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

Transcript

1. 0QUVOB.FFUVQ
   ෺࣭ͷ݁থߏ଄ղੳʹ͓͚Δ
   0QUVOBͷԠ༻
   ླ໦༤ଠʢ૯߹ݚڀେֶӃେֶɺߴΤωϧΪʔՃ଎ثݚڀػߏʣ
   
   

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2. 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
   

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3. wϒϥοΫϘοΫε࠷దԽΛԠ༻ͯ݁͠থߏ଄ղੳΛࣗಈԽͨ͠࿩
   w ʮͳʹͬͯʜ0QUVOBΛ࢖ͬͯ࠷దԽ͚͕ͨͩͩ͠ʁʯ
   wݚڀॴͷ3FTFBSDI)JHIMJHIUʹબग़
   w์ࣹޫֶձֶੜൃද৆ʢ೥݄ʣ
   wࠓ೔ͷߨԋ͸͜ͷ࿦จˣͷ࿩
   
   ࠓ೔ͷߨԋʛࡐྉݚڀʹ͓͚ΔOptunaͷԠ༻ࣄྫ
   Ozaki, Y., Suzuki, Y., Hawai, T., Saito, K., Onishi, M. & Ono, K.
   Automated crystal structure analysis based on blackbox
   optimisation. npj Comput. Mater 6, 75 (2020). Խֶ޻ۀ೔ใ
   

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4. • ೔ຊ࠷େͷ෺ཧɾࡐྉͷݚڀॴʢ෺ཧతʹ΋େ͖͍ʣ
   • Ӊ஦ɾૉཻࢠ͔Βࡐྉɾੜ෺·Ͱ෯޿͍ݚڀ
   • զʑ͸Xઢʢ์ࣹޫʣΛ࢖ͬͯ෺࣭Λௐ΂ΔݚڀΛ͍ͯ͠·͢
   • ์ࣹޫɿ΄΅ޫ଎Ͱӡಈ͢Δిࢠ͔Β์ࣹ͞ΕΔ์ࣹઢ
   • KEK stands for ߴΤωϧΪʔՃ଎ثݚڀػߏ
   
   ߴΤωϧΪʔՃ଎ثݚڀػߏʢKEKʣ
   

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5. 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).
   ݁থߏ଄ղੳɿ෺࣭ɾࡐྉݚڀͷ࢝఺
   

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6. w͸΍Ϳ͞ͷϦϡ΢ά΢ࢼྉղੳͰ΋93%͕׆༂
   wඇഁյ͔ͭɺඍখͳࢼྉͰ΋ଌఆ͕Ͱ͖Δ
   wࠓि͔Β,&,1IPUPO'BDUPSZͰ΋ଌఆ͕ਐߦத
   
   ݁থߏ଄ղੳɿ෺࣭ɾࡐྉݚڀͷ࢝఺
   ͜Ε͕Ϧϡ΢ά΢ͷ࠭
   ʢଟ෼NN͙Β͍ʣ
   1IPUPO'BDUPSZ#-"ɹʢۃݶ৚݅Լਫ਼ີ୯݁থ9ઢճં#-ʣ
   $
   ߴΤωϧΪʔՃ଎ثݚڀػߏ෺࣭ߏ଄Պֶݚڀॴ
   $
   ߴΤωϧΪʔՃ଎ثݚڀػߏ෺࣭ߏ଄Պֶݚڀॴ
   

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7. 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఺
   

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8. 
   ࣮ࡍͷଌఆͷ༷ࢠ
   ͍͋ͪ43ɹߴ଎93%ϏʔϜϥΠϯ#-4
   •ଌఆσʔλͷղੳ͕ݚڀͷϘτϧωοΫʹ
   •93%ଌఆɿ݅EBZ
   •93%ղੳɿ ݅EBZɹˠσʔλͷେ൒͸ଌ͚ͬͨͩͰະ׆༻ʹʜ
   93%ύλʔϯͷྫ
   

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9. 
   XRDύλʔϯղੳͷྲྀΕ
   • Ϧʔτϕϧτղੳɿ෺ཧϞσϧͷ͋ͯ͸Ίʹجͮ͘ค຤ճંύλʔϯͷղੳ๏
   • ॳظ݁থߏ଄͔Βܭࢉ͞ΕΔXRD͕ܭଌXRDʹҰக͢ΔΑ͏ɺߏ଄ΛΞοϓσʔτ͢Δ
   
   1SPT
   wચ࿅͞Ε࢖͍΍͍͢ख๏
   w݁থͷ༷ʑͳ৘ใ͕ಘΒΕΔ
   $POT
   wࢼߦࡨޡͰܾΊΔύϥϝʔλଟ਺
   wखؒͱ͕͔͔࣌ؒΔʢ݅਺࣌ؒʣ
   wύϥϝʔλௐ੔ʹܦݧ͕ඞཁ
   

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10. 
    ݚڀͷ֓ཁ
    • ϦʔτϕϧτղੳΛϒϥοΫϘοΫε࠷దԽʢBBOʣͷ࿮૊ΈͰࣗಈԽͨ͠ʢBBO-Rietveldʣ
    • BBOɿ਺ཧ࠷దԽͷ໰୊ઃఆͷҰͭɻؔ਺ܗ΍ޯ഑͕Θ͔Βͳ͍ؔ਺ͷ࠷దԽΛѻ͏
    • ػցֶशϞσϧͷϋΠύʔύϥϝʔλ࠷దԽʢHPOʣ͸ɺBBOͷ୅දతͳԠ༻
    • ίΞΞΠσΟΞɿϦʔτϕϧτղੳͷࢼߦࡨޡ΋ɺHPOಉ༷ʹղ͚ΔͷͰ͸ʁ
    
    ϦʔτϕϧτղੳͷϫʔΫϑϩʔ
    

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11. 
    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
    

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12. 
    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
    -
    -
    

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13. 
    ख๏ʛΞϧΰϦζϜɾ୳ࡧۭؒʹ͍ͭͯ
    • ##0ͷΞϧΰϦζϜʹ͸5SFFTUSVDUVSFE1BS[FO&TUJNBUPSʢ51&ʣΛ༻͍ͨ
    • ϕΠζ࠷దԽͷҰछ
    • ͭͷࡐྉΛ༻͍ͯݕূͨ͠ʢલऀͭʹ͍ͭͯ঺հʣ
    • :0 %4.0 %Z4S.O0
    -J$P0
    • ࠷దԽͨ͠(4"4ͷઃఆม਺Ұཡʢ࿈ଓɺΧςΰϦΧϧɺίϯσΟγϣφϧม਺͕ࠞࡏʣ
    

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14. 
    ख๏ʛ࣮૷ͷҰ෦Λ঺հ
    • ίʔυΑΓҰ෦ൈਮIUUQTHJUIVCDPNRVBOUVNCFBN##03JFUWFME
    • ֤ม਺ͷϑΟοςΟϯάॱ͸యܕతͳॱ൪ʹैͬͨ
    ࠷ॳʹண໨͢ΔUIFUBྖҬΛࢦఆ
    όοΫάϥ΢ϯυؔ਺Λઃఆ
    ʢؔ਺ܗɾ࣍਺ʣ
    όοΫάϥ΢ϯυΛϑΟοςΟϯά
    ʢଓ͘ʣ
    ໨తؔ਺ɿ(4"4**ΛɺύϥϝʔλΛೖΕΔͱ3XQΛฦؔ͢਺ͱΈͳ͢
    

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15. 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༝
    

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16. 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
    

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17. Demo
    ʢˡಈըʣ
    

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18. (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
    
    

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19. (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๏
    
    

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20. • 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
    
    
    

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21. 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
    
    

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22. 
    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
    

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