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 
2. wླ໦༤ଠ
   ʢYuta SUZUKIʣ IUUQTSFTOBOUHJUIVCJP • ૯߹ݚڀେֶӃେֶɹߴΤωϧΪʔՃ଎ثՊֶݚڀՊɹ5೥Ұ؏੍ത࢜՝ఔ5೥ •@resnant (Twitter, GitHub) w3FTFBSDI
   *OUFSFTUɿ"*BTTJTUFEͳ෺࣭ɾࡐྉͷཧղ
   wػցֶशΛԠ༻ͨ͠৽ͨͳ෺࣭ܭଌٕज़ͷ։ൃ
   w࣮ݧσʔλʹ͓͚ΔσʔλϚΠχϯά
   w+45
   "$5*ݚڀऀʰࡐྉܭଌσʔλͷϞμϦςΟม׵ʱʢ৘ใͱະདྷ
   ྖҬʣ
   w$PMMBCPSBUPSTʢܟশུʣ
   wඌ࡚Յ඙ɺେ੢ਖ਼ًʢ࢈૯ݚ
   ਓ޻஌ೳݚڀηϯλʔʣ
   wڇٱ঵޹ɺ୩߹ཽయɺઍ༿௚໵
   ΦϜϩϯαΠχοΫΤοΫε
   w೔໺ӳҳʢ౷ܭ਺ཧݚڀॴʣ
   wখ໺ɺ੪౻ɺӋ߹ʢখ໺ݚڀࣨʣ  About me 
3. wϒϥοΫϘοΫε࠷దԽΛԠ༻ͯ݁͠থߏ଄ղੳΛࣗಈԽͨ͠࿩
   w ʮͳʹͬͯʜ0QUVOBΛ࢖ͬͯ࠷దԽ͚͕ͨͩͩ͠ʁʯ
   wݚڀॴͷ3FTFBSDI
   )JHIMJHIUʹબग़
   w์ࣹޫֶձ
   ֶੜൃද৆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
   
4. • ೔ຊ࠷େͷ෺ཧɾࡐྉͷݚڀॴʢ෺ཧతʹ΋େ͖͍ʣ • Ӊ஦ɾૉཻࢠ͔Βࡐྉɾੜ෺·Ͱ෯޿͍ݚڀ • զʑ͸Xઢʢ์ࣹޫʣΛ࢖ͬͯ෺࣭Λௐ΂ΔݚڀΛ͍ͯ͠·͢ • ์ࣹޫɿ΄΅ޫ଎Ͱӡಈ͢Δిࢠ͔Β์ࣹ͞ΕΔ์ࣹઢ • KEK stands for ߴΤωϧΪʔՃ଎ثݚڀػߏ  ߴΤωϧΪʔՃ଎ثݚڀػߏʢKEKʣ 
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఺
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
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఺
8.  ࣮ࡍͷଌఆͷ༷ࢠ  ͍͋ͪ43ɹߴ଎93%ϏʔϜϥΠϯ
   #-4 •ଌఆσʔλͷղੳ͕ݚڀͷϘτϧωοΫʹ
   •93%ଌఆɿ݅EBZ
   •93%ղੳɿ
   
   
   
   
   
   
   
   ݅EBZɹˠσʔλͷେ൒͸ଌ͚ͬͨͩͰະ׆༻ʹʜ 93%ύλʔϯͷྫ
9.  XRDύλʔϯղੳͷྲྀΕ • Ϧʔτϕϧτղੳɿ෺ཧϞσϧͷ͋ͯ͸Ίʹجͮ͘ค຤ճંύλʔϯͷղੳ๏ • ॳظ݁থߏ଄͔Βܭࢉ͞ΕΔXRD͕ܭଌXRDʹҰக͢ΔΑ͏ɺߏ଄ΛΞοϓσʔτ͢Δ  1SPT wચ࿅͞Ε࢖͍΍͍͢ख๏
   w݁থͷ༷ʑͳ৘ใ͕ಘΒΕΔ $POT wࢼߦࡨޡͰܾΊΔύϥϝʔλଟ਺
   wखؒͱ͕͔͔࣌ؒΔʢ݅਺࣌ؒʣ
   wύϥϝʔλௐ੔ʹܦݧ͕ඞཁ
10.  ݚڀͷ֓ཁ • ϦʔτϕϧτղੳΛϒϥοΫϘοΫε࠷దԽʢBBOʣͷ࿮૊ΈͰࣗಈԽͨ͠ʢBBO-Rietveldʣ • BBOɿ਺ཧ࠷దԽͷ໰୊ઃఆͷҰͭɻؔ਺ܗ΍ޯ഑͕Θ͔Βͳ͍ؔ਺ͷ࠷దԽΛѻ͏ • ػցֶशϞσϧͷϋΠύʔύϥϝʔλ࠷దԽʢHPOʣ͸ɺBBOͷ୅දతͳԠ༻ • ίΞΞΠσΟΞɿϦʔτϕϧτղੳͷࢼߦࡨޡ΋ɺHPOಉ༷ʹղ͚ΔͷͰ͸ʁ  ϦʔτϕϧτղੳͷϫʔΫϑϩʔ
11.  ݚڀͷ֓ཁ  f Blackbox function R
    Λ࠷খԽ͢ΔઃఆΛ୳͢໰୊ͱͯ͠ղ͚Δ PQUJNJ[BUJPO
    MPPQ ϦʔτϕϧτղੳͷϫʔΫϑϩʔ • ϦʔτϕϧτղੳΛϒϥοΫϘοΫε࠷దԽʢBBOʣͷ࿮૊ΈͰࣗಈԽͨ͠ʢBBO-Rietveldʣ • BBOɿ਺ཧ࠷దԽͷ໰୊ઃఆͷҰͭɻؔ਺ܗ΍ޯ഑͕Θ͔Βͳ͍ؔ਺ͷ࠷దԽΛѻ͏ • ػցֶशϞσϧͷϋΠύʔύϥϝʔλ࠷దԽʢHPOʣ͸ɺBBOͷ୅දతͳԠ༻ • ίΞΞΠσΟΞɿϦʔτϕϧτղੳͷࢼߦࡨޡ΋ɺHPOಉ༷ʹղ͚ΔͷͰ͸ʁ
12.  ݚڀͷ֓ཁ  • ۩ମతͳϫʔΫϑϩʔ • Ϧʔτϕϧτղੳͦͷ΋ͷ͸طଘιϑτ΢ΣΞʢGSAS-IIʣͰ࣮ߦ • BBOͰ୳ࡧ͢Δͷ͸GSASͷઃఆʢ݁থߏ଄ͷॳظ஋Ͱ͸ͳ͍ɻޙड़ʣ • Rwp ʢXRDύλʔϯͷ࢒ࠩʣΛখ͘͢͞ΔઃఆΛ୳͢ ϒϥοΫϘοΫε࠷దԽ ෺ཧϞσϧઃఆ ॳظύϥϝʔλ Ϧʔτϕϧτਫ਼ີԽ ਫ਼ີԽ͞Εͨ݁থߏ଄ Rwp(x) background function : Chebyshev degree of background function : 9 background refinement : True peak shape refinement : True etc. ϒϥοΫϘοΫε࠷దԽϧʔϓ ઃఆʹج͖ͮɺ Ϧʔ τϕϧ τਫ਼ີԽΛ࣮ߦ Minimise Rwp(x) subject to c(x) ... initial crystal structure instrument parameters etc. ... Trial 1 Trial 2 Trial 3 ͜Ε·Ͱͷਫ਼ີԽ݁ՌΛجʹ ৽͍͠ઃఆxΛੜ੒ ੍໿৚݅Λຬ͔ͨ֬͢ೝ - -
13.  ख๏ʛΞϧΰϦζϜɾ୳ࡧۭؒʹ͍ͭͯ  • ##0ͷΞϧΰϦζϜʹ͸5SFFTUSVDUVSFE
    1BS[FO
    &TUJNBUPSʢ51&ʣΛ༻͍ͨ
    • ϕΠζ࠷దԽͷҰछ
    • ͭͷࡐྉΛ༻͍ͯݕূͨ͠ʢલऀͭʹ͍ͭͯ঺հʣ
    • :0
    %4.0
    %Z4S.O0
    -J$P0
    • ࠷దԽͨ͠(4"4ͷઃఆม਺Ұཡʢ࿈ଓɺΧςΰϦΧϧɺίϯσΟγϣφϧม਺͕ࠞࡏʣ
14.  ख๏ʛ࣮૷ͷҰ෦Λ঺հ  • ίʔυΑΓҰ෦ൈਮ
    IUUQTHJUIVCDPNRVBOUVNCFBN##03JFUWFME
    • ֤ม਺ͷϑΟοςΟϯάॱ͸యܕతͳॱ൪ʹैͬͨ
    ࠷ॳʹண໨͢ΔUIFUBྖҬΛࢦఆ όοΫάϥ΢ϯυؔ਺Λઃఆ
    ʢؔ਺ܗɾ࣍਺ʣ όοΫάϥ΢ϯυΛϑΟοςΟϯά ʢଓ͘ʣ ໨తؔ਺ɿ(4"4**ΛɺύϥϝʔλΛೖΕΔͱ3XQΛฦؔ͢਺ͱΈͳ͢
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༝ 
16. w 3%#ͷύϑΥʔϚϯε͕໰୊ʹͳͬͨʢղܾࡁʣ
    w ॳظͷ0QUVOBͰ͸3%#͔ΒͷಡΈग़͕͠஗͘ɺ
    ඇৗʹେ͖͍O@USJBMʢສͱ͔ʣͰTUVEZΛ࣮ߦ͢ΔͱɺͦͷTUVEZΛMPBEͰ͖ͳ͔ͬͨ
    w 0QUVOB
    ͋ͨΓͷόʔδϣϯΞοϓͰղܾ͞Εͨ
    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 
17. Demo  ʢˡಈըʣ
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๏ 5IF
    PQUJNJTBUJPO
    IJTUPSZ
    PG
    3XQ
    3JFUWFME
    QMPU
    PG
    UIF
    CFTU
    DPOpHVSBUJPO BBO-Rietveldͷ݁ՌʛY2O3 
19. (a) (b) 5IF
    PQUJNJTBUJPO
    IJTUPSZ
    PG
    3XQ
    3JFUWFME
    QMPU
    PG
    UIF
    CFTU
    DPOpHVSBUJPO BBO-Rietveldͷ݁ՌʛDSMO • 30෼ఔ౓Ͱख़࿅ऀΑΓྑ͍͋ͯ͸Ί݁ՌΛಘͨ • best Rwp = 9.211% • 9.76% by human expert, 12.8% by Auto FP • AutoFPɿΤΩεύʔτγεςϜʢϧʔϧͷ૊Έ߹Θͤʣʹجͮ͘طଘख๏ 
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 
21. w ఏҊख๏ʹΑΓɺ΄΅ಉ͡
    3XQ͕ͩߏ଄͕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%) CZ
    IVNBO
    FYQFSU
    3XQ PVUMJFS
    CZ
    ##0
    3XQ ݁ՌʛಘΒΕͨ݁থߏ଄ͷ෼ੳ .O0ͷ݁߹͕֯ҟͳΔ ֤఺͕ͭͷ݁থߏ଄ʹରԠɺڑ཭͸ߏ଄ͷྨࣅ౓Λද͢ 
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 HSBEJFOU
    BTDFOU͢Δླ໦ˠ