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Generalization properties of restricted Boltzmann machine for short-range order |
| M A Timirgazin† and A K Arzhnikov |
| Udmurt Federal Research Center, Ural Branch of RAS, Izhevsk 426067, Russia |
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Abstract A biased sampling algorithm for the restricted Boltzmann machine (RBM) is proposed, which allows generating configurations with a conserved quantity. To validate the method, a study of the short-range order in binary alloys with positive and negative exchange interactions is carried out. The network is trained on the data collected by Monte-Carlo simulations for a simple Ising-like binary alloy model and used to calculate the Warren-Cowley short-range order parameter and other thermodynamic properties. We demonstrate that the proposed method allows us not only to correctly reproduce the order parameters for the alloy concentration at which the network was trained, but can also predict them for any other concentrations.
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Received: 27 July 2022
Revised: 20 September 2022
Accepted manuscript online: 10 October 2022
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PACS:
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74.70.Ad
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(Metals; alloys and binary compounds)
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07.05.Mh
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(Neural networks, fuzzy logic, artificial intelligence)
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64.60.De
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(Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.))
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Corresponding Authors:
M A Timirgazin
E-mail: timirgazin@gmail.com
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Cite this article:
M A Timirgazin and A K Arzhnikov Generalization properties of restricted Boltzmann machine for short-range order 2023 Chin. Phys. B 32 067401
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[1] Wang L2016 Phys. Rev. B 94 195105
[2] Carrasquilla J and Melko R G2017 Nat. Phys. 13 431
[3] Hu W, Singh R R P and Scalettar R T2017 Phys. Rev. E 95 062122
[4] Shiina K, Mori H, Okabe Y and Lee H K2020 Scientific Reports 10 2177
[5] Wetzel S J2017 Phys. Rev. E 96 022140
[6] Ch'ng K, Carrasquilla J, Melko R G and Khatami E2017 Phys. Rev. X 7 031038
[7] Westerhout T, Astrakhantsev N, Tikhonov K S, Katsnelson M I and Bagrov A2020 Nat. Commun. 11 1593
[8] Noé F, Tkatchenko A, Müller K R and Clementi C2020 Annual Review of Physical Chemistry 71 361
[9] Smith J S, Isayev O and Roitberg A E2017 Chem. Sci. 8 3192
[10] Liu J, Qi Y, Meng Z Y and Fu L2017 Phys. Rev. B 95 041101
[11] Huang L and Wang L2017 Phys. Rev. B 95 035105
[12] Shen H, Liu J and Fu L2018 Phys. Rev. B 97 205140
[13] Yu W, Liu Y, Chen Y, Jiang Y and Chen J Z Y2019 The Journal of Chemical Physics 151 031101
[14] Carleo G, Cirac I, Cranmer K, Daudet L, Schuld M, Tishby N, Vogt-Maranto L and Zdeborová L2019 Rev. Mod. Phys. 91 045002
[15] Mehta P, Bukov M, Wang C H, Day A G, Richardson C, Fisher C K and Schwab D J2019 Physics Reports 810 1
[16] Ackley D H, Hinton G E and Sejnowski T J1985 Cognitive Science 9 147
[17] Stratonovich R L 1957 Soviet Physics Doklady 2 416
[18] Groshev A and Arzhnikov A2020 Journal of Experimental and Theoretical Physics 130 247
[19] Rrapaj E and Roggero A2021 Phys. Rev. E 103 013302
[20] Torlai G and Melko R G2016 Phys. Rev. B 94 165134
[21] Nomura Y, Darmawan A S, Yamaji Y and Imada M2017 Phys. Rev. B 96 205152
[22] Vieijra T, Casert C, Nys J, De Neve W, Haegeman J, Ryckebusch J and Verstraete F2020 Phys. Rev. Lett. 124 097201
[23] Carleo G and Troyer M2017 Science 355 602
[24] Hinton G E, Osindero S and Teh Y W2006 Neural Comput. 18 1527
[25] Morningstar A and Melko R G 2017 J. Mach. Learn. Res. 18 5975 ISSN 1532-4435
[26] Azizi A and Pleimling M2021 Scientific Reports 11 1
[27] Ziman J and Ziman P1979 Models of Disorder: The Theoretical Physics of Homogeneously Disordered Systems (Cambridge University Press) ISBN 9780521217842
[28] Binder K, Lebowitz J L, Phani M K and Kalos M H1981 Acta Metallurgica 29 1655
[29] Arzhnikov A, Bagrets A and Bagrets D1996 J. Magn. Magn. Mater. 153 195
[30] Müller M and Albe K2005 Phys. Rev. B 72 094203
[31] Cowley J M1950 Phys. Rev. 77 669
[32] Warren B E 1969 X-ray Diffraction (Addison-Wesley, Reading, MA)
[33] Scholten P D1985 Phys. Rev. B 32 345
[34] Newman M and Barkema G1999 Monte Carlo Methods in Statistical Physics (Clarendon Press)
[35] Kawasaki K1966 Phys. Rev. 145 224
[36] Baxter R1982 Exactly Solved Models in Statistical Mechanics (Academic Press)
[37] Binder K and Landau D P1980 Phys. Rev. B 21 1941
[38] Lourenço B J and Dickman R2016 J. Stat. Mech.: Theo. Exper. 2016 033107
[39] Arzhnikov A K, Dobysheva L V, Konygin G N, Voronina E V and Yelsukov E P2001 Phys. Rev. B 65 024419
[40] Kozak R, Sologubenko A and Steurer W2015 Zeitschrift für Kristallographie-Crystalline Materials 230 55
[41] Steurer W2020 Materials Characterization 162 110179
[42] Smolensky P 1986 Parallel Distributed Process 1
[43] Hinton G E2002 Neural Computation 14 1771
[44] Hinton G E2012 A Practical Guide to Training Restricted Boltzmann Machines (Berlin, Heidelberg: Springer) pp. 599-619
[45] Hyvärinen A2006 Neural Computation 18 2283
[46] Schönfeld B, Sax C R, Zemp J, Engelke M, Boesecke P, Kresse T, Boll T, Al-Kassab T, Peil O E and Ruban A V2019 Phys. Rev. B 99 014206 |
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