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物質の結晶構造解析におけるOptunaの応用/Optuna application of crystal structure analysis [Optuna Meetup #1]

物質の結晶構造解析におけるOptunaの応用/Optuna application of crystal structure analysis [Optuna Meetup #1]

2021/06/26のOptuna Meetup #1 で講演した内容です。
対応する論文とGitHub repoはこちらです
Ozaki, Y., Suzuki, Y., Hawai, T., Saito, K., Onishi, M., and Ono, K.
Automated crystal structure analysis based on blackbox optimisation.
npj Computational Materials 6, 75 (2020).
https://www.nature.com/articles/s41524-020-0330-9
https://github.com/quantumbeam/BBO-Rietveld

Yuta Suzuki

June 26, 2021
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  1. wླ໦༤ଠʢYuta SUZUKIʣ IUUQTSFTOBOUHJUIVCJP • ૯߹ݚڀେֶӃେֶɹߴΤωϧΪʔՃ଎ثՊֶݚڀՊɹ5೥Ұ؏੍ത࢜՝ఔ5೥ •@resnant (Twitter, GitHub) w3FTFBSDI*OUFSFTUɿ"*BTTJTUFEͳ෺࣭ɾࡐྉͷཧղ wػցֶशΛԠ༻ͨ͠৽ͨͳ෺࣭ܭଌٕज़ͷ։ൃ

    w࣮ݧσʔλʹ͓͚ΔσʔλϚΠχϯά w+45"$5*ݚڀऀʰࡐྉܭଌσʔλͷϞμϦςΟม׵ʱʢ৘ใͱະདྷྖҬʣ w$PMMBCPSBUPSTʢܟশུʣ wඌ࡚Յ඙ɺେ੢ਖ਼ًʢ࢈૯ݚਓ޻஌ೳݚڀηϯλʔʣ wڇٱ঵޹ɺ୩߹ཽయɺઍ༿௚໵ ΦϜϩϯαΠχοΫΤοΫε  w೔໺ӳҳʢ౷ܭ਺ཧݚڀॴʣ wখ໺ɺ੪౻ɺӋ߹ʢখ໺ݚڀࣨʣ  About me 
  2. w9ઢճંʢ93%ʣ͸݁থߏ଄ղੳͷجຊख๏ͱͯ͠ීٴ w93%ύλʔϯ͔Β݁থߏ଄͕Θ͔Δʢ೥ϊʔϕϧ৆ʣ w෺࣭ݚڀɾ࢈ۀΛࢧ͑ΔෆՄܽͳπʔϧͷҰͭ  93%ଌఆ૷ஔ /E࣓ੴͷ93%ύλʔϯ /E࣓ੴͷ݁থߏ଄ ωΦδϜʢ/Eʣ࣓ੴ ʢ/E 'F

    #ʣ ϐ ʔΫϑΟοςΟϯά * Chen, P. A. et al. J. Magn. Mag. Mater. 370, 45–53 (2014). w93%ύλʔϯͷղੳʹ͸ɺ෺ཧϞσϧΛ༻͍ͨσʔλղੳ͕ඞཁ w͔͠͠ɺ͜ͷखؒͱ͕࣌ؒ՝୊ʹɾɾɾ😭 ݁থߏ଄ղੳɿ෺࣭ɾࡐྉݚڀͷ࢝఺
  3.  ݚڀͷ֓ཁ  f Blackbox function RΛ࠷খԽ͢ΔઃఆΛ୳͢໰୊ͱͯ͠ղ͚Δ PQUJNJ[BUJPOMPPQ ϦʔτϕϧτղੳͷϫʔΫϑϩʔ •

    ϦʔτϕϧτղੳΛϒϥοΫϘοΫε࠷దԽʢBBOʣͷ࿮૊ΈͰࣗಈԽͨ͠ʢBBO-Rietveldʣ • BBOɿ਺ཧ࠷దԽͷ໰୊ઃఆͷҰͭɻؔ਺ܗ΍ޯ഑͕Θ͔Βͳ͍ؔ਺ͷ࠷దԽΛѻ͏ • ػցֶशϞσϧͷϋΠύʔύϥϝʔλ࠷దԽʢHPOʣ͸ɺBBOͷ୅දతͳԠ༻ • ίΞΞΠσΟΞɿϦʔτϕϧτղੳͷࢼߦࡨޡ΋ɺHPOಉ༷ʹղ͚ΔͷͰ͸ʁ
  4.  ݚڀͷ֓ཁ  • ۩ମతͳϫʔΫϑϩʔ • Ϧʔτϕϧτղੳͦͷ΋ͷ͸طଘιϑτ΢ΣΞʢGSAS-IIʣͰ࣮ߦ • BBOͰ୳ࡧ͢Δͷ͸GSASͷઃఆʢ݁থߏ଄ͷॳظ஋Ͱ͸ͳ͍ɻޙड़ʣ •

    Rwp ʢXRDύλʔϯͷ࢒ࠩʣΛখ͘͢͞ΔઃఆΛ୳͢ ϒϥοΫϘοΫε࠷దԽ ෺ཧϞσϧઃఆ ॳظύϥϝʔλ Ϧʔτϕϧτਫ਼ີԽ ਫ਼ີԽ͞Εͨ݁থߏ଄ Rwp(x) background function : Chebyshev degree of background function : 9 background refinement : True peak shape refinement : True etc. ϒϥοΫϘοΫε࠷దԽϧʔϓ ઃఆʹج͖ͮɺ Ϧʔ τϕϧ τਫ਼ີԽΛ࣮ߦ Minimise Rwp(x) subject to c(x) ... initial crystal structure instrument parameters etc. ... Trial 1 Trial 2 Trial 3 ͜Ε·Ͱͷਫ਼ີԽ݁ՌΛجʹ ৽͍͠ઃఆxΛੜ੒ ੍໿৚݅Λຬ͔ͨ֬͢ೝ - -
  5. w ιϑτ΢ΣΞͷग़དྷ͕ྑ͔ͬͨ w ࢖͍΍͍͢"1* w ୳ࡧۭؒͷఆ͕ٛॻ͖΍͍͢ w EFpOFCZSVOελΠϧ͸΍͸Γศར w Ϛϧνϊʔυ΁ͷεέʔϧ͕༰қ

    w εύίϯʢϊʔυɺ෺ཧ$16ʣ্Ͱͷ Քಇ࣮੷͋Γ w ৴པͰ͖Δ։ൃମ੍ w ܧଓత͔ͭ׆ൃͳ։ൃ͕ݟࠐ·Εͨ w ՄࢹԽͳͲ݁Ռͷ෼ੳػೳ΋ॆ࣮ͭͭ͋͠Δ w ࠃ࢈ιϑτ΢ΣΞΛԠԉ͍ͨ͠ OptunaΛ࠾༻͢Δʹࢸͬͨཧ༝ 
  6. w 3%#ͷύϑΥʔϚϯε͕໰୊ʹͳͬͨʢղܾࡁʣ w ॳظͷ0QUVOBͰ͸3%#͔ΒͷಡΈग़͕͠஗͘ɺ ඇৗʹେ͖͍O@USJBMʢສͱ͔ʣͰTUVEZΛ࣮ߦ͢ΔͱɺͦͷTUVEZΛMPBEͰ͖ͳ͔ͬͨ w 0QUVOB͋ͨΓͷόʔδϣϯΞοϓͰղܾ͞Εͨ w O@KPCTҾ਺Λେ͖͘͢Δͱ3%#͕σουϩοΫ͢Δʢղܾࡁʣ w

    3%#΁ͷίωΫγϣϯϓʔϧͷσϑΥϧτ͕ʢ͔֬ʣ w O@KPCTΛΑΓେ͖͘͢Δ৔߹ɺίωΫγϣϯϓʔϧΛେ͖͘͢Δඞཁ͋Γ • optuna.storages.RDBStorage(url, engine_kwargs={“pool_size”: 128}) w O@KPCT͸ݱࡏEFQSFDBUF͞Εͨʢ͕෮׆͢Δ͔΋͠Εͳ͍Β͍͠ʣ w (4"4**ʢϦʔτϕϧτղੳιϑτʣͷṖόάΛ౿Ή w ਓ͕ؒ(6*Ͱૢ࡞͢ΔલఏͰฒྻԽ͸૝ఆ͞Ε͍ͯͳ͍ w PCKFDUJWFͷதͰ(4"4ΛJNQPSUͯ͠ରԠ ࣮૷தʹۤ࿑ͨ͠఺ͳͲ 
  7. (a) (b) • 30෼ఔ౓Ͱख़࿅ऀΑΓྑ͍͋ͯ͸Ί݁ՌΛಘͨ • best Rwp = 6.610% •

    6.96% by human expert, 7.23% by Auto FP • AutoFPɿΤΩεύʔτγεςϜʢϧʔϧͷ૊Έ߹Θͤʣʹجͮ͘طଘख๏ 5IFPQUJNJTBUJPOIJTUPSZPG3XQ 3JFUWFMEQMPUPGUIFCFTUDPOpHVSBUJPO BBO-Rietveldͷ݁ՌʛY2O3 
  8. (a) (b) 5IFPQUJNJTBUJPOIJTUPSZPG3XQ 3JFUWFMEQMPUPGUIFCFTUDPOpHVSBUJPO BBO-Rietveldͷ݁ՌʛDSMO • 30෼ఔ౓Ͱख़࿅ऀΑΓྑ͍͋ͯ͸Ί݁ՌΛಘͨ • best Rwp

    = 9.211% • 9.76% by human expert, 12.8% by Auto FP • AutoFPɿΤΩεύʔτγεςϜʢϧʔϧͷ૊Έ߹Θͤʣʹجͮ͘طଘख๏ 
  9. • ཚ਺Λม͑ͯ100ճࢼߦ͠ɺ୳ࡧͷ҆ఆੑΛௐ΂ͨ • Y2O3 Ͱ90%ɺDSMOͰ99%͸ख़࿅ऀΑΓྑ͍͋ͯ͸Ί͕ಘΒΕͨ • ʮRwp ͕খ͍͞ʯ= ྑ͍͋ͯ͸Ίͱఆٛ •

    طଘख๏ʢAutoFPʣ͸ط஌෺࣭ʹΦʔόʔϑΟοτ͍ͯ͠Δʁ ݁Ռʛ୳ࡧͷ҆ఆੑධՁ ճͷࢼߦʹΑΓಘΒΕͨ3XQͷώετάϥϜ :0 "VUP'1͸%4.0Ͱ͸ඍົ 3XQ ճͷࢼߦʹΑΓಘΒΕͨ3XQͷώετάϥϜ %4.0 
  10. w ఏҊख๏ʹΑΓɺ΄΅ಉ͡3XQ͕ͩߏ଄͕ҟͳΔީิ͕ݟ͔ͭͬͨ w ख़࿅ऀͱ΄΅ಉ͡ߏ଄ w શ͘ҟͳΔߏ଄΋ݟ͚ͭͨ Best by BBO (Rwp

    = 9.211%) Similar to human expert by BBO (Rwp = 9.577%) Best by human expert (Rwp = 9.775%) Another interesting candidate by BBO (Rwp =9.484%) CZIVNBOFYQFSU 3XQ PVUMJFSCZ##0 3XQ ݁ՌʛಘΒΕͨ݁থߏ଄ͷ෼ੳ .O0ͷ݁߹͕֯ҟͳΔ ֤఺͕ͭͷ݁থߏ଄ʹରԠɺڑ཭͸ߏ଄ͷྨࣅ౓Λද͢ 
  11.  αϚϦʔ  w ܭଌσʔλ΁ͷ෺ཧϞσϧ͋ͯ͸ΊΛ##0ͷ໰୊ͱͯ͠ఆࣜԽͨ͠ • BBO-Rietveld ʢhttps://github.com/quantumbeam/BBO-Rietveldʣ w ͋ͯ͸ΊΛվળ͢ΔͨΊͷࢼߦࡨޡΛࣗಈԽͰ͖ͨ

    w ख़࿅ऀͷ݁Ռͱಉ౳ͷ݁থߏ଄ɾΑΓྑ͍͋ͯ͸·ΓΛಘͨ w ܭࢉ࣌ؒ͸ϊʔυͰ෼ఔ౓ʢฒྻԽ΋Մೳʣ • ҟ෼໺ͷࢹ఺Ͱࡐྉͷ໰୊Λଊ͑௚͢ͱγϯϓϧʹղ͚ͨ • ֶࡍݚڀͷ͓΋͠Ζ͞ • ܭࢉػͱΞϧΰϦζϜͰղܾՄೳͳࡐྉͷ໰୊͸·ͩ·ͩ͋Δ • ʰਓؒɾ"*ɾϩϘοτ͕ڠಇ͢Δࡐྉ։ൃʱΛ໨ࢦ͍ͯ͠·͢ • ΫϥΠϛϯάߦ͖·͠ΐ͏ HSBEJFOUBTDFOU͢Δླ໦ˠ