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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

31bf3df4bac9b584c89bc11b0c84e132?s=128

Yuta Suzuki

June 26, 2021
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Transcript

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

  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 
  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
  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 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
  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͸5SFFTUSVDUVSFE1BS[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  • ίʔυΑΓҰ෦ൈਮIUUQTHJUIVCDPNRVBOUVNCFBN##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 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 
  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๏ 5IFPQUJNJTBUJPOIJTUPSZPG3XQ 3JFUWFMEQMPUPGUIFCFTUDPOpHVSBUJPO BBO-Rietveldͷ݁ՌʛY2O3 
  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๏ 
  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΄΅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 
  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