doi.org/10.1038/ncomms11241

    work page doi:10.1038/ncomms11241 2016

  5. [5]

    & Ulissi, Z

    Tran, K. & Ulissi, Z. W. Active learning across intermetallics for the discovery of sta- ble electrocatalysts.Nat. Catal.1, 696–703 (2018). URLhttps://doi.org/10.1038/ s41929-018-0142-1

    2018

  6. [6]

    URLhttps: //doi.org/10.1017/9781108348973

    Garnett, R.Bayesian Optimization(Cambridge University Press, 2023). URLhttps: //doi.org/10.1017/9781108348973

    work page doi:10.1017/9781108348973 2023

  7. [7]

    & Peng, W

    Li, Z., Xu, Q., Sun, Q., Hou, A. & Peng, W. Rapid discovery of high-performance per- ovskites via Bayesian optimization.Joule2, 1561–1572 (2018). URLhttps://doi.org/ 10.1016/j.joule.2018.06.001

    work page doi:10.1016/j.joule.2018.06.001 2018

  8. [8]

    Mater.10, 156 (2024)

    Liang, Q.et al.Targeted materials discovery using Bayesian algorithm execution.npj Comput. Mater.10, 156 (2024). URLhttps://doi.org/10.1038/s41524-024-01326-2

    work page doi:10.1038/s41524-024-01326-2 2024

  9. [9]

    S.et al.Deep Gaussian process-based cost-aware batch Bayesian optimization for materials design.npj Comput

    Alvi, A. S.et al.Deep Gaussian process-based cost-aware batch Bayesian optimization for materials design.npj Comput. Mater.12, 85 (2026). URLhttps://doi.org/10.1038/ s41524-026-01981-7

    2026

  10. [10]

    Baird, S. G. & Sparks, T. D. Best practices for multi-fidelity Bayesian optimization in materials and molecular research.Digital Discovery(2024). URLhttps://doi.org/10. 1039/D4DD00239C

    2024

  11. [11]

    Schoenholz, Muratahan Aykol, Gowoon Cheon, and Ekin Do- gus Cubuk

    Merchant, A.et al.Scaling deep learning for materials discovery.Nature624, 80–85 (2023). URLhttps://doi.org/10.1038/s41586-023-06735-9

    work page doi:10.1038/s41586-023-06735-9 2023

  12. [12]

    Zhu, S., Xie, Z., Zheng, Z.et al.Accelerating computational materials discovery with machine learning and cloud high-performance computing.J. Am. Chem. Soc.146, 20009– 20018 (2024). URLhttps://doi.org/10.1021/jacs.4c03849

    work page doi:10.1021/jacs.4c03849 2024

  13. [13]

    Takeno, S.et al.Multi-fidelity Bayesian optimization with max-value entropy search and its parallelization.Proc. Mach. Learn. Res.119, 9334–9345 (2020). URLhttps: //proceedings.mlr.press/v119/takeno20a.html. 22

    2020

  14. [14]

    & Szepesv´ ari, C

    Abbasi-Yadkori, Y. & Szepesv´ ari, C. Improved algorithms for linear stochastic ban- dits.Adv. Neural Inf. Process. Syst.24, 2312–2320 (2011). URLhttps://proceedings. neurips.cc/paper/2011/hash/e1d5be1c7f2f456670de3d53c7b54f4a-Abstract.html

    2011

  15. [15]

    & Frazier, P

    Poloczek, M., Wang, J. & Frazier, P. I. Multi-information source optimization.Adv. Neural Inf. Process. Syst.30, 4288–4298 (2017). URLhttps://proceedings.neurips. cc/paper/2017/hash/df1f1d20ee86704251795841e6a9405a-Abstract.html

    2017

  16. [16]

    & P´ oczos, B

    Kandasamy, K., Dasarathy, G., Schneider, J. & P´ oczos, B. Multi-fidelity Bayesian opti- misation with continuous approximations.Proc. Mach. Learn. Res.70, 1799–1808 (2017). URLhttps://proceedings.mlr.press/v70/kandasamy17a.html

    2017

  17. [17]

    Pilania, G., Gubernatis, J. E. & Lookman, T. Multi-fidelity machine learning models for accurate bandgap predictions of solids.Comput. Mater. Sci.129, 156–163 (2017). URL https://doi.org/10.1016/j.commatsci.2016.12.004

    work page doi:10.1016/j.commatsci.2016.12.004 2017

  18. [18]

    Guo, H., Zhu, Q. & Xu, K. Stochastic constrained contextual bandits via Lyapunov optimization based estimation to decision framework.Proc. Mach. Learn. Res. (COLT) 247(2024). URLhttps://proceedings.mlr.press/v247/guo24a.html

    2024

  19. [19]

    S., Emberson, J

    Horby, P., Lim, W. S., Emberson, J. R.et al.Dexamethasone in hospitalized patients with COVID-19.N. Engl. J. Med.384, 693–704 (2021). URLhttps://doi.org/10.1056/ NEJMoa2021436

    2021

  20. [20]

    & Tanaka, I

    Seko, A., Hayashi, H. & Tanaka, I. Recommender system for discovery of inorganic compounds.npj Comput. Mater.8, 230 (2022). URLhttps://doi.org/10.1038/ s41524-022-00899-0

    2022

  21. [21]

    Computer 42(8):30--37

    Koren, Y., Bell, R. & Volinsky, C. Matrix factorization techniques for recommender sys- tems.Computer42, 30–37 (2009). URLhttps://doi.org/10.1109/MC.2009.263

    work page doi:10.1109/mc.2009.263 2009

  22. [22]

    & Tanaka, I

    Seko, A., Maekawa, T., Tsuda, K. & Tanaka, I. Machine learning with systematic density- functional theory calculations.Phys. Rev. B89, 054303 (2014). URLhttps://doi.org/ 10.1103/PhysRevB.89.054303

    work page doi:10.1103/physrevb.89.054303 2014

  23. [23]

    Mater.2, 16031 (2016)

    Nikolaev, P.et al.Autonomy in materials research: a case study in carbon nan- otube growth.npj Comput. Mater.2, 16031 (2016). URLhttps://doi.org/10.1038/ npjcompumats.2016.31

    2016

  24. [24]

    https://doi

    Jain, A., Ong, S. P., Hautier, G.et al.Commentary: The Materials Project.APL Mater. 1, 011002 (2013). URLhttps://doi.org/10.1063/1.4812323

    work page doi:10.1063/1.4812323 2013

  25. [25]

    & de Gironcoli, S

    Cococcioni, M. & de Gironcoli, S. Linear response approach to the calculation of the effective interaction parameters in the LDA+U method.Phys. Rev. B71, 035105 (2005). URLhttps://doi.org/10.1103/PhysRevB.71.035105

    work page doi:10.1103/physrevb.71.035105 2005

  26. [26]

    Garrido-Merch´ an, E. C. & Hern´ andez-Lobato, D. Dealing with categorical and integer- valued variables in Bayesian optimization.Neurocomputing380, 20–35 (2020). URL https://doi.org/10.1016/j.neucom.2019.11.004

    work page doi:10.1016/j.neucom.2019.11.004 2020

  27. [27]

    Kennedy, M. C. & O’Hagan, A. Predicting the output of a complex computer code when fast approximations are available.Biometrika87, 1–13 (2000). URLhttps://doi.org/ 10.1093/biomet/87.1.1

    work page doi:10.1093/biomet/87.1.1 2000

  28. [28]

    Gupta, T., Zaki, M., Krishnamurthy, N. M. & Mausam. MatSciBERT: A materials domain language model.npj Comput. Mater.8, 102 (2022). URLhttps://doi.org/10.1038/ s41524-022-00784-w. 23

    2022

  29. [29]

    Freysoldt, C., Grabowski, B., Hickel, T.et al.First-principles calculations for point de- fects in solids.Rev. Mod. Phys.86, 253–305 (2014). URLhttps://doi.org/10.1103/ RevModPhys.86.253

    2014

  30. [30]

    P., Simm, G

    Batatia, I., Kov´ acs, D. P., Simm, G. N. C., Ortner, C. & Cs´ anyi, G. MACE: Higher order equivariant message passing neural networks for fast and accurate force fields.Adv. Neural Inf. Process. Syst.35, 11423–11436 (2022). URLhttps://doi.org/10.52202/ 068431-0830

    2022

  31. [31]

    & Ong, S

    Chen, C. & Ong, S. P. A universal graph deep learning interatomic potential for the periodic table.Nat. Comput. Sci.2, 718–728 (2022). URLhttps://doi.org/10.1038/ s43588-022-00349-3

    2022

  32. [32]

    Deng, B.et al.CHGNet as a pretrained universal neural network potential for charge- informed atomistic modelling.Nat. Mach. Intell.5, 1031–1041 (2023). URLhttps:// doi.org/10.1038/s42256-023-00716-3

    work page doi:10.1038/s42256-023-00716-3 2023

  33. [33]

    Dataset: Accelerated dopant screening in oxide semiconductors via multi-fidelity contextual bandits and a three-tier DFT validation funnel (2026)

    Basu, A. Dataset: Accelerated dopant screening in oxide semiconductors via multi-fidelity contextual bandits and a three-tier DFT validation funnel (2026). URLhttps://doi. org/10.5281/zenodo.19501400

    work page doi:10.5281/zenodo.19501400 2026

  34. [34]

    Shannon, R. D. Revised effective ionic radii.Acta Crystallogr. A32, 751–767 (1976). URL https://doi.org/10.1107/S0567739476001551

    work page doi:10.1107/s0567739476001551 1976

  35. [35]

    R., Pleiss, G., Bindel, D., Weinberger, K

    Gardner, J. R., Pleiss, G., Bindel, D., Weinberger, K. Q. & Wilson, A. G. GPyTorch: Blackbox matrix-matrix Gaussian process inference with GPU acceleration.Adv. Neural Inf. Process. Syst.31, 7576–7586 (2018). URLhttps://arxiv.org/abs/1809.11165

    work page arXiv 2018

  36. [36]

    & Korn, E

    Freidlin, B. & Korn, E. L. Monitoring futility: Bayesian and frequentist approaches.Clin. Trials2, 141–147 (2005). URLhttps://doi.org/10.1191/1740774505cn081oa

    work page doi:10.1191/1740774505cn081oa 2005

  37. [37]

    & Ullrich, S

    de Moura, L. & Ullrich, S. The Lean 4 theorem prover and programming language. Lect. Notes Comput. Sci.12699, 625–635 (2021). URLhttps://doi.org/10.1007/ 978-3-030-79876-5_37

    2021

  38. [38]

    Advanced capabilities for materials modelling with Quantum

    Giannozzi, P., Andreussi, O., Brumme, T.et al.Advanced capabilities for materials mod- elling with Quantum ESPRESSO.J. Phys.: Condens. Matter29, 465901 (2017). URL https://doi.org/10.1088/1361-648X/aa8f79

    work page doi:10.1088/1361-648x/aa8f79 2017

  39. [39]

    Pseudopotentials periodic table: From H to Pu,

    Dal Corso, A. Pseudopotentials periodic table: From H to Pu.Comput. Mater. Sci.95, 337–350 (2014). URLhttps://doi.org/10.1016/j.commatsci.2014.07.043

    work page doi:10.1016/j.commatsci.2014.07.043 2014

  40. [40]

    & Metiu, H

    Hu, Z. & Metiu, H. Choice of U for DFT+U calculations for titanium oxides.J. Phys. Chem. C115, 5841–5845 (2011). URLhttps://doi.org/10.1021/jp111350u

    work page doi:10.1021/jp111350u 2011

  41. [41]

    & Ceder, G

    Wang, L., Maxisch, T. & Ceder, G. Oxidation energies of transition metal oxides within the GGA+U framework.Phys. Rev. B73, 195107 (2006). URLhttps://doi.org/10. 1103/PhysRevB.73.195107

    2006

  42. [42]

    & Zurek, E

    Baral, K., Bajracharya, P. & Zurek, E. DFT+U study of Cu-doped ZnO.J. Phys. Chem. C122, 156–165 (2018). URLhttps://doi.org/10.1021/acs.jpcc.7b10386

    work page doi:10.1021/acs.jpcc.7b10386 2018

  43. [43]

    Biometrics Bulletin , author =

    Wilcoxon, F. Individual comparisons by ranking methods.Biometrics Bull.1, 80–83 (1945). URLhttps://doi.org/10.2307/3001968. 24 Supplementary Figures Supplementary Figure 1: Lyapunov function decomposition (a)Lyapunov functionL(t) = Φ(t)+µ·B(t) averaged over 10 seeds on 1,000-candidate synthetic benchmarks.(b)Information deficit Φ(t) = log detV full −log d...

    work page doi:10.2307/3001968 1945