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Ab Initio to Activity: Machine Learning-Assisted Optimization of High-Entropy Alloy Catalytic Activity

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Abstract

High-entropy alloys are slowly making their debut as a platform for catalyst discovery, but conventional methods, theoretical as well as experimental, may fall short of screening the vast composition space inhabited by this class of materials. New theoretical approaches are needed to gauge the catalytic activity of high-entropy alloys and optimize the alloy composition within a feasible time frame as a prerequisite for further experimental studies. Herein, we establish a workflow for simulations of catalysis on high-entropy alloy surfaces. For each step of the modeling we present our choice of method, however, we also acknowledge that alternative options are available. We apply the developed methodology to predict the net catalytic activity of any alloy composition, within the composition space spanned by Ag–Ir–Pd–Pt–Ru, for the oxygen reduction reaction. Based on first-principle calculations, a graph convolution neural network is used to predict adsorption energies of *OH and *O. Subsequently, taking competitive co-adsorption of reaction intermediates into account, we couple the net adsorption energy distribution of a high-entropy alloy surface to the expected current density. Lastly, this procedure is used in conjunction with a Bayesian optimization scheme to search for optimal alloy compositions, which yields several promising compositions. This result shows that an unbiased in silico pre-screening and discovery of catalyst candidates is viable and will help scale the otherwise insurmountable challenge of searching for high-entropy alloy catalysts. It is our hope that our computational framework, which is freely available on GitHub, will aid other research groups to efficiently identify promising high-entropy alloy catalysts.

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Data Availability

A working example of all steps used in this work is freely available at our repository in Github along with guidance for use in other projects: https://github.com/cmclausen/cheat/. All DFT calculations used in this work are available from https://nano.ku.dk/english/research/theoretical-electrocatalysis/katladb/ab-initio-to-activity/.

References

  1. P. **e, Y. Yao, Z. Huang, Z. Liu, J. Zhang, T. Li, G. Wang, R. Shahbazian-Yassar, L. Hu, C. Wang, Highly efficient decomposition of ammonia using high-entropy alloy catalysts. Nat. Commun. 10(1), 1–12 (2019)

    Article  Google Scholar 

  2. C. Zhan, Y. Xu, L. Bu, H. Zhu, Y. Feng, T. Yang, Y. Zhang, Z. Yang, B. Huang, Q. Shao, X. Huang, Subnanometer high-entropy alloy nanowires enable remarkable hydrogen oxidation catalysis. Nat. Commun. 12(1), 1–8 (2021)

    Google Scholar 

  3. G. Zhang, K. Ming, J. Kang, Q. Huang, Z. Zhang, X. Zheng, X. Bi, High entropy alloy as a highly active and stable electrocatalyst for hydrogen evolution reaction. Electrochim. Acta 279, 19–23 (2018)

    Article  CAS  Google Scholar 

  4. S. Nellaiappan, N.K. Katiyar, R. Kumar, A. Parui, K.D. Malviya, K.G. Pradeep, A.K. Singh, S. Sharma, C.S. Tiwary, K. Biswas, High-entropy alloys as catalysts for the CO2 and CO reduction reactions: experimental realization. ACS Catal. 10(6), 3658–3663 (2020)

    Article  CAS  Google Scholar 

  5. S. Li, X. Tang, H. Jia, H. Li, G. **e, X. Liu, X. Lin, H.J. Qiu, Nanoporous high-entropy alloys with low Pt loadings for high-performance electrochemical oxygen reduction. J. Catal. 383, 164–171 (2020)

    Article  CAS  Google Scholar 

  6. D. Wu, K. Kusada, T. Yamamoto, T. Toriyama, S. Matsumura, S. Kawaguchi, Y. Kubota, H. Kitagawa, Platinum-group-metal high-entropy-alloy nanoparticles. J. Am. Chem. Soc. 142(32), 13833–13838 (2020)

    Article  CAS  Google Scholar 

  7. D. Wu, K. Kusada, Y. Nanba, M. Koyama, T. Yamamoto, T. Toriyama, S. Matsumura, O. Seo, I. Gueye, J. Kim, L. Kumara, O. Sakata, S. Kawaguchi, Y. Kubota, H. Kitagawa, Noble-metal high-entropy-alloy nanoparticles: atomic-level insight into the electronic structure. J. Am. Chem. Soc. 144(8), 3365–3369 (2022)

    Article  CAS  Google Scholar 

  8. J. Cavin, A. Ahmadiparidari, L. Majidi, A.S. Thind, S.N. Misal, A. Prajapati, Z. Hemmat, S. Rastegar, A. Beukelman, M.R. Singh, K.A. Unocic, A. Salehi-Kho**, R. Mishra, 2D high-entropy transition metal dichalcogenides for carbon dioxide electrocatalysis. Adv. Mater. 33(31), 2100347 (2021)

    Article  CAS  Google Scholar 

  9. P. Sabatier, La Catalyze En Chimie Organique, Encyclopédie de Chimique Appliquée (1913)

  10. E.J. Kluender, J.L. Hedrick, K.A. Brown, R. Rao, B. Meckes, J.S. Du, L.M. Moreau, C.A. Mirkin, Catalyst discovery through megalibraries of nanomaterials. PNAS 116(1), 40–45 (2019)

    Article  CAS  Google Scholar 

  11. Y. Yao, Z. Huang, T. Li, H. Wang, Y. Liu, H.S. Stein, Y. Mao, J. Gao, M. Jiao, Q. Dong, J. Dai, P. **e, H. **e, S.D. Lacey, I. Takeuchi, J.M. Gregoire, R. Jiang, C. Wang, A.D. Taylor, R. Shahbazian-Yassar, L. Hu, High-throughput, combinatorial synthesis of multimetallic nanoclusters. PNAS 117(12), 6316–6322 (2020)

    Article  CAS  Google Scholar 

  12. L. Banko, O.A. Krysiak, J.K. Pedersen, B. **ao, A. Savan, T. Löffler, S. Baha, J. Rossmeisl, W. Schuhmann, A. Ludwig, Unravelling composition–activity–stability trends in high entropy alloy electrocatalysts by using a data-guided combinatorial synthesis strategy and computational modeling. Adv. Energy Mater. 12, 2103–312 (2022)

    Article  Google Scholar 

  13. J.K. Pedersen, T.A.A. Batchelor, A. Bagger, J. Rossmeisl, High-entropy alloys as catalysts for the CO2 and CO reduction reactions. ACS Catal. 10(3), 2169–2176 (2020)

    Article  CAS  Google Scholar 

  14. A. Bagger, W. Ju, A.S. Varela, P. Strasser, J. Rossmeisl, Electrochemical CO2 reduction: a classification problem. Chem. Phys. Chem. 18(22), 3266–3273 (2017)

    Article  CAS  Google Scholar 

  15. A.A. Peterson, J.K. Nørskov, Activity descriptors for CO2 electroreduction to methane on transition-metal catalysts. J. Phys. Chem. Lett. 3(2), 251–258 (2012)

    Article  CAS  Google Scholar 

  16. Y. Hori, H. Wakebe, T. Tsukamoto, O. Koga, Electrocatalytic process of CO selectivity in electrochemical reduction of CO2 at metal electrodes in aqueous media. Electrochim. Acta 39(11–12), 1833–1839 (1994)

    Article  CAS  Google Scholar 

  17. N. Brønsted, Acid and basic catalysis. Chem. Rev. 5, 231 (1928)

    Article  Google Scholar 

  18. M.G. Evans, N.P. Polanyi, Inertia and driving force of chemical reactions. Trans. Faraday Soc. 34, 11–24 (1938)

    Article  CAS  Google Scholar 

  19. J.K. Nørskov, T. Bligaard, A. Logadottir, S. Bahn, L.B. Hansen, M. Bollinger, H. Bengaard, B. Hammer, Z. Sljivancanin, M. Mavrikakis, Y. Xu, S. Dahl, C.J.H. Jacobsen, Universality in heterogeneous catalysis. J. Catal. 209(2), 275–278 (2002)

    Article  Google Scholar 

  20. F. Abild-Pedersen, J. Greeley, F. Studt, J. Rossmeisl, T.R. Munter, P.G. Moses, E. Skulason, T. Bligaard, J.K. Nørskov, Scaling properties of adsorption energies for hydrogen-containing molecules on transition-metal surfaces. Phys. Rev. Lett. 99(1), 016105 (2007)

    Article  CAS  Google Scholar 

  21. J. Rossmeisl, A. Logadottir, J.K. Nørskov, Electrolysis of water on (oxidized) metal surfaces. Chem. Phys. 319(1–3), 178–184 (2005)

    Article  CAS  Google Scholar 

  22. E.G. del Río, J.J. Mortensen, K.W. Jacobsen, Local Bayesian optimizer for atomic structures. Phys. Rev. B 100(10), 104103 (2019)

    Article  Google Scholar 

  23. E.G. del Río, S. Kaappa, J.A.G. Torres, T. Bligaard, K.W. Jacobsen, Machine learning with bond information for local structure optimizations in surface science. J. Chem. Phys. 153(23), 234116 (2020)

    Article  Google Scholar 

  24. M. Zhong, K. Tran, Y. Min, C. Wang, Z. Wang, C.T. Dinh, P. De Luna, Z. Yu, A.S. Rasouli, P. Brodersen, S. Sun, O. Voznyy, C. Tan, M. Askerka, F. Che, M. Liu, A. Seifitokaldani, Y. Pang, S. Lo, A. Ip, Z. Ulissi, E.H. Sargent, Accelerated discovery of CO2 electrocatalysts using active machine learning. Nature 581(7807), 178–183 (2020)

    Article  CAS  Google Scholar 

  25. R.B. Wexler, J.M.P. Martirez, A.M. Rappe, Chemical pressure-driven enhancement of the hydrogen evolving activity of Ni2P from nonmetal surface do** interpreted via machine learning. J. Am. Chem. Soc. 140(13), 4678–4683 (2018)

    Article  CAS  Google Scholar 

  26. R. **nouchi, R. Asahi, Predicting catalytic activity of nanoparticles by a DFT-aided machine-learning algorithm. J. Phys. Chem. Lett. 8(17), 4279–4283 (2017)

    Article  CAS  Google Scholar 

  27. Z.W. Ulissi, A.J. Medford, T. Bligaard, J.K. Nørskov, To address surface reaction network complexity using scaling relations machine learning and DFT calculations. Nat. Commun. 8(1), 1–7 (2017)

    Article  Google Scholar 

  28. M. Andersen, K. Reuter, Adsorption enthalpies for catalysis modeling through machine-learned descriptors. Acc. Chem. Res. 54(12), 2741–2749 (2021)

    Article  CAS  Google Scholar 

  29. J.K. Pedersen, T.A.A. Batchelor, D. Yan, L.E.J. Skjegstad, J. Rossmeisl, Surface electrocatalysis on high-entropy alloys. Curr Opin Electrochem 26, 100651 (2021)

    Article  CAS  Google Scholar 

  30. T.A.A. Batchelor, J.K. Pedersen, S.H. Winther, I.E. Castelli, K.W. Jacobsen, J. Rossmeisl, High-entropy alloys as a discovery platform for electrocatalysis. Joule 3(3), 834–845 (2019)

    Article  CAS  Google Scholar 

  31. T. Löffler, A. Ludwig, J. Rossmeisl, W. Schuhmann, What makes high-entropy alloys exceptional electrocatalysis. Angew. Chem. Int. Ed. 60(52), 26894–26903 (2021)

    Article  Google Scholar 

  32. J. Rossmeisl, G.S. Karlberg, T. Jaramillo, J.K. Nørskov, Steady state oxygen reduction and cyclic voltammetry. Faraday Discuss. 140, 337–346 (2008)

    Article  CAS  Google Scholar 

  33. T.A.A. Batchelor, T. Löffler, B. **ao, O.A. Krysiak, V. Strotkötter, J.K. Pedersen, C.M. Clausen, A. Savan, Y. Li, W. Schuhmann, J. Rossmeisl, A. Ludwig, Complex-solid-solutions electrocatalyst discovery by computational prediction and high-throughput experimentation. Angew. Chem. Int. Ed. 60(13), 6932–6937 (2020)

    Article  Google Scholar 

  34. D. Wu, K. Kusada, T. Yamamoto, T. Toriyama, S. Mutsumara, I. Gueye, O. Seo, J. Kim, S. Hiroi, O. Sakata, S. Kawaguchi, Y. Kuboto, H. Kitagawa, On the electronic structure and hydrogen evolution reaction activity of platinum group metal-based high-entropy-alloy nanoparticles. Chem. Sci. 11(47), 12731–12736 (2020)

    Article  CAS  Google Scholar 

  35. J.K. Nørskov, J. Rossmeisl, A. Logadottir, L. Lindqvist, J.R. Kitchin, T. Bligaard, Jónsson: origin of the overpotential at a fuel-cell cathode. J. Phys. Chem. B 108(46), 17886–17892 (2004)

    Article  Google Scholar 

  36. S. Divanis, T. Kutlusoy, I.M.I. Boye, I.C. Man, J. Rossmeisl, Oxygen evolution reaction: a perspective on a decade of atomic scale simulations. Chem. Sci. 11(11), 2943–2950 (2020)

    Article  CAS  Google Scholar 

  37. C.M. Clausen, T.A. Batchelor, J.K. Pedersen, J. Rossmeisl, What atomic positions determines reactivity of a surface? Long-range, directional ligand effects in metallic alloys. Adv. Sci. 8(9), 2003357 (2021)

    Article  CAS  Google Scholar 

  38. C.M. Clausen, J.K. Pedersen, T.A. Batchelor, J. Rossmeisl, Lattice distortion releasing local surface strain on high-entropy alloys. Nano Res. 15, 4775 (2021)

    Article  Google Scholar 

  39. L. Wang, Z. Zeng, W. Gao, T. Maxson, D. Raciti, M. Giroux, X. Pan, C. Wang, J. Greeley, Tunable intrinsic strain in two-dimensional transition metal electrocatalysts. Science 363(6429), 870–874 (2019)

    Article  CAS  Google Scholar 

  40. M. Escudero-Escribano, P. Malacrida, M.H. Hansen, U.G. Vej-Hansen, A. Velázquez-Palenzuela, V. Tripkovich, J. Schiøtz, J. Rossmeisl, I.E.L. Stephens, I. Chorkendorff, Tuning the activity of Pt alloy electrocatalysts by means of the lanthanide contraction. Science 352(6281), 73–76 (2016)

    Article  CAS  Google Scholar 

  41. M. Mavrikakis, B. Hammer, J.K. Nørskov, Effect of Strain on the Reactivity of Metal Surfaces. Phys. Rev. Lett. 81(13), 2819 (1998)

    Article  Google Scholar 

  42. L. Vegard, Die konstitution der mischkristalle und die raumfüllung der atome. Z. Phys. 5, 17 (1921)

    Article  CAS  Google Scholar 

  43. 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. Adv. Eng. Mater. 6(5), 299–303 (2004)

    Article  CAS  Google Scholar 

  44. H. Li, K. Shin, G. Henkelman, Effects of ensembles, ligand, and strain on adsorbate binding to alloy surfaces. J. Chem. Phys. 149(17), 174705 (2018)

    Article  Google Scholar 

  45. J.K. Pedersen, C.M. Clausen, O.A. Krysiak, B. **ao, T.A. Batchelor, T. Löffler, V.A. Mints, L. Banko, M. Arenz, A. Savan, W. Schuhmann, A. Ludwig, J. Rossmeisl, Bayesian optimization of high-entropy alloy compositions for electrocatalytic oxygen reduction. Angew. Chem. 133(45), 24346–24354 (2021)

    Article  Google Scholar 

  46. V. Fung, J. Zhang, E. Juarez, B.G. Sumpter, Benchmarking graph neural networks for materials chemistry. NPJ Comput. Mater. 7(1), 1–8 (2021)

    Article  Google Scholar 

  47. J. Gilmer, S.S. Schoenholz, P.F. Riley, O. Vinyals, G.E. Dahl, Neural message passing for quantum chemistry. (2017). https://arxiv.org/abs/1704.01212v2

  48. C. Chen, W. Ye, Y. Zuo, C. Zheng, S.P. Ong, Graph networks as a universal machine learning framework for molecules and crystals. Chem. Mater. 31(9), 3564–3572 (2019)

    Article  CAS  Google Scholar 

  49. T. **e, J.C. Grossman, Crystal graph convolutional neural networks for an accurate and interpretable prediction of materials chemistry. Phys. Rev. Lett. 120(14), 145301 (2018)

    Article  CAS  Google Scholar 

  50. V. Fung, J. Zhang, E. Juarez, B.G. Sumpter, Benchmarking graph neural networks for materials chemistry. NPJ Comp. Mater. 7(1), 1–8 (2021)

    Google Scholar 

  51. Y. Li, D. Tarlow, M. Brockschmidt, R. Zemel, Gated graph sequence neural networks. (2015). https://doi.org/10.48550/ar**v.1511.05493

  52. L. Chanussot, A. Das, S. Goyal, T. Lavril, M. Shuaibi, M. Riviere, K. Tran, J. Heras-Domingo, C. Ho, W. Hu, A. Palizhati, A. Sriram, B. Wood, J. Yoon, D. Parihk, C.L. Zitnick, Z. Ulissi, Open catalyst 2020 (OC20) dataset and community challenges. ACS Catal. 11(10), 6059–6072 (2021)

    Article  CAS  Google Scholar 

  53. H.H. Kristoffersen, T. Vegge, H.A. Hansen, OH formation and H 2 adsorption at the liquid water–Pt (111) interface. Chem. Sci. 9(34), 6912–6921 (2018)

    Article  CAS  Google Scholar 

  54. M.H. Hansen, A. Nilsson, J. Rossmeisl, Modelling pH and potential in dynamic structures of the water/Pt(111) interface on the atomic scale. Phys. Chem. Chem. Phys. 19(34), 23505–23514 (2017)

    Article  CAS  Google Scholar 

  55. W.A. Brown, R. Kose, D.A. King, Femtomole adsorption calorimetry on single-crystal surfaces. Chem. Rev. 98(2), 797–831 (1998)

    Article  CAS  Google Scholar 

  56. D.J. Miller, H. Öberg, L.-Å. Näslund, T. Anniyev, H. Ogasawara, L.G.M. Petterson, A. Nilsson, Low O2 dissociation barrier on Pt(111) due to adsorbate–adsorbate interactions. J. Chem. Phys. 133(22), 224701 (2010)

    Article  CAS  Google Scholar 

  57. S.D. Miller, J.R. Kitchin, Relating the coverage dependence of oxygen adsorption on Au and Pt fcc(1 1 1) surfaces through adsorbate-induced surface electronic structure effects. Surf. Sci. 603(5), 794–801 (2009)

    Article  CAS  Google Scholar 

  58. T. Schiros, L.-Å. Näslund, K. Andersson, J. Gyllenpalm, G.S. Karlberg, M. Odelius, H. Ogasawara, L.G.M. Pettersson, A. Nilsson, Structure and bonding of the water−hydroxyl mixed phase on Pt(111). J. Phys. Chem. C 111(41), 15003–15012 (2007)

    Article  CAS  Google Scholar 

  59. S. Schnur, A. Groß, Properties of metal–water interfaces studied from first principles. New J. Phys. 11(12), 125003 (2009)

    Article  Google Scholar 

  60. V. Tripkovic, T. Vegge, Potential- and rate-determining step for oxygen reduction on Pt(111). J. Phys. Chem. C 121(48), 26785–26793 (2017)

    Article  CAS  Google Scholar 

  61. T. Bligaard, J.K. Nørskov, S. Dahl, J. Matthiesen, C.H. Christensen, J. Sehested, The Brønsted–Evans–Polanyi relation and the volcano curve in heterogeneous catalysis. J. Catal. 224(1), 206–217 (2004)

    Article  CAS  Google Scholar 

  62. I.E. Stephens, A.S. Bondarenko, U. Grønbjerg, J. Rossmeisl, I. Chorkendorff, Understanding the electrocatalysis of oxygen reduction on platinum and its alloys. Energy Environ. Sci. 5(5), 6744–6762 (2012)

    Article  CAS  Google Scholar 

  63. M.T.M. Koper, Thermodynamic theory of multi-electron transfer reactions: Implications for electrocatalysis. J. Electroanal. Chem. 660(2), 254–260 (2011)

    Article  CAS  Google Scholar 

  64. J. Greeley, I.E.L. Stephens, A.S. Bondarenko, T.P. Johansson, H.A. Hansen, T.F. Jaramillo, J. Rossmeisl, I. Chorkendorff, J.K. Nørskov, Alloys of platinum and early transition metals as oxygen reduction electrocatalysts. Nat. Chem. 1(7), 552–556 (2009)

    Article  CAS  Google Scholar 

  65. D.R. Jones, M. Schonlau, W.J. Welch, Efficient global optimization of expensive Black-Box functions. J. Glob. Optim. 13(4), 455–492 (1998)

    Article  Google Scholar 

  66. J.A.Z. Zeledón, M.B. Stevens, G.T.K.K. Gunasooriya, A. Gallo, A.T. Landers, M.E. Kreider, C. Hahn, J.K. Nørskov, T.F. Jaramillo, Tuning the electronic structure of Ag-Pd alloys to enhance performance for alkaline oxygen reduction. Nat. Commun. 12(1), 1–9 (2021)

    Google Scholar 

  67. T. Ioroi, K. Yasuda, Platinum-iridium as oxygen reduction electrocatalysts for polymer electrolyte fuel cells. J. Electrochem. Soc. 152(10), A1917 (2005)

    Article  CAS  Google Scholar 

  68. B.H.L.B. Hammer, L.B. Hansen, J.K. Nørskov, Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals. Phys. Rev. B 59(11), 7413 (1999)

    Article  Google Scholar 

  69. J.J. Mortensen, L.B. Hansen, K.W. Jacobsen, Real-space grid implementation of the projector augmented wave method. Phys. Rev. B 71(3), 035109 (2005)

    Article  Google Scholar 

  70. J. Enkovaara, C. Rostgaard, J.J. Mortensen, J. Chen, M. Dulak, L. Ferrighi, J. Gavnholt, C. Glinsvad, V. Haikola, H.A. Hansen, H.H. Kristoffersen, M. Kuisma, A.H. Larsen, L. Lehtovaara, M. Ljungberg, O. Lopez-Acevedo, P.G. Moses, J. Ojanen, T. Olsen, V. Petzold, N.A. Romero, J. Stausholm-Møller, M. Strange, G.A. Tritsaris, M. Vanin, M. Walter, B. Hammer, H. Häkkinen, G.K.H. Madsen, R.M. Nieminen, J.K. Nørskov, M. Puska, T.T. Rantala, J. Schiøtz, K.S. Thygesen, K.W. Jacobsen, Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method. J. Phys.: Condens. Matter 22(25), 253202 (2010)

    CAS  Google Scholar 

  71. A.H. Larsen, J.J. Mortensen, J. Blomqvist, I.E. Castelli, R. Christensen, M. Dulak, M.G. Friis, B. Hammer, C. Hargus, E. Hermes, P.C. Jennings, P.B. Jensen, J. Kermode, J. Kitchin, E. Kolsbjerg, J. Kubal, K. Kaasbjerg, S. Lysgaard, J.B. Maronsson, T. Maxson, T. Olsen, L. Pastewka, A. Peterson, C. Rostgaard, J. Schiøtz, O. Schütt, M. Strange, K.S. Thygesen, T. Vegge, L. Vilhelmsen, M. Walter, Z. Zeng, K.W. Jacobsen, The atomic simulation environment - a python library for working with atoms. J. Phys.: Condens. Matter 29(27), 273002 (2017)

    Google Scholar 

  72. H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations. Phys. Rev. B 13(12), 5188 (1976)

    Article  Google Scholar 

  73. B. Cordero, V. Gómez, A.E. Platero-Prats, M. Revés, J. Echeverría, E. Cremades, F. Barragán, S. Alvarez, Covalent radii revisited. Dalton Trans. 21, 2832–2838 (2008)

    Article  Google Scholar 

  74. A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Kopf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, S. Chintala, Pytorch: an imperative style, high-performance deep learning library. Adv. Neural Inf. Process. Syst. 32, 8026 (2019)

    Google Scholar 

  75. I. Loshchilov, F. Hutter, Decoupled weight decay regularization (2017) https://doi.org/10.48550/ar**v.1711.05101

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Acknowledgements

All authors acknowledge support from the Danish National Research Foundation Center for High-Entropy Alloy Catalysis (CHEAC) DNRF-149.

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  1. Department of Chemistry, Center for High Entropy Alloy Catalysis (CHEAC), University of Copenhagen, Universitetsparken 5, 2100, Copenhagen Ø, Denmark

    Christian M. Clausen, Martin L. S. Nielsen, Jack K. Pedersen & Jan Rossmeisl

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Clausen, C.M., Nielsen, M.L.S., Pedersen, J.K. et al. Ab Initio to Activity: Machine Learning-Assisted Optimization of High-Entropy Alloy Catalytic Activity. High Entropy Alloys & Materials 1, 120–133 (2023). https://doi.org/10.1007/s44210-022-00006-4

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