Upgrade to Pro — share decks privately, control downloads, hide ads and more …

(2020.01) 機械学習による化学反応の予測と設計

itakigawa
September 27, 2023
190

(2020.01) 機械学習による化学反応の予測と設計

近畿化学協会コンピュータ化学部会 公開講演会(第107回例会), 2020年1月27日, 大阪科学技術センター.
http://www.kinka.or.jp/compchem/prog/20200127_107prog.pdf

itakigawa

September 27, 2023
Tweet

Transcript

  1. 組織の紹介① 理化学研究所 ⾰新知能統合研究センター(AIP) • ⽂部科学省の⼈⼯知能基盤技術に関する研究拠点 • 2016年度設置、2017年活動開始 • 本部は東京・⽇本橋 (東京駅近く)

    COREDO⽇本橋のある⽇本橋⼀丁⽬三井ビルディング15階 • 所属チーム勤務地:京阪奈地区 ATR内 礵螟٥銮加峸㖑⼒խ䒉暟ꂁ縧㔳
  2. AFIR for automated reaction path searching AIMD for dynamical simulation

    of chemical reactions DFT for transition state calculation Chemoinformatics Large-scale simulation Machine-learning Mathematical modeling Making full use of available computational / informatics tools, we establish chemical reaction design and discovery lead by computation / informatics ICReDDのテクノロジー
  3. 10年 北⼤ (1995〜2004) 7年 京⼤ (2005〜2011) 7年 北⼤ (2012〜2018) 統計的信号処理とパターン認識

    (⼯学研究科) "劣決定信号源分離のL1ノルム最⼩解の理論分析" バイオインフォマティクス (化学研究所) ケモインフォマティクス (薬学研究科) データ駆動科学・ 離散構造を伴う機械学習 (情報科学研究科) + JSTさきがけ: 材料インフォマティクス ?年 理研(京都) (2019〜) AIPセンター iPS細胞連携医学的リスク回避チーム (北⼤ 化学反応創成研究拠点とクロアポ) 専⾨:機械学習・データマイニングとその⾃然科学での利活⽤   「データからの学習」をどう問題解決に活⽤できるのか? ⾃⼰紹介:瀧川 ⼀学 (たきがわ・いちがく) https://itakigawa.github.io/
  4. データ 駆動科学 −情報と科学− v h(1) v =  xv 0

    <latexit sha1_base64="t0YIAtusNim9537WktegaHytwZo=">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</latexit> <latexit sha1_base64="t0YIAtusNim9537WktegaHytwZo=">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</latexit> <latexit sha1_base64="t0YIAtusNim9537WktegaHytwZo=">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</latexit> <latexit sha1_base64="t0YIAtusNim9537WktegaHytwZo=">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</latexit> h(t 1) v a(t) v h(t) v (36 "⒏OF // // yv zv  h(T ) v xv  *OJUJBMJ[BUJPO  /PEF8JTF3FDVSSFOU6QEBUF  (SBQI(BUIFSJOH tanh X v2V (yv) tanh(zv) ! hG = <latexit sha1_base64="ARMGXVwsPnaLefmPlcb2NUBMhVE=">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</latexit> <latexit sha1_base64="ARMGXVwsPnaLefmPlcb2NUBMhVE=">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</latexit> <latexit sha1_base64="ARMGXVwsPnaLefmPlcb2NUBMhVE=">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</latexit> <latexit sha1_base64="ARMGXVwsPnaLefmPlcb2NUBMhVE=">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</latexit> "EBQUJWF8FJHIUJOH
 4PGU"UUFOUJPO .FTTBHF 6QEBUF 3FBEPVU 離散構造 −構造と知識− 離散構造の表現と構成法 離散構造を⼊⼒・制約とする機械学習 機械学習 −学習と知能− ⽊構造アンサンブル 深層学習/計算グラフ 確率的プログラミング LightGBM (Microsoft) See5/C5.0 & Cubist (RuleQuest) CART® MARS® TreeNet®
 Random Forests® (Salford Systems) CatBoost (Yandex) TFBoost (Google) TenscentBoost (Tenscent) Sherwood decision forests  TM <latexit sha1_base64="3lNT6fDKJcuWlwKB3nTYE+9PbNM=">AAAB+nicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sREi5gXJEmYns8mQeSwzs0JY8wm22tuJrT9j65c4SbbQ6IELh3Pu5VxOlHBmrO9/eoWV1bX1jeJmaWt7Z3evvH/QMirVhDaJ4kp3ImwoZ5I2LbOcdhJNsYg4bUfj65nffqDaMCUbdpLQUOChZDEj2DrpvtG/7ZcrftWfA/0lQU4qkKPeL3/1BoqkgkpLODamG/iJDTOsLSOcTku91NAEkzEe0q6jEgtqwmz+6hSdOGWAYqXdSIvm6s+LDAtjJiJymwLbkVn2ZuK/XiSWkm18GWZMJqmlkiyC45Qjq9CsBzRgmhLLJ45gopn7HZER1phY11bJlRIsV/CXtM6qgV8N7s4rtau8niIcwTGcQgAXUIMbqEMTCAzhCZ7hxXv0Xr03732xWvDym0P4Be/jG0AQlD4=</latexit> <latexit sha1_base64="3lNT6fDKJcuWlwKB3nTYE+9PbNM=">AAAB+nicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sREi5gXJEmYns8mQeSwzs0JY8wm22tuJrT9j65c4SbbQ6IELh3Pu5VxOlHBmrO9/eoWV1bX1jeJmaWt7Z3evvH/QMirVhDaJ4kp3ImwoZ5I2LbOcdhJNsYg4bUfj65nffqDaMCUbdpLQUOChZDEj2DrpvtG/7ZcrftWfA/0lQU4qkKPeL3/1BoqkgkpLODamG/iJDTOsLSOcTku91NAEkzEe0q6jEgtqwmz+6hSdOGWAYqXdSIvm6s+LDAtjJiJymwLbkVn2ZuK/XiSWkm18GWZMJqmlkiyC45Qjq9CsBzRgmhLLJ45gopn7HZER1phY11bJlRIsV/CXtM6qgV8N7s4rtau8niIcwTGcQgAXUIMbqEMTCAzhCZ7hxXv0Xr03732xWvDym0P4Be/jG0AQlD4=</latexit> <latexit sha1_base64="3lNT6fDKJcuWlwKB3nTYE+9PbNM=">AAAB+nicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sREi5gXJEmYns8mQeSwzs0JY8wm22tuJrT9j65c4SbbQ6IELh3Pu5VxOlHBmrO9/eoWV1bX1jeJmaWt7Z3evvH/QMirVhDaJ4kp3ImwoZ5I2LbOcdhJNsYg4bUfj65nffqDaMCUbdpLQUOChZDEj2DrpvtG/7ZcrftWfA/0lQU4qkKPeL3/1BoqkgkpLODamG/iJDTOsLSOcTku91NAEkzEe0q6jEgtqwmz+6hSdOGWAYqXdSIvm6s+LDAtjJiJymwLbkVn2ZuK/XiSWkm18GWZMJqmlkiyC45Qjq9CsBzRgmhLLJ45gopn7HZER1phY11bJlRIsV/CXtM6qgV8N7s4rtau8niIcwTGcQgAXUIMbqEMTCAzhCZ7hxXv0Xr03732xWvDym0P4Be/jG0AQlD4=</latexit> <latexit sha1_base64="3lNT6fDKJcuWlwKB3nTYE+9PbNM=">AAAB+nicbVC7SgNBFL0bXzG+opY2g0GwCrsiaBm0sREi5gXJEmYns8mQeSwzs0JY8wm22tuJrT9j65c4SbbQ6IELh3Pu5VxOlHBmrO9/eoWV1bX1jeJmaWt7Z3evvH/QMirVhDaJ4kp3ImwoZ5I2LbOcdhJNsYg4bUfj65nffqDaMCUbdpLQUOChZDEj2DrpvtG/7ZcrftWfA/0lQU4qkKPeL3/1BoqkgkpLODamG/iJDTOsLSOcTku91NAEkzEe0q6jEgtqwmz+6hSdOGWAYqXdSIvm6s+LDAtjJiJymwLbkVn2ZuK/XiSWkm18GWZMJqmlkiyC45Qjq9CsBzRgmhLLJ45gopn7HZER1phY11bJlRIsV/CXtM6qgV8N7s4rtau8niIcwTGcQgAXUIMbqEMTCAzhCZ7hxXv0Xr03732xWvDym0P4Be/jG0AQlD4=</latexit> FAB/HME (NEC) n0 <latexit sha1_base64="SMDvU+/yhJKBfKVBzE02+wp2S94=">AAAB+nicbVA9SwNBFHwXv2L8ilraLAbBKtyJoGXQxjKiiYHkCHubd8mS3b1jd08IMT/BVns7sfXP2PpL3CRXaOLAg2HmPeYxUSq4sb7/5RVWVtfWN4qbpa3tnd298v5B0ySZZthgiUh0K6IGBVfYsNwKbKUaqYwEPkTD66n/8Ija8ETd21GKoaR9xWPOqHXSner63XLFr/ozkGUS5KQCOerd8nenl7BMorJMUGPagZ/acEy15UzgpNTJDKaUDWkf244qKtGE49mrE3LilB6JE+1GWTJTf1+MqTRmJCO3KakdmEVvKv7rRXIh2caX4ZirNLOo2Dw4zgSxCZn2QHpcI7Ni5AhlmrvfCRtQTZl1bZVcKcFiBcukeVYN/Gpwe16pXeX1FOEIjuEUAriAGtxAHRrAoA/P8AKv3pP35r17H/PVgpffHMIfeJ8/O4iUOw==</latexit> <latexit sha1_base64="SMDvU+/yhJKBfKVBzE02+wp2S94=">AAAB+nicbVA9SwNBFHwXv2L8ilraLAbBKtyJoGXQxjKiiYHkCHubd8mS3b1jd08IMT/BVns7sfXP2PpL3CRXaOLAg2HmPeYxUSq4sb7/5RVWVtfWN4qbpa3tnd298v5B0ySZZthgiUh0K6IGBVfYsNwKbKUaqYwEPkTD66n/8Ija8ETd21GKoaR9xWPOqHXSner63XLFr/ozkGUS5KQCOerd8nenl7BMorJMUGPagZ/acEy15UzgpNTJDKaUDWkf244qKtGE49mrE3LilB6JE+1GWTJTf1+MqTRmJCO3KakdmEVvKv7rRXIh2caX4ZirNLOo2Dw4zgSxCZn2QHpcI7Ni5AhlmrvfCRtQTZl1bZVcKcFiBcukeVYN/Gpwe16pXeX1FOEIjuEUAriAGtxAHRrAoA/P8AKv3pP35r17H/PVgpffHMIfeJ8/O4iUOw==</latexit> <latexit sha1_base64="SMDvU+/yhJKBfKVBzE02+wp2S94=">AAAB+nicbVA9SwNBFHwXv2L8ilraLAbBKtyJoGXQxjKiiYHkCHubd8mS3b1jd08IMT/BVns7sfXP2PpL3CRXaOLAg2HmPeYxUSq4sb7/5RVWVtfWN4qbpa3tnd298v5B0ySZZthgiUh0K6IGBVfYsNwKbKUaqYwEPkTD66n/8Ija8ETd21GKoaR9xWPOqHXSner63XLFr/ozkGUS5KQCOerd8nenl7BMorJMUGPagZ/acEy15UzgpNTJDKaUDWkf244qKtGE49mrE3LilB6JE+1GWTJTf1+MqTRmJCO3KakdmEVvKv7rRXIh2caX4ZirNLOo2Dw4zgSxCZn2QHpcI7Ni5AhlmrvfCRtQTZl1bZVcKcFiBcukeVYN/Gpwe16pXeX1FOEIjuEUAriAGtxAHRrAoA/P8AKv3pP35r17H/PVgpffHMIfeJ8/O4iUOw==</latexit> <latexit sha1_base64="SMDvU+/yhJKBfKVBzE02+wp2S94=">AAAB+nicbVA9SwNBFHwXv2L8ilraLAbBKtyJoGXQxjKiiYHkCHubd8mS3b1jd08IMT/BVns7sfXP2PpL3CRXaOLAg2HmPeYxUSq4sb7/5RVWVtfWN4qbpa3tnd298v5B0ySZZthgiUh0K6IGBVfYsNwKbKUaqYwEPkTD66n/8Ija8ETd21GKoaR9xWPOqHXSner63XLFr/ozkGUS5KQCOerd8nenl7BMorJMUGPagZ/acEy15UzgpNTJDKaUDWkf244qKtGE49mrE3LilB6JE+1GWTJTf1+MqTRmJCO3KakdmEVvKv7rRXIh2caX4ZirNLOo2Dw4zgSxCZn2QHpcI7Ni5AhlmrvfCRtQTZl1bZVcKcFiBcukeVYN/Gpwe16pXeX1FOEIjuEUAriAGtxAHRrAoA/P8AKv3pP35r17H/PVgpffHMIfeJ8/O4iUOw==</latexit> `5 <latexit sha1_base64="QskAqT0/sBw5YFuiSWAeedquLV0=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKosegF48RzAOSJcxOepMxM7vLzKwQluAveNW7N/Hqt3j1S5wke9DEgoaiqptqKkgE18Z1v5zCyura+kZxs7S1vbO7V94/aOo4VQwbLBaxagdUo+ARNgw3AtuJQioDga1gdDP1W4+oNI+jezNO0Jd0EPGQM2qs1OyiEL2LXrniVt0ZyDLxclKBHPVe+bvbj1kqMTJMUK07npsYP6PKcCZwUuqmGhPKRnSAHUsjKlH72ezbCTmxSp+EsbITGTJTf19kVGo9loHdlNQM9aI3Ff/1ArmQbMIrP+NRkhqM2Dw4TAUxMZlWQfpcITNibAllitvfCRtSRZmxhZVsKd5iBcukeVb13Kp3d16pXef1FOEIjuEUPLiEGtxCHRrA4AGe4QVenSfnzXl3PuarBSe/OYQ/cD5/AI70lYk=</latexit> <latexit sha1_base64="QskAqT0/sBw5YFuiSWAeedquLV0=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKosegF48RzAOSJcxOepMxM7vLzKwQluAveNW7N/Hqt3j1S5wke9DEgoaiqptqKkgE18Z1v5zCyura+kZxs7S1vbO7V94/aOo4VQwbLBaxagdUo+ARNgw3AtuJQioDga1gdDP1W4+oNI+jezNO0Jd0EPGQM2qs1OyiEL2LXrniVt0ZyDLxclKBHPVe+bvbj1kqMTJMUK07npsYP6PKcCZwUuqmGhPKRnSAHUsjKlH72ezbCTmxSp+EsbITGTJTf19kVGo9loHdlNQM9aI3Ff/1ArmQbMIrP+NRkhqM2Dw4TAUxMZlWQfpcITNibAllitvfCRtSRZmxhZVsKd5iBcukeVb13Kp3d16pXef1FOEIjuEUPLiEGtxCHRrA4AGe4QVenSfnzXl3PuarBSe/OYQ/cD5/AI70lYk=</latexit> <latexit sha1_base64="QskAqT0/sBw5YFuiSWAeedquLV0=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKosegF48RzAOSJcxOepMxM7vLzKwQluAveNW7N/Hqt3j1S5wke9DEgoaiqptqKkgE18Z1v5zCyura+kZxs7S1vbO7V94/aOo4VQwbLBaxagdUo+ARNgw3AtuJQioDga1gdDP1W4+oNI+jezNO0Jd0EPGQM2qs1OyiEL2LXrniVt0ZyDLxclKBHPVe+bvbj1kqMTJMUK07npsYP6PKcCZwUuqmGhPKRnSAHUsjKlH72ezbCTmxSp+EsbITGTJTf19kVGo9loHdlNQM9aI3Ff/1ArmQbMIrP+NRkhqM2Dw4TAUxMZlWQfpcITNibAllitvfCRtSRZmxhZVsKd5iBcukeVb13Kp3d16pXef1FOEIjuEUPLiEGtxCHRrA4AGe4QVenSfnzXl3PuarBSe/OYQ/cD5/AI70lYk=</latexit> <latexit sha1_base64="QskAqT0/sBw5YFuiSWAeedquLV0=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKosegF48RzAOSJcxOepMxM7vLzKwQluAveNW7N/Hqt3j1S5wke9DEgoaiqptqKkgE18Z1v5zCyura+kZxs7S1vbO7V94/aOo4VQwbLBaxagdUo+ARNgw3AtuJQioDga1gdDP1W4+oNI+jezNO0Jd0EPGQM2qs1OyiEL2LXrniVt0ZyDLxclKBHPVe+bvbj1kqMTJMUK07npsYP6PKcCZwUuqmGhPKRnSAHUsjKlH72ezbCTmxSp+EsbITGTJTf19kVGo9loHdlNQM9aI3Ff/1ArmQbMIrP+NRkhqM2Dw4TAUxMZlWQfpcITNibAllitvfCRtSRZmxhZVsKd5iBcukeVb13Kp3d16pXef1FOEIjuEUPLiEGtxCHRrA4AGe4QVenSfnzXl3PuarBSe/OYQ/cD5/AI70lYk=</latexit> `6 <latexit sha1_base64="Q4tv+ZRiuwOORgtlcQaGfjaE4O0=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKqMegF48RzAOSJcxOepMxM7vLzKwQluAveNW7N/Hqt3j1S5wke9DEgoaiqptqKkgE18Z1v5zCyura+kZxs7S1vbO7V94/aOo4VQwbLBaxagdUo+ARNgw3AtuJQioDga1gdDP1W4+oNI+jezNO0Jd0EPGQM2qs1OyiEL2LXrniVt0ZyDLxclKBHPVe+bvbj1kqMTJMUK07npsYP6PKcCZwUuqmGhPKRnSAHUsjKlH72ezbCTmxSp+EsbITGTJTf19kVGo9loHdlNQM9aI3Ff/1ArmQbMIrP+NRkhqM2Dw4TAUxMZlWQfpcITNibAllitvfCRtSRZmxhZVsKd5iBcukeVb13Kp3d16pXef1FOEIjuEUPLiEGtxCHRrA4AGe4QVenSfnzXl3PuarBSe/OYQ/cD5/AJCIlYo=</latexit> <latexit sha1_base64="Q4tv+ZRiuwOORgtlcQaGfjaE4O0=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKqMegF48RzAOSJcxOepMxM7vLzKwQluAveNW7N/Hqt3j1S5wke9DEgoaiqptqKkgE18Z1v5zCyura+kZxs7S1vbO7V94/aOo4VQwbLBaxagdUo+ARNgw3AtuJQioDga1gdDP1W4+oNI+jezNO0Jd0EPGQM2qs1OyiEL2LXrniVt0ZyDLxclKBHPVe+bvbj1kqMTJMUK07npsYP6PKcCZwUuqmGhPKRnSAHUsjKlH72ezbCTmxSp+EsbITGTJTf19kVGo9loHdlNQM9aI3Ff/1ArmQbMIrP+NRkhqM2Dw4TAUxMZlWQfpcITNibAllitvfCRtSRZmxhZVsKd5iBcukeVb13Kp3d16pXef1FOEIjuEUPLiEGtxCHRrA4AGe4QVenSfnzXl3PuarBSe/OYQ/cD5/AJCIlYo=</latexit> <latexit sha1_base64="Q4tv+ZRiuwOORgtlcQaGfjaE4O0=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKqMegF48RzAOSJcxOepMxM7vLzKwQluAveNW7N/Hqt3j1S5wke9DEgoaiqptqKkgE18Z1v5zCyura+kZxs7S1vbO7V94/aOo4VQwbLBaxagdUo+ARNgw3AtuJQioDga1gdDP1W4+oNI+jezNO0Jd0EPGQM2qs1OyiEL2LXrniVt0ZyDLxclKBHPVe+bvbj1kqMTJMUK07npsYP6PKcCZwUuqmGhPKRnSAHUsjKlH72ezbCTmxSp+EsbITGTJTf19kVGo9loHdlNQM9aI3Ff/1ArmQbMIrP+NRkhqM2Dw4TAUxMZlWQfpcITNibAllitvfCRtSRZmxhZVsKd5iBcukeVb13Kp3d16pXef1FOEIjuEUPLiEGtxCHRrA4AGe4QVenSfnzXl3PuarBSe/OYQ/cD5/AJCIlYo=</latexit> <latexit sha1_base64="Q4tv+ZRiuwOORgtlcQaGfjaE4O0=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKqMegF48RzAOSJcxOepMxM7vLzKwQluAveNW7N/Hqt3j1S5wke9DEgoaiqptqKkgE18Z1v5zCyura+kZxs7S1vbO7V94/aOo4VQwbLBaxagdUo+ARNgw3AtuJQioDga1gdDP1W4+oNI+jezNO0Jd0EPGQM2qs1OyiEL2LXrniVt0ZyDLxclKBHPVe+bvbj1kqMTJMUK07npsYP6PKcCZwUuqmGhPKRnSAHUsjKlH72ezbCTmxSp+EsbITGTJTf19kVGo9loHdlNQM9aI3Ff/1ArmQbMIrP+NRkhqM2Dw4TAUxMZlWQfpcITNibAllitvfCRtSRZmxhZVsKd5iBcukeVb13Kp3d16pXef1FOEIjuEUPLiEGtxCHRrA4AGe4QVenSfnzXl3PuarBSe/OYQ/cD5/AJCIlYo=</latexit> n4 <latexit sha1_base64="bUaWPk2ZV8CUf2V+neJgjqjSYgo=">AAAB+nicbVDLSgMxFL2pr1pfVZdugkVwVWakoMuiG5cV7QPaoWTSTBuaZIYkI5Sxn+BW9+7ErT/j1i8xbWehrQcuHM65l3M5YSK4sZ73hQpr6xubW8Xt0s7u3v5B+fCoZeJUU9aksYh1JySGCa5Y03IrWCfRjMhQsHY4vpn57UemDY/Vg50kLJBkqHjEKbFOulf9Wr9c8areHHiV+DmpQI5Gv/zdG8Q0lUxZKogxXd9LbJARbTkVbFrqpYYlhI7JkHUdVUQyE2TzV6f4zCkDHMXajbJ4rv6+yIg0ZiJDtymJHZllbyb+64VyKdlGV0HGVZJapugiOEoFtjGe9YAHXDNqxcQRQjV3v2M6IppQ69oquVL85QpWSeui6ntV/65WqV/n9RThBE7hHHy4hDrcQgOaQGEIz/ACr+gJvaF39LFYLaD85hj+AH3+AEHYlD8=</latexit> <latexit sha1_base64="bUaWPk2ZV8CUf2V+neJgjqjSYgo=">AAAB+nicbVDLSgMxFL2pr1pfVZdugkVwVWakoMuiG5cV7QPaoWTSTBuaZIYkI5Sxn+BW9+7ErT/j1i8xbWehrQcuHM65l3M5YSK4sZ73hQpr6xubW8Xt0s7u3v5B+fCoZeJUU9aksYh1JySGCa5Y03IrWCfRjMhQsHY4vpn57UemDY/Vg50kLJBkqHjEKbFOulf9Wr9c8areHHiV+DmpQI5Gv/zdG8Q0lUxZKogxXd9LbJARbTkVbFrqpYYlhI7JkHUdVUQyE2TzV6f4zCkDHMXajbJ4rv6+yIg0ZiJDtymJHZllbyb+64VyKdlGV0HGVZJapugiOEoFtjGe9YAHXDNqxcQRQjV3v2M6IppQ69oquVL85QpWSeui6ntV/65WqV/n9RThBE7hHHy4hDrcQgOaQGEIz/ACr+gJvaF39LFYLaD85hj+AH3+AEHYlD8=</latexit> <latexit sha1_base64="bUaWPk2ZV8CUf2V+neJgjqjSYgo=">AAAB+nicbVDLSgMxFL2pr1pfVZdugkVwVWakoMuiG5cV7QPaoWTSTBuaZIYkI5Sxn+BW9+7ErT/j1i8xbWehrQcuHM65l3M5YSK4sZ73hQpr6xubW8Xt0s7u3v5B+fCoZeJUU9aksYh1JySGCa5Y03IrWCfRjMhQsHY4vpn57UemDY/Vg50kLJBkqHjEKbFOulf9Wr9c8areHHiV+DmpQI5Gv/zdG8Q0lUxZKogxXd9LbJARbTkVbFrqpYYlhI7JkHUdVUQyE2TzV6f4zCkDHMXajbJ4rv6+yIg0ZiJDtymJHZllbyb+64VyKdlGV0HGVZJapugiOEoFtjGe9YAHXDNqxcQRQjV3v2M6IppQ69oquVL85QpWSeui6ntV/65WqV/n9RThBE7hHHy4hDrcQgOaQGEIz/ACr+gJvaF39LFYLaD85hj+AH3+AEHYlD8=</latexit> <latexit sha1_base64="bUaWPk2ZV8CUf2V+neJgjqjSYgo=">AAAB+nicbVDLSgMxFL2pr1pfVZdugkVwVWakoMuiG5cV7QPaoWTSTBuaZIYkI5Sxn+BW9+7ErT/j1i8xbWehrQcuHM65l3M5YSK4sZ73hQpr6xubW8Xt0s7u3v5B+fCoZeJUU9aksYh1JySGCa5Y03IrWCfRjMhQsHY4vpn57UemDY/Vg50kLJBkqHjEKbFOulf9Wr9c8areHHiV+DmpQI5Gv/zdG8Q0lUxZKogxXd9LbJARbTkVbFrqpYYlhI7JkHUdVUQyE2TzV6f4zCkDHMXajbJ4rv6+yIg0ZiJDtymJHZllbyb+64VyKdlGV0HGVZJapugiOEoFtjGe9YAHXDNqxcQRQjV3v2M6IppQ69oquVL85QpWSeui6ntV/65WqV/n9RThBE7hHHy4hDrcQgOaQGEIz/ACr+gJvaF39LFYLaD85hj+AH3+AEHYlD8=</latexit> n1 <latexit sha1_base64="mqAc8GlBhT6sx/DyDGgioJj1ayE=">AAAB+nicbVA9SwNBFHwXv2L8ilraLAbBKtyJoGXQxjKiiYHkCHubvWTJ7t6x+04IMT/BVns7sfXP2PpL3CRXaOLAg2HmPeYxUSqFRd//8gorq2vrG8XN0tb2zu5eef+gaZPMMN5giUxMK6KWS6F5AwVK3koNpyqS/CEaXk/9h0durEj0PY5SHira1yIWjKKT7nQ36JYrftWfgSyTICcVyFHvlr87vYRlimtkklrbDvwUwzE1KJjkk1InszylbEj7vO2oporbcDx7dUJOnNIjcWLcaCQz9ffFmCprRypym4riwC56U/FfL1ILyRhfhmOh0wy5ZvPgOJMEEzLtgfSE4QzlyBHKjHC/EzaghjJ0bZVcKcFiBcukeVYN/Gpwe16pXeX1FOEIjuEUAriAGtxAHRrAoA/P8AKv3pP35r17H/PVgpffHMIfeJ8/PRyUPA==</latexit> <latexit sha1_base64="mqAc8GlBhT6sx/DyDGgioJj1ayE=">AAAB+nicbVA9SwNBFHwXv2L8ilraLAbBKtyJoGXQxjKiiYHkCHubvWTJ7t6x+04IMT/BVns7sfXP2PpL3CRXaOLAg2HmPeYxUSqFRd//8gorq2vrG8XN0tb2zu5eef+gaZPMMN5giUxMK6KWS6F5AwVK3koNpyqS/CEaXk/9h0durEj0PY5SHira1yIWjKKT7nQ36JYrftWfgSyTICcVyFHvlr87vYRlimtkklrbDvwUwzE1KJjkk1InszylbEj7vO2oporbcDx7dUJOnNIjcWLcaCQz9ffFmCprRypym4riwC56U/FfL1ILyRhfhmOh0wy5ZvPgOJMEEzLtgfSE4QzlyBHKjHC/EzaghjJ0bZVcKcFiBcukeVYN/Gpwe16pXeX1FOEIjuEUAriAGtxAHRrAoA/P8AKv3pP35r17H/PVgpffHMIfeJ8/PRyUPA==</latexit> <latexit sha1_base64="mqAc8GlBhT6sx/DyDGgioJj1ayE=">AAAB+nicbVA9SwNBFHwXv2L8ilraLAbBKtyJoGXQxjKiiYHkCHubvWTJ7t6x+04IMT/BVns7sfXP2PpL3CRXaOLAg2HmPeYxUSqFRd//8gorq2vrG8XN0tb2zu5eef+gaZPMMN5giUxMK6KWS6F5AwVK3koNpyqS/CEaXk/9h0durEj0PY5SHira1yIWjKKT7nQ36JYrftWfgSyTICcVyFHvlr87vYRlimtkklrbDvwUwzE1KJjkk1InszylbEj7vO2oporbcDx7dUJOnNIjcWLcaCQz9ffFmCprRypym4riwC56U/FfL1ILyRhfhmOh0wy5ZvPgOJMEEzLtgfSE4QzlyBHKjHC/EzaghjJ0bZVcKcFiBcukeVYN/Gpwe16pXeX1FOEIjuEUAriAGtxAHRrAoA/P8AKv3pP35r17H/PVgpffHMIfeJ8/PRyUPA==</latexit> <latexit sha1_base64="mqAc8GlBhT6sx/DyDGgioJj1ayE=">AAAB+nicbVA9SwNBFHwXv2L8ilraLAbBKtyJoGXQxjKiiYHkCHubvWTJ7t6x+04IMT/BVns7sfXP2PpL3CRXaOLAg2HmPeYxUSqFRd//8gorq2vrG8XN0tb2zu5eef+gaZPMMN5giUxMK6KWS6F5AwVK3koNpyqS/CEaXk/9h0durEj0PY5SHira1yIWjKKT7nQ36JYrftWfgSyTICcVyFHvlr87vYRlimtkklrbDvwUwzE1KJjkk1InszylbEj7vO2oporbcDx7dUJOnNIjcWLcaCQz9ffFmCprRypym4riwC56U/FfL1ILyRhfhmOh0wy5ZvPgOJMEEzLtgfSE4QzlyBHKjHC/EzaghjJ0bZVcKcFiBcukeVYN/Gpwe16pXeX1FOEIjuEUAriAGtxAHRrAoA/P8AKv3pP35r17H/PVgpffHMIfeJ8/PRyUPA==</latexit> `1 <latexit sha1_base64="08fK0P4FbLL8ccSSHDRGsI2CLU4=">AAAB/XicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj04jGCeUCyhNlJJxkzM7vMzAphCf6CV717E69+i1e/xEmyB00saCiquqmmokRwY33/y1tZXVvf2CxsFbd3dvf2SweHDROnmmGdxSLWrYgaFFxh3XIrsJVopDIS2IxGN1O/+Yja8Fjd23GCoaQDxfucUeukRgeF6AbdUtmv+DOQZRLkpAw5at3Sd6cXs1SiskxQY9qBn9gwo9pyJnBS7KQGE8pGdIBtRxWVaMJs9u2EnDqlR/qxdqMsmam/LzIqjRnLyG1Kaodm0ZuK/3qRXEi2/asw4ypJLSo2D+6ngtiYTKsgPa6RWTF2hDLN3e+EDammzLrCiq6UYLGCZdI4rwR+Jbi7KFev83oKcAwncAYBXEIVbqEGdWDwAM/wAq/ek/fmvXsf89UVL785gj/wPn8AiKSVhQ==</latexit> <latexit sha1_base64="08fK0P4FbLL8ccSSHDRGsI2CLU4=">AAAB/XicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj04jGCeUCyhNlJJxkzM7vMzAphCf6CV717E69+i1e/xEmyB00saCiquqmmokRwY33/y1tZXVvf2CxsFbd3dvf2SweHDROnmmGdxSLWrYgaFFxh3XIrsJVopDIS2IxGN1O/+Yja8Fjd23GCoaQDxfucUeukRgeF6AbdUtmv+DOQZRLkpAw5at3Sd6cXs1SiskxQY9qBn9gwo9pyJnBS7KQGE8pGdIBtRxWVaMJs9u2EnDqlR/qxdqMsmam/LzIqjRnLyG1Kaodm0ZuK/3qRXEi2/asw4ypJLSo2D+6ngtiYTKsgPa6RWTF2hDLN3e+EDammzLrCiq6UYLGCZdI4rwR+Jbi7KFev83oKcAwncAYBXEIVbqEGdWDwAM/wAq/ek/fmvXsf89UVL785gj/wPn8AiKSVhQ==</latexit> <latexit sha1_base64="08fK0P4FbLL8ccSSHDRGsI2CLU4=">AAAB/XicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj04jGCeUCyhNlJJxkzM7vMzAphCf6CV717E69+i1e/xEmyB00saCiquqmmokRwY33/y1tZXVvf2CxsFbd3dvf2SweHDROnmmGdxSLWrYgaFFxh3XIrsJVopDIS2IxGN1O/+Yja8Fjd23GCoaQDxfucUeukRgeF6AbdUtmv+DOQZRLkpAw5at3Sd6cXs1SiskxQY9qBn9gwo9pyJnBS7KQGE8pGdIBtRxWVaMJs9u2EnDqlR/qxdqMsmam/LzIqjRnLyG1Kaodm0ZuK/3qRXEi2/asw4ypJLSo2D+6ngtiYTKsgPa6RWTF2hDLN3e+EDammzLrCiq6UYLGCZdI4rwR+Jbi7KFev83oKcAwncAYBXEIVbqEGdWDwAM/wAq/ek/fmvXsf89UVL785gj/wPn8AiKSVhQ==</latexit> <latexit sha1_base64="08fK0P4FbLL8ccSSHDRGsI2CLU4=">AAAB/XicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj04jGCeUCyhNlJJxkzM7vMzAphCf6CV717E69+i1e/xEmyB00saCiquqmmokRwY33/y1tZXVvf2CxsFbd3dvf2SweHDROnmmGdxSLWrYgaFFxh3XIrsJVopDIS2IxGN1O/+Yja8Fjd23GCoaQDxfucUeukRgeF6AbdUtmv+DOQZRLkpAw5at3Sd6cXs1SiskxQY9qBn9gwo9pyJnBS7KQGE8pGdIBtRxWVaMJs9u2EnDqlR/qxdqMsmam/LzIqjRnLyG1Kaodm0ZuK/3qRXEi2/asw4ypJLSo2D+6ngtiYTKsgPa6RWTF2hDLN3e+EDammzLrCiq6UYLGCZdI4rwR+Jbi7KFev83oKcAwncAYBXEIVbqEGdWDwAM/wAq/ek/fmvXsf89UVL785gj/wPn8AiKSVhQ==</latexit> `2 <latexit sha1_base64="xx+vRlfG+/KUMdANsZIc7AhzLqw=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKewGQY9BLx4jmAckS5id9CZjZmeXmVkhLMFf8Kp3b+LVb/HqlzhJ9qCJBQ1FVTfVVJAIro3rfjmFtfWNza3idmlnd2//oHx41NJxqhg2WSxi1QmoRsElNg03AjuJQhoFAtvB+Gbmtx9RaR7LezNJ0I/oUPKQM2qs1OqhEP1av1xxq+4cZJV4OalAjka//N0bxCyNUBomqNZdz02Mn1FlOBM4LfVSjQllYzrErqWSRqj9bP7tlJxZZUDCWNmRhszV3xcZjbSeRIHdjKgZ6WVvJv7rBdFSsgmv/IzLJDUo2SI4TAUxMZlVQQZcITNiYgllitvfCRtRRZmxhZVsKd5yBaukVat6btW7u6jUr/N6inACp3AOHlxCHW6hAU1g8ADP8AKvzpPz5rw7H4vVgpPfHMMfOJ8/ijiVhg==</latexit> <latexit sha1_base64="xx+vRlfG+/KUMdANsZIc7AhzLqw=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKewGQY9BLx4jmAckS5id9CZjZmeXmVkhLMFf8Kp3b+LVb/HqlzhJ9qCJBQ1FVTfVVJAIro3rfjmFtfWNza3idmlnd2//oHx41NJxqhg2WSxi1QmoRsElNg03AjuJQhoFAtvB+Gbmtx9RaR7LezNJ0I/oUPKQM2qs1OqhEP1av1xxq+4cZJV4OalAjka//N0bxCyNUBomqNZdz02Mn1FlOBM4LfVSjQllYzrErqWSRqj9bP7tlJxZZUDCWNmRhszV3xcZjbSeRIHdjKgZ6WVvJv7rBdFSsgmv/IzLJDUo2SI4TAUxMZlVQQZcITNiYgllitvfCRtRRZmxhZVsKd5yBaukVat6btW7u6jUr/N6inACp3AOHlxCHW6hAU1g8ADP8AKvzpPz5rw7H4vVgpPfHMMfOJ8/ijiVhg==</latexit> <latexit sha1_base64="xx+vRlfG+/KUMdANsZIc7AhzLqw=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKewGQY9BLx4jmAckS5id9CZjZmeXmVkhLMFf8Kp3b+LVb/HqlzhJ9qCJBQ1FVTfVVJAIro3rfjmFtfWNza3idmlnd2//oHx41NJxqhg2WSxi1QmoRsElNg03AjuJQhoFAtvB+Gbmtx9RaR7LezNJ0I/oUPKQM2qs1OqhEP1av1xxq+4cZJV4OalAjka//N0bxCyNUBomqNZdz02Mn1FlOBM4LfVSjQllYzrErqWSRqj9bP7tlJxZZUDCWNmRhszV3xcZjbSeRIHdjKgZ6WVvJv7rBdFSsgmv/IzLJDUo2SI4TAUxMZlVQQZcITNiYgllitvfCRtRRZmxhZVsKd5yBaukVat6btW7u6jUr/N6inACp3AOHlxCHW6hAU1g8ADP8AKvzpPz5rw7H4vVgpPfHMMfOJ8/ijiVhg==</latexit> <latexit sha1_base64="xx+vRlfG+/KUMdANsZIc7AhzLqw=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKewGQY9BLx4jmAckS5id9CZjZmeXmVkhLMFf8Kp3b+LVb/HqlzhJ9qCJBQ1FVTfVVJAIro3rfjmFtfWNza3idmlnd2//oHx41NJxqhg2WSxi1QmoRsElNg03AjuJQhoFAtvB+Gbmtx9RaR7LezNJ0I/oUPKQM2qs1OqhEP1av1xxq+4cZJV4OalAjka//N0bxCyNUBomqNZdz02Mn1FlOBM4LfVSjQllYzrErqWSRqj9bP7tlJxZZUDCWNmRhszV3xcZjbSeRIHdjKgZ6WVvJv7rBdFSsgmv/IzLJDUo2SI4TAUxMZlVQQZcITNiYgllitvfCRtRRZmxhZVsKd5yBaukVat6btW7u6jUr/N6inACp3AOHlxCHW6hAU1g8ADP8AKvzpPz5rw7H4vVgpPfHMMfOJ8/ijiVhg==</latexit> n2 <latexit sha1_base64="LVlZqkyUUwwivewzBxJfdeyse2A=">AAAB+nicbVDLSgMxFL2pr1pfVZdugkVwVWaKoMuiG5cV7QPaoWTSTBuaZIYkI5Sxn+BW9+7ErT/j1i8xbWehrQcuHM65l3M5YSK4sZ73hQpr6xubW8Xt0s7u3v5B+fCoZeJUU9aksYh1JySGCa5Y03IrWCfRjMhQsHY4vpn57UemDY/Vg50kLJBkqHjEKbFOulf9Wr9c8areHHiV+DmpQI5Gv/zdG8Q0lUxZKogxXd9LbJARbTkVbFrqpYYlhI7JkHUdVUQyE2TzV6f4zCkDHMXajbJ4rv6+yIg0ZiJDtymJHZllbyb+64VyKdlGV0HGVZJapugiOEoFtjGe9YAHXDNqxcQRQjV3v2M6IppQ69oquVL85QpWSatW9b2qf3dRqV/n9RThBE7hHHy4hDrcQgOaQGEIz/ACr+gJvaF39LFYLaD85hj+AH3+AD6wlD0=</latexit> <latexit sha1_base64="LVlZqkyUUwwivewzBxJfdeyse2A=">AAAB+nicbVDLSgMxFL2pr1pfVZdugkVwVWaKoMuiG5cV7QPaoWTSTBuaZIYkI5Sxn+BW9+7ErT/j1i8xbWehrQcuHM65l3M5YSK4sZ73hQpr6xubW8Xt0s7u3v5B+fCoZeJUU9aksYh1JySGCa5Y03IrWCfRjMhQsHY4vpn57UemDY/Vg50kLJBkqHjEKbFOulf9Wr9c8areHHiV+DmpQI5Gv/zdG8Q0lUxZKogxXd9LbJARbTkVbFrqpYYlhI7JkHUdVUQyE2TzV6f4zCkDHMXajbJ4rv6+yIg0ZiJDtymJHZllbyb+64VyKdlGV0HGVZJapugiOEoFtjGe9YAHXDNqxcQRQjV3v2M6IppQ69oquVL85QpWSatW9b2qf3dRqV/n9RThBE7hHHy4hDrcQgOaQGEIz/ACr+gJvaF39LFYLaD85hj+AH3+AD6wlD0=</latexit> <latexit sha1_base64="LVlZqkyUUwwivewzBxJfdeyse2A=">AAAB+nicbVDLSgMxFL2pr1pfVZdugkVwVWaKoMuiG5cV7QPaoWTSTBuaZIYkI5Sxn+BW9+7ErT/j1i8xbWehrQcuHM65l3M5YSK4sZ73hQpr6xubW8Xt0s7u3v5B+fCoZeJUU9aksYh1JySGCa5Y03IrWCfRjMhQsHY4vpn57UemDY/Vg50kLJBkqHjEKbFOulf9Wr9c8areHHiV+DmpQI5Gv/zdG8Q0lUxZKogxXd9LbJARbTkVbFrqpYYlhI7JkHUdVUQyE2TzV6f4zCkDHMXajbJ4rv6+yIg0ZiJDtymJHZllbyb+64VyKdlGV0HGVZJapugiOEoFtjGe9YAHXDNqxcQRQjV3v2M6IppQ69oquVL85QpWSatW9b2qf3dRqV/n9RThBE7hHHy4hDrcQgOaQGEIz/ACr+gJvaF39LFYLaD85hj+AH3+AD6wlD0=</latexit> <latexit sha1_base64="LVlZqkyUUwwivewzBxJfdeyse2A=">AAAB+nicbVDLSgMxFL2pr1pfVZdugkVwVWaKoMuiG5cV7QPaoWTSTBuaZIYkI5Sxn+BW9+7ErT/j1i8xbWehrQcuHM65l3M5YSK4sZ73hQpr6xubW8Xt0s7u3v5B+fCoZeJUU9aksYh1JySGCa5Y03IrWCfRjMhQsHY4vpn57UemDY/Vg50kLJBkqHjEKbFOulf9Wr9c8areHHiV+DmpQI5Gv/zdG8Q0lUxZKogxXd9LbJARbTkVbFrqpYYlhI7JkHUdVUQyE2TzV6f4zCkDHMXajbJ4rv6+yIg0ZiJDtymJHZllbyb+64VyKdlGV0HGVZJapugiOEoFtjGe9YAHXDNqxcQRQjV3v2M6IppQ69oquVL85QpWSatW9b2qf3dRqV/n9RThBE7hHHy4hDrcQgOaQGEIz/ACr+gJvaF39LFYLaD85hj+AH3+AD6wlD0=</latexit> `3 <latexit sha1_base64="1fiJpXzKJyzZjXax2Hf9Utae4IA=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKeyqoMegF48RzAOSJcxOepMxM7vLzKwQluAveNW7N/Hqt3j1S5wke9DEgoaiqptqKkgE18Z1v5zCyura+kZxs7S1vbO7V94/aOo4VQwbLBaxagdUo+ARNgw3AtuJQioDga1gdDP1W4+oNI+jezNO0Jd0EPGQM2qs1OyiEL3zXrniVt0ZyDLxclKBHPVe+bvbj1kqMTJMUK07npsYP6PKcCZwUuqmGhPKRnSAHUsjKlH72ezbCTmxSp+EsbITGTJTf19kVGo9loHdlNQM9aI3Ff/1ArmQbMIrP+NRkhqM2Dw4TAUxMZlWQfpcITNibAllitvfCRtSRZmxhZVsKd5iBcukeVb13Kp3d1GpXef1FOEIjuEUPLiEGtxCHRrA4AGe4QVenSfnzXl3PuarBSe/OYQ/cD5/AIvMlYc=</latexit> <latexit sha1_base64="1fiJpXzKJyzZjXax2Hf9Utae4IA=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKeyqoMegF48RzAOSJcxOepMxM7vLzKwQluAveNW7N/Hqt3j1S5wke9DEgoaiqptqKkgE18Z1v5zCyura+kZxs7S1vbO7V94/aOo4VQwbLBaxagdUo+ARNgw3AtuJQioDga1gdDP1W4+oNI+jezNO0Jd0EPGQM2qs1OyiEL3zXrniVt0ZyDLxclKBHPVe+bvbj1kqMTJMUK07npsYP6PKcCZwUuqmGhPKRnSAHUsjKlH72ezbCTmxSp+EsbITGTJTf19kVGo9loHdlNQM9aI3Ff/1ArmQbMIrP+NRkhqM2Dw4TAUxMZlWQfpcITNibAllitvfCRtSRZmxhZVsKd5iBcukeVb13Kp3d1GpXef1FOEIjuEUPLiEGtxCHRrA4AGe4QVenSfnzXl3PuarBSe/OYQ/cD5/AIvMlYc=</latexit> <latexit sha1_base64="1fiJpXzKJyzZjXax2Hf9Utae4IA=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKeyqoMegF48RzAOSJcxOepMxM7vLzKwQluAveNW7N/Hqt3j1S5wke9DEgoaiqptqKkgE18Z1v5zCyura+kZxs7S1vbO7V94/aOo4VQwbLBaxagdUo+ARNgw3AtuJQioDga1gdDP1W4+oNI+jezNO0Jd0EPGQM2qs1OyiEL3zXrniVt0ZyDLxclKBHPVe+bvbj1kqMTJMUK07npsYP6PKcCZwUuqmGhPKRnSAHUsjKlH72ezbCTmxSp+EsbITGTJTf19kVGo9loHdlNQM9aI3Ff/1ArmQbMIrP+NRkhqM2Dw4TAUxMZlWQfpcITNibAllitvfCRtSRZmxhZVsKd5iBcukeVb13Kp3d1GpXef1FOEIjuEUPLiEGtxCHRrA4AGe4QVenSfnzXl3PuarBSe/OYQ/cD5/AIvMlYc=</latexit> <latexit sha1_base64="1fiJpXzKJyzZjXax2Hf9Utae4IA=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKeyqoMegF48RzAOSJcxOepMxM7vLzKwQluAveNW7N/Hqt3j1S5wke9DEgoaiqptqKkgE18Z1v5zCyura+kZxs7S1vbO7V94/aOo4VQwbLBaxagdUo+ARNgw3AtuJQioDga1gdDP1W4+oNI+jezNO0Jd0EPGQM2qs1OyiEL3zXrniVt0ZyDLxclKBHPVe+bvbj1kqMTJMUK07npsYP6PKcCZwUuqmGhPKRnSAHUsjKlH72ezbCTmxSp+EsbITGTJTf19kVGo9loHdlNQM9aI3Ff/1ArmQbMIrP+NRkhqM2Dw4TAUxMZlWQfpcITNibAllitvfCRtSRZmxhZVsKd5iBcukeVb13Kp3d1GpXef1FOEIjuEUPLiEGtxCHRrA4AGe4QVenSfnzXl3PuarBSe/OYQ/cD5/AIvMlYc=</latexit> `4 <latexit sha1_base64="wwECV7GFS15ao7B8GVdRIhs9WFk=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKexKQI9BLx4jmAckS5id9CZjZmeXmVkhLMFf8Kp3b+LVb/HqlzhJ9qCJBQ1FVTfVVJAIro3rfjmFtfWNza3idmlnd2//oHx41NJxqhg2WSxi1QmoRsElNg03AjuJQhoFAtvB+Gbmtx9RaR7LezNJ0I/oUPKQM2qs1OqhEP1av1xxq+4cZJV4OalAjka//N0bxCyNUBomqNZdz02Mn1FlOBM4LfVSjQllYzrErqWSRqj9bP7tlJxZZUDCWNmRhszV3xcZjbSeRIHdjKgZ6WVvJv7rBdFSsgmv/IzLJDUo2SI4TAUxMZlVQQZcITNiYgllitvfCRtRRZmxhZVsKd5yBaukdVH13Kp3V6vUr/N6inACp3AOHlxCHW6hAU1g8ADP8AKvzpPz5rw7H4vVgpPfHMMfOJ8/jWCViA==</latexit> <latexit sha1_base64="wwECV7GFS15ao7B8GVdRIhs9WFk=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKexKQI9BLx4jmAckS5id9CZjZmeXmVkhLMFf8Kp3b+LVb/HqlzhJ9qCJBQ1FVTfVVJAIro3rfjmFtfWNza3idmlnd2//oHx41NJxqhg2WSxi1QmoRsElNg03AjuJQhoFAtvB+Gbmtx9RaR7LezNJ0I/oUPKQM2qs1OqhEP1av1xxq+4cZJV4OalAjka//N0bxCyNUBomqNZdz02Mn1FlOBM4LfVSjQllYzrErqWSRqj9bP7tlJxZZUDCWNmRhszV3xcZjbSeRIHdjKgZ6WVvJv7rBdFSsgmv/IzLJDUo2SI4TAUxMZlVQQZcITNiYgllitvfCRtRRZmxhZVsKd5yBaukdVH13Kp3V6vUr/N6inACp3AOHlxCHW6hAU1g8ADP8AKvzpPz5rw7H4vVgpPfHMMfOJ8/jWCViA==</latexit> <latexit sha1_base64="wwECV7GFS15ao7B8GVdRIhs9WFk=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKexKQI9BLx4jmAckS5id9CZjZmeXmVkhLMFf8Kp3b+LVb/HqlzhJ9qCJBQ1FVTfVVJAIro3rfjmFtfWNza3idmlnd2//oHx41NJxqhg2WSxi1QmoRsElNg03AjuJQhoFAtvB+Gbmtx9RaR7LezNJ0I/oUPKQM2qs1OqhEP1av1xxq+4cZJV4OalAjka//N0bxCyNUBomqNZdz02Mn1FlOBM4LfVSjQllYzrErqWSRqj9bP7tlJxZZUDCWNmRhszV3xcZjbSeRIHdjKgZ6WVvJv7rBdFSsgmv/IzLJDUo2SI4TAUxMZlVQQZcITNiYgllitvfCRtRRZmxhZVsKd5yBaukdVH13Kp3V6vUr/N6inACp3AOHlxCHW6hAU1g8ADP8AKvzpPz5rw7H4vVgpPfHMMfOJ8/jWCViA==</latexit> <latexit sha1_base64="wwECV7GFS15ao7B8GVdRIhs9WFk=">AAAB/XicbVDLSgNBEOyNrxhfUY9eBoPgKexKQI9BLx4jmAckS5id9CZjZmeXmVkhLMFf8Kp3b+LVb/HqlzhJ9qCJBQ1FVTfVVJAIro3rfjmFtfWNza3idmlnd2//oHx41NJxqhg2WSxi1QmoRsElNg03AjuJQhoFAtvB+Gbmtx9RaR7LezNJ0I/oUPKQM2qs1OqhEP1av1xxq+4cZJV4OalAjka//N0bxCyNUBomqNZdz02Mn1FlOBM4LfVSjQllYzrErqWSRqj9bP7tlJxZZUDCWNmRhszV3xcZjbSeRIHdjKgZ6WVvJv7rBdFSsgmv/IzLJDUo2SI4TAUxMZlVQQZcITNiYgllitvfCRtRRZmxhZVsKd5yBaukdVH13Kp3V6vUr/N6inACp3AOHlxCHW6hAU1g8ADP8AKvzpPz5rw7H4vVgpPfHMMfOJ8/jWCViA==</latexit> n3 <latexit sha1_base64="70h+QPp6c8pbvwZHIxSV9o2SlGE=">AAAB+nicbVC7SgNBFL0bXzG+opY2g0GwCrsqaBm0sYxoHpAsYXYymwyZxzIzK4Q1n2CrvZ3Y+jO2fomTZAtNPHDhcM69nMuJEs6M9f0vr7Cyura+UdwsbW3v7O6V9w+aRqWa0AZRXOl2hA3lTNKGZZbTdqIpFhGnrWh0M/Vbj1QbpuSDHSc0FHggWcwItk66l73zXrniV/0Z0DIJclKBHPVe+bvbVyQVVFrCsTGdwE9smGFtGeF0UuqmhiaYjPCAdhyVWFATZrNXJ+jEKX0UK+1GWjRTf19kWBgzFpHbFNgOzaI3Ff/1IrGQbOOrMGMySS2VZB4cpxxZhaY9oD7TlFg+dgQTzdzviAyxxsS6tkqulGCxgmXSPKsGfjW4u6jUrvN6inAEx3AKAVxCDW6hDg0gMIBneIFX78l78969j/lqwctvDuEPvM8fQESUPg==</latexit> <latexit sha1_base64="70h+QPp6c8pbvwZHIxSV9o2SlGE=">AAAB+nicbVC7SgNBFL0bXzG+opY2g0GwCrsqaBm0sYxoHpAsYXYymwyZxzIzK4Q1n2CrvZ3Y+jO2fomTZAtNPHDhcM69nMuJEs6M9f0vr7Cyura+UdwsbW3v7O6V9w+aRqWa0AZRXOl2hA3lTNKGZZbTdqIpFhGnrWh0M/Vbj1QbpuSDHSc0FHggWcwItk66l73zXrniV/0Z0DIJclKBHPVe+bvbVyQVVFrCsTGdwE9smGFtGeF0UuqmhiaYjPCAdhyVWFATZrNXJ+jEKX0UK+1GWjRTf19kWBgzFpHbFNgOzaI3Ff/1IrGQbOOrMGMySS2VZB4cpxxZhaY9oD7TlFg+dgQTzdzviAyxxsS6tkqulGCxgmXSPKsGfjW4u6jUrvN6inAEx3AKAVxCDW6hDg0gMIBneIFX78l78969j/lqwctvDuEPvM8fQESUPg==</latexit> <latexit sha1_base64="70h+QPp6c8pbvwZHIxSV9o2SlGE=">AAAB+nicbVC7SgNBFL0bXzG+opY2g0GwCrsqaBm0sYxoHpAsYXYymwyZxzIzK4Q1n2CrvZ3Y+jO2fomTZAtNPHDhcM69nMuJEs6M9f0vr7Cyura+UdwsbW3v7O6V9w+aRqWa0AZRXOl2hA3lTNKGZZbTdqIpFhGnrWh0M/Vbj1QbpuSDHSc0FHggWcwItk66l73zXrniV/0Z0DIJclKBHPVe+bvbVyQVVFrCsTGdwE9smGFtGeF0UuqmhiaYjPCAdhyVWFATZrNXJ+jEKX0UK+1GWjRTf19kWBgzFpHbFNgOzaI3Ff/1IrGQbOOrMGMySS2VZB4cpxxZhaY9oD7TlFg+dgQTzdzviAyxxsS6tkqulGCxgmXSPKsGfjW4u6jUrvN6inAEx3AKAVxCDW6hDg0gMIBneIFX78l78969j/lqwctvDuEPvM8fQESUPg==</latexit> <latexit sha1_base64="70h+QPp6c8pbvwZHIxSV9o2SlGE=">AAAB+nicbVC7SgNBFL0bXzG+opY2g0GwCrsqaBm0sYxoHpAsYXYymwyZxzIzK4Q1n2CrvZ3Y+jO2fomTZAtNPHDhcM69nMuJEs6M9f0vr7Cyura+UdwsbW3v7O6V9w+aRqWa0AZRXOl2hA3lTNKGZZbTdqIpFhGnrWh0M/Vbj1QbpuSDHSc0FHggWcwItk66l73zXrniV/0Z0DIJclKBHPVe+bvbVyQVVFrCsTGdwE9smGFtGeF0UuqmhiaYjPCAdhyVWFATZrNXJ+jEKX0UK+1GWjRTf19kWBgzFpHbFNgOzaI3Ff/1IrGQbOOrMGMySS2VZB4cpxxZhaY9oD7TlFg+dgQTzdzviAyxxsS6tkqulGCxgmXSPKsGfjW4u6jUrvN6inAEx3AKAVxCDW6hDg0gMIBneIFX78l78969j/lqwctvDuEPvM8fQESUPg==</latexit> x1 <latexit sha1_base64="sGJ7Rlh7M0CzOKNI4jm2qKakYVA=">AAAB+nicbVDLSgMxFL1TX7W+qi7dBIvgqkxE0GXRjcuK9gHtUDJppg1NMkOSEcvYT3Cre3fi1p9x65eYtrPQ1gMXDufcy7mcMBHcWN//8gorq2vrG8XN0tb2zu5eef+gaeJUU9agsYh1OySGCa5Yw3IrWDvRjMhQsFY4up76rQemDY/VvR0nLJBkoHjEKbFOunvs4V654lf9GdAywTmpQI56r/zd7cc0lUxZKogxHewnNsiItpwKNil1U8MSQkdkwDqOKiKZCbLZqxN04pQ+imLtRlk0U39fZEQaM5ah25TEDs2iNxX/9UK5kGyjyyDjKkktU3QeHKUC2RhNe0B9rhm1YuwIoZq73xEdEk2odW2VXCl4sYJl0jyrYr+Kb88rtau8niIcwTGcAoYLqMEN1KEBFAbwDC/w6j15b9679zFfLXj5zSH8gff5A0z4lEY=</latexit> <latexit sha1_base64="sGJ7Rlh7M0CzOKNI4jm2qKakYVA=">AAAB+nicbVDLSgMxFL1TX7W+qi7dBIvgqkxE0GXRjcuK9gHtUDJppg1NMkOSEcvYT3Cre3fi1p9x65eYtrPQ1gMXDufcy7mcMBHcWN//8gorq2vrG8XN0tb2zu5eef+gaeJUU9agsYh1OySGCa5Yw3IrWDvRjMhQsFY4up76rQemDY/VvR0nLJBkoHjEKbFOunvs4V654lf9GdAywTmpQI56r/zd7cc0lUxZKogxHewnNsiItpwKNil1U8MSQkdkwDqOKiKZCbLZqxN04pQ+imLtRlk0U39fZEQaM5ah25TEDs2iNxX/9UK5kGyjyyDjKkktU3QeHKUC2RhNe0B9rhm1YuwIoZq73xEdEk2odW2VXCl4sYJl0jyrYr+Kb88rtau8niIcwTGcAoYLqMEN1KEBFAbwDC/w6j15b9679zFfLXj5zSH8gff5A0z4lEY=</latexit> <latexit sha1_base64="sGJ7Rlh7M0CzOKNI4jm2qKakYVA=">AAAB+nicbVDLSgMxFL1TX7W+qi7dBIvgqkxE0GXRjcuK9gHtUDJppg1NMkOSEcvYT3Cre3fi1p9x65eYtrPQ1gMXDufcy7mcMBHcWN//8gorq2vrG8XN0tb2zu5eef+gaeJUU9agsYh1OySGCa5Yw3IrWDvRjMhQsFY4up76rQemDY/VvR0nLJBkoHjEKbFOunvs4V654lf9GdAywTmpQI56r/zd7cc0lUxZKogxHewnNsiItpwKNil1U8MSQkdkwDqOKiKZCbLZqxN04pQ+imLtRlk0U39fZEQaM5ah25TEDs2iNxX/9UK5kGyjyyDjKkktU3QeHKUC2RhNe0B9rhm1YuwIoZq73xEdEk2odW2VXCl4sYJl0jyrYr+Kb88rtau8niIcwTGcAoYLqMEN1KEBFAbwDC/w6j15b9679zFfLXj5zSH8gff5A0z4lEY=</latexit> <latexit sha1_base64="sGJ7Rlh7M0CzOKNI4jm2qKakYVA=">AAAB+nicbVDLSgMxFL1TX7W+qi7dBIvgqkxE0GXRjcuK9gHtUDJppg1NMkOSEcvYT3Cre3fi1p9x65eYtrPQ1gMXDufcy7mcMBHcWN//8gorq2vrG8XN0tb2zu5eef+gaeJUU9agsYh1OySGCa5Yw3IrWDvRjMhQsFY4up76rQemDY/VvR0nLJBkoHjEKbFOunvs4V654lf9GdAywTmpQI56r/zd7cc0lUxZKogxHewnNsiItpwKNil1U8MSQkdkwDqOKiKZCbLZqxN04pQ+imLtRlk0U39fZEQaM5ah25TEDs2iNxX/9UK5kGyjyyDjKkktU3QeHKUC2RhNe0B9rhm1YuwIoZq73xEdEk2odW2VXCl4sYJl0jyrYr+Kb88rtau8niIcwTGcAoYLqMEN1KEBFAbwDC/w6j15b9679zFfLXj5zSH8gff5A0z4lEY=</latexit> x2 <latexit sha1_base64="iO1hVqVh56H563bnCTDCXZls070=">AAAB+nicbVDLSgMxFL3xWeur6tJNsAiuykwRdFl047KifUA7lEyaaUOTzJBkxDL2E9zq3p249Wfc+iWm7Sy09cCFwzn3ci4nTAQ31vO+0Mrq2vrGZmGruL2zu7dfOjhsmjjVlDVoLGLdDolhgivWsNwK1k40IzIUrBWOrqd+64Fpw2N1b8cJCyQZKB5xSqyT7h571V6p7FW8GfAy8XNShhz1Xum7249pKpmyVBBjOr6X2CAj2nIq2KTYTQ1LCB2RAes4qohkJshmr07wqVP6OIq1G2XxTP19kRFpzFiGblMSOzSL3lT81wvlQrKNLoOMqyS1TNF5cJQKbGM87QH3uWbUirEjhGrufsd0SDSh1rVVdKX4ixUsk2a14nsV//a8XLvK6ynAMZzAGfhwATW4gTo0gMIAnuEFXtETekPv6GO+uoLymyP4A/T5A06MlEc=</latexit> <latexit sha1_base64="iO1hVqVh56H563bnCTDCXZls070=">AAAB+nicbVDLSgMxFL3xWeur6tJNsAiuykwRdFl047KifUA7lEyaaUOTzJBkxDL2E9zq3p249Wfc+iWm7Sy09cCFwzn3ci4nTAQ31vO+0Mrq2vrGZmGruL2zu7dfOjhsmjjVlDVoLGLdDolhgivWsNwK1k40IzIUrBWOrqd+64Fpw2N1b8cJCyQZKB5xSqyT7h571V6p7FW8GfAy8XNShhz1Xum7249pKpmyVBBjOr6X2CAj2nIq2KTYTQ1LCB2RAes4qohkJshmr07wqVP6OIq1G2XxTP19kRFpzFiGblMSOzSL3lT81wvlQrKNLoOMqyS1TNF5cJQKbGM87QH3uWbUirEjhGrufsd0SDSh1rVVdKX4ixUsk2a14nsV//a8XLvK6ynAMZzAGfhwATW4gTo0gMIAnuEFXtETekPv6GO+uoLymyP4A/T5A06MlEc=</latexit> <latexit sha1_base64="iO1hVqVh56H563bnCTDCXZls070=">AAAB+nicbVDLSgMxFL3xWeur6tJNsAiuykwRdFl047KifUA7lEyaaUOTzJBkxDL2E9zq3p249Wfc+iWm7Sy09cCFwzn3ci4nTAQ31vO+0Mrq2vrGZmGruL2zu7dfOjhsmjjVlDVoLGLdDolhgivWsNwK1k40IzIUrBWOrqd+64Fpw2N1b8cJCyQZKB5xSqyT7h571V6p7FW8GfAy8XNShhz1Xum7249pKpmyVBBjOr6X2CAj2nIq2KTYTQ1LCB2RAes4qohkJshmr07wqVP6OIq1G2XxTP19kRFpzFiGblMSOzSL3lT81wvlQrKNLoOMqyS1TNF5cJQKbGM87QH3uWbUirEjhGrufsd0SDSh1rVVdKX4ixUsk2a14nsV//a8XLvK6ynAMZzAGfhwATW4gTo0gMIAnuEFXtETekPv6GO+uoLymyP4A/T5A06MlEc=</latexit> <latexit sha1_base64="iO1hVqVh56H563bnCTDCXZls070=">AAAB+nicbVDLSgMxFL3xWeur6tJNsAiuykwRdFl047KifUA7lEyaaUOTzJBkxDL2E9zq3p249Wfc+iWm7Sy09cCFwzn3ci4nTAQ31vO+0Mrq2vrGZmGruL2zu7dfOjhsmjjVlDVoLGLdDolhgivWsNwK1k40IzIUrBWOrqd+64Fpw2N1b8cJCyQZKB5xSqyT7h571V6p7FW8GfAy8XNShhz1Xum7249pKpmyVBBjOr6X2CAj2nIq2KTYTQ1LCB2RAes4qohkJshmr07wqVP6OIq1G2XxTP19kRFpzFiGblMSOzSL3lT81wvlQrKNLoOMqyS1TNF5cJQKbGM87QH3uWbUirEjhGrufsd0SDSh1rVVdKX4ixUsk2a14nsV//a8XLvK6ynAMZzAGfhwATW4gTo0gMIAnuEFXtETekPv6GO+uoLymyP4A/T5A06MlEc=</latexit> dn0 <latexit sha1_base64="YAr9h4HXgUn70stuHGnvQ4SOiR8=">AAAB/nicdVDLSsNAFJ3UV62vqks3g0VwFSaxxXZXdOOygn1AG8JkMmmHTiZhZiKUUPAX3Orenbj1V9z6JU4fghY9cOFwzr3ce0+QcqY0Qh9WYW19Y3OruF3a2d3bPygfHnVUkklC2yThiewFWFHOBG1rpjntpZLiOOC0G4yvZ373nkrFEnGnJyn1YjwULGIEayN1Qz8XPpr65QqyGw1UrdYgsmvIdd26IejCrTcc6NhojgpYouWXPwdhQrKYCk04VqrvoFR7OZaaEU6npUGmaIrJGA9p31CBY6q8fH7uFJ4ZJYRRIk0JDefqz4kcx0pN4sB0xliP1Ko3E//0gnhls47qXs5EmmkqyGJxlHGoEzjLAoZMUqL5xBBMJDO3QzLCEhNtEiuZUL4/h/+Tjms7yHZuq5Xm1TKeIjgBp+AcOOASNMENaIE2IGAMHsETeLYerBfr1XpbtBas5cwx+AXr/QsAXZZn</latexit> <latexit sha1_base64="YAr9h4HXgUn70stuHGnvQ4SOiR8=">AAAB/nicdVDLSsNAFJ3UV62vqks3g0VwFSaxxXZXdOOygn1AG8JkMmmHTiZhZiKUUPAX3Orenbj1V9z6JU4fghY9cOFwzr3ce0+QcqY0Qh9WYW19Y3OruF3a2d3bPygfHnVUkklC2yThiewFWFHOBG1rpjntpZLiOOC0G4yvZ373nkrFEnGnJyn1YjwULGIEayN1Qz8XPpr65QqyGw1UrdYgsmvIdd26IejCrTcc6NhojgpYouWXPwdhQrKYCk04VqrvoFR7OZaaEU6npUGmaIrJGA9p31CBY6q8fH7uFJ4ZJYRRIk0JDefqz4kcx0pN4sB0xliP1Ko3E//0gnhls47qXs5EmmkqyGJxlHGoEzjLAoZMUqL5xBBMJDO3QzLCEhNtEiuZUL4/h/+Tjms7yHZuq5Xm1TKeIjgBp+AcOOASNMENaIE2IGAMHsETeLYerBfr1XpbtBas5cwx+AXr/QsAXZZn</latexit> <latexit sha1_base64="YAr9h4HXgUn70stuHGnvQ4SOiR8=">AAAB/nicdVDLSsNAFJ3UV62vqks3g0VwFSaxxXZXdOOygn1AG8JkMmmHTiZhZiKUUPAX3Orenbj1V9z6JU4fghY9cOFwzr3ce0+QcqY0Qh9WYW19Y3OruF3a2d3bPygfHnVUkklC2yThiewFWFHOBG1rpjntpZLiOOC0G4yvZ373nkrFEnGnJyn1YjwULGIEayN1Qz8XPpr65QqyGw1UrdYgsmvIdd26IejCrTcc6NhojgpYouWXPwdhQrKYCk04VqrvoFR7OZaaEU6npUGmaIrJGA9p31CBY6q8fH7uFJ4ZJYRRIk0JDefqz4kcx0pN4sB0xliP1Ko3E//0gnhls47qXs5EmmkqyGJxlHGoEzjLAoZMUqL5xBBMJDO3QzLCEhNtEiuZUL4/h/+Tjms7yHZuq5Xm1TKeIjgBp+AcOOASNMENaIE2IGAMHsETeLYerBfr1XpbtBas5cwx+AXr/QsAXZZn</latexit> <latexit sha1_base64="YAr9h4HXgUn70stuHGnvQ4SOiR8=">AAAB/nicdVDLSsNAFJ3UV62vqks3g0VwFSaxxXZXdOOygn1AG8JkMmmHTiZhZiKUUPAX3Orenbj1V9z6JU4fghY9cOFwzr3ce0+QcqY0Qh9WYW19Y3OruF3a2d3bPygfHnVUkklC2yThiewFWFHOBG1rpjntpZLiOOC0G4yvZ373nkrFEnGnJyn1YjwULGIEayN1Qz8XPpr65QqyGw1UrdYgsmvIdd26IejCrTcc6NhojgpYouWXPwdhQrKYCk04VqrvoFR7OZaaEU6npUGmaIrJGA9p31CBY6q8fH7uFJ4ZJYRRIk0JDefqz4kcx0pN4sB0xliP1Ko3E//0gnhls47qXs5EmmkqyGJxlHGoEzjLAoZMUqL5xBBMJDO3QzLCEhNtEiuZUL4/h/+Tjms7yHZuq5Xm1TKeIjgBp+AcOOASNMENaIE2IGAMHsETeLYerBfr1XpbtBas5cwx+AXr/QsAXZZn</latexit> dn4 <latexit sha1_base64="tB7a3mPJw8v8KXSV3nPzqr0D75E=">AAAB/nicdVDLSsNAFJ3UV62vqks3g0VwFSYxxXZXdOOygn1AG8JkMm2HTiZhZiKUUPAX3Orenbj1V9z6JU4fghY9cOFwzr3ce0+YcqY0Qh9WYW19Y3OruF3a2d3bPygfHrVVkklCWyThieyGWFHOBG1ppjntppLiOOS0E46vZ37nnkrFEnGnJyn1YzwUbMAI1kbqREEuAm8alCvIrteR51UhsqvIdd2aIejCrdUd6NhojgpYohmUP/tRQrKYCk04VqrnoFT7OZaaEU6npX6maIrJGA9pz1CBY6r8fH7uFJ4ZJYKDRJoSGs7VnxM5jpWaxKHpjLEeqVVvJv7phfHKZj2o+TkTaaapIIvFg4xDncBZFjBikhLNJ4ZgIpm5HZIRlphok1jJhPL9OfyftF3bQbZz61UaV8t4iuAEnIJz4IBL0AA3oAlagIAxeARP4Nl6sF6sV+tt0VqwljPH4Bes9y8GsZZr</latexit> <latexit sha1_base64="tB7a3mPJw8v8KXSV3nPzqr0D75E=">AAAB/nicdVDLSsNAFJ3UV62vqks3g0VwFSYxxXZXdOOygn1AG8JkMm2HTiZhZiKUUPAX3Orenbj1V9z6JU4fghY9cOFwzr3ce0+YcqY0Qh9WYW19Y3OruF3a2d3bPygfHrVVkklCWyThieyGWFHOBG1ppjntppLiOOS0E46vZ37nnkrFEnGnJyn1YzwUbMAI1kbqREEuAm8alCvIrteR51UhsqvIdd2aIejCrdUd6NhojgpYohmUP/tRQrKYCk04VqrnoFT7OZaaEU6npX6maIrJGA9pz1CBY6r8fH7uFJ4ZJYKDRJoSGs7VnxM5jpWaxKHpjLEeqVVvJv7phfHKZj2o+TkTaaapIIvFg4xDncBZFjBikhLNJ4ZgIpm5HZIRlphok1jJhPL9OfyftF3bQbZz61UaV8t4iuAEnIJz4IBL0AA3oAlagIAxeARP4Nl6sF6sV+tt0VqwljPH4Bes9y8GsZZr</latexit> <latexit sha1_base64="tB7a3mPJw8v8KXSV3nPzqr0D75E=">AAAB/nicdVDLSsNAFJ3UV62vqks3g0VwFSYxxXZXdOOygn1AG8JkMm2HTiZhZiKUUPAX3Orenbj1V9z6JU4fghY9cOFwzr3ce0+YcqY0Qh9WYW19Y3OruF3a2d3bPygfHrVVkklCWyThieyGWFHOBG1ppjntppLiOOS0E46vZ37nnkrFEnGnJyn1YzwUbMAI1kbqREEuAm8alCvIrteR51UhsqvIdd2aIejCrdUd6NhojgpYohmUP/tRQrKYCk04VqrnoFT7OZaaEU6npX6maIrJGA9pz1CBY6r8fH7uFJ4ZJYKDRJoSGs7VnxM5jpWaxKHpjLEeqVVvJv7phfHKZj2o+TkTaaapIIvFg4xDncBZFjBikhLNJ4ZgIpm5HZIRlphok1jJhPL9OfyftF3bQbZz61UaV8t4iuAEnIJz4IBL0AA3oAlagIAxeARP4Nl6sF6sV+tt0VqwljPH4Bes9y8GsZZr</latexit> <latexit sha1_base64="tB7a3mPJw8v8KXSV3nPzqr0D75E=">AAAB/nicdVDLSsNAFJ3UV62vqks3g0VwFSYxxXZXdOOygn1AG8JkMm2HTiZhZiKUUPAX3Orenbj1V9z6JU4fghY9cOFwzr3ce0+YcqY0Qh9WYW19Y3OruF3a2d3bPygfHrVVkklCWyThieyGWFHOBG1ppjntppLiOOS0E46vZ37nnkrFEnGnJyn1YzwUbMAI1kbqREEuAm8alCvIrteR51UhsqvIdd2aIejCrdUd6NhojgpYohmUP/tRQrKYCk04VqrnoFT7OZaaEU6npX6maIrJGA9pz1CBY6r8fH7uFJ4ZJYKDRJoSGs7VnxM5jpWaxKHpjLEeqVVvJv7phfHKZj2o+TkTaaapIIvFg4xDncBZFjBikhLNJ4ZgIpm5HZIRlphok1jJhPL9OfyftF3bQbZz61UaV8t4iuAEnIJz4IBL0AA3oAlagIAxeARP4Nl6sF6sV+tt0VqwljPH4Bes9y8GsZZr</latexit> dn1 <latexit sha1_base64="d5TWhZzhDIbIwXRUu9+oVadQK90=">AAAB/nicdVDLSsNAFJ3UV62vqks3g0VwFSaxxXZXdOOygn1AG8JkMmmHTiZhZiKUUPAX3Orenbj1V9z6JU4fghY9cOFwzr3ce0+QcqY0Qh9WYW19Y3OruF3a2d3bPygfHnVUkklC2yThiewFWFHOBG1rpjntpZLiOOC0G4yvZ373nkrFEnGnJyn1YjwULGIEayN1Qz8XvjP1yxVkNxqoWq1BZNeQ67p1Q9CFW2840LHRHBWwRMsvfw7ChGQxFZpwrFTfQan2ciw1I5xOS4NM0RSTMR7SvqECx1R5+fzcKTwzSgijRJoSGs7VnxM5jpWaxIHpjLEeqVVvJv7pBfHKZh3VvZyJNNNUkMXiKONQJ3CWBQyZpETziSGYSGZuh2SEJSbaJFYyoXx/Dv8nHdd2kO3cVivNq2U8RXACTsE5cMAlaIIb0AJtQMAYPIIn8Gw9WC/Wq/W2aC1Yy5lj8AvW+xcB8pZo</latexit> <latexit sha1_base64="d5TWhZzhDIbIwXRUu9+oVadQK90=">AAAB/nicdVDLSsNAFJ3UV62vqks3g0VwFSaxxXZXdOOygn1AG8JkMmmHTiZhZiKUUPAX3Orenbj1V9z6JU4fghY9cOFwzr3ce0+QcqY0Qh9WYW19Y3OruF3a2d3bPygfHnVUkklC2yThiewFWFHOBG1rpjntpZLiOOC0G4yvZ373nkrFEnGnJyn1YjwULGIEayN1Qz8XvjP1yxVkNxqoWq1BZNeQ67p1Q9CFW2840LHRHBWwRMsvfw7ChGQxFZpwrFTfQan2ciw1I5xOS4NM0RSTMR7SvqECx1R5+fzcKTwzSgijRJoSGs7VnxM5jpWaxIHpjLEeqVVvJv7pBfHKZh3VvZyJNNNUkMXiKONQJ3CWBQyZpETziSGYSGZuh2SEJSbaJFYyoXx/Dv8nHdd2kO3cVivNq2U8RXACTsE5cMAlaIIb0AJtQMAYPIIn8Gw9WC/Wq/W2aC1Yy5lj8AvW+xcB8pZo</latexit> <latexit sha1_base64="d5TWhZzhDIbIwXRUu9+oVadQK90=">AAAB/nicdVDLSsNAFJ3UV62vqks3g0VwFSaxxXZXdOOygn1AG8JkMmmHTiZhZiKUUPAX3Orenbj1V9z6JU4fghY9cOFwzr3ce0+QcqY0Qh9WYW19Y3OruF3a2d3bPygfHnVUkklC2yThiewFWFHOBG1rpjntpZLiOOC0G4yvZ373nkrFEnGnJyn1YjwULGIEayN1Qz8XvjP1yxVkNxqoWq1BZNeQ67p1Q9CFW2840LHRHBWwRMsvfw7ChGQxFZpwrFTfQan2ciw1I5xOS4NM0RSTMR7SvqECx1R5+fzcKTwzSgijRJoSGs7VnxM5jpWaxIHpjLEeqVVvJv7pBfHKZh3VvZyJNNNUkMXiKONQJ3CWBQyZpETziSGYSGZuh2SEJSbaJFYyoXx/Dv8nHdd2kO3cVivNq2U8RXACTsE5cMAlaIIb0AJtQMAYPIIn8Gw9WC/Wq/W2aC1Yy5lj8AvW+xcB8pZo</latexit> <latexit sha1_base64="d5TWhZzhDIbIwXRUu9+oVadQK90=">AAAB/nicdVDLSsNAFJ3UV62vqks3g0VwFSaxxXZXdOOygn1AG8JkMmmHTiZhZiKUUPAX3Orenbj1V9z6JU4fghY9cOFwzr3ce0+QcqY0Qh9WYW19Y3OruF3a2d3bPygfHnVUkklC2yThiewFWFHOBG1rpjntpZLiOOC0G4yvZ373nkrFEnGnJyn1YjwULGIEayN1Qz8XvjP1yxVkNxqoWq1BZNeQ67p1Q9CFW2840LHRHBWwRMsvfw7ChGQxFZpwrFTfQan2ciw1I5xOS4NM0RSTMR7SvqECx1R5+fzcKTwzSgijRJoSGs7VnxM5jpWaxIHpjLEeqVVvJv7pBfHKZh3VvZyJNNNUkMXiKONQJ3CWBQyZpETziSGYSGZuh2SEJSbaJFYyoXx/Dv8nHdd2kO3cVivNq2U8RXACTsE5cMAlaIIb0AJtQMAYPIIn8Gw9WC/Wq/W2aC1Yy5lj8AvW+xcB8pZo</latexit> dn2 <latexit sha1_base64="ffiueiebPCrCKMDMy/GagXBHKhw=">AAAB/nicdVDLSsNAFJ3UV62vqks3g0VwFSaxxXZXdOOygn1AG8JkMmmHTiZhZiKUUPAX3Orenbj1V9z6JU4fghY9cOFwzr3ce0+QcqY0Qh9WYW19Y3OruF3a2d3bPygfHnVUkklC2yThiewFWFHOBG1rpjntpZLiOOC0G4yvZ373nkrFEnGnJyn1YjwULGIEayN1Qz8Xvjv1yxVkNxqoWq1BZNeQ67p1Q9CFW2840LHRHBWwRMsvfw7ChGQxFZpwrFTfQan2ciw1I5xOS4NM0RSTMR7SvqECx1R5+fzcKTwzSgijRJoSGs7VnxM5jpWaxIHpjLEeqVVvJv7pBfHKZh3VvZyJNNNUkMXiKONQJ3CWBQyZpETziSGYSGZuh2SEJSbaJFYyoXx/Dv8nHdd2kO3cVivNq2U8RXACTsE5cMAlaIIb0AJtQMAYPIIn8Gw9WC/Wq/W2aC1Yy5lj8AvW+xcDh5Zp</latexit> <latexit sha1_base64="ffiueiebPCrCKMDMy/GagXBHKhw=">AAAB/nicdVDLSsNAFJ3UV62vqks3g0VwFSaxxXZXdOOygn1AG8JkMmmHTiZhZiKUUPAX3Orenbj1V9z6JU4fghY9cOFwzr3ce0+QcqY0Qh9WYW19Y3OruF3a2d3bPygfHnVUkklC2yThiewFWFHOBG1rpjntpZLiOOC0G4yvZ373nkrFEnGnJyn1YjwULGIEayN1Qz8Xvjv1yxVkNxqoWq1BZNeQ67p1Q9CFW2840LHRHBWwRMsvfw7ChGQxFZpwrFTfQan2ciw1I5xOS4NM0RSTMR7SvqECx1R5+fzcKTwzSgijRJoSGs7VnxM5jpWaxIHpjLEeqVVvJv7pBfHKZh3VvZyJNNNUkMXiKONQJ3CWBQyZpETziSGYSGZuh2SEJSbaJFYyoXx/Dv8nHdd2kO3cVivNq2U8RXACTsE5cMAlaIIb0AJtQMAYPIIn8Gw9WC/Wq/W2aC1Yy5lj8AvW+xcDh5Zp</latexit> <latexit sha1_base64="ffiueiebPCrCKMDMy/GagXBHKhw=">AAAB/nicdVDLSsNAFJ3UV62vqks3g0VwFSaxxXZXdOOygn1AG8JkMmmHTiZhZiKUUPAX3Orenbj1V9z6JU4fghY9cOFwzr3ce0+QcqY0Qh9WYW19Y3OruF3a2d3bPygfHnVUkklC2yThiewFWFHOBG1rpjntpZLiOOC0G4yvZ373nkrFEnGnJyn1YjwULGIEayN1Qz8Xvjv1yxVkNxqoWq1BZNeQ67p1Q9CFW2840LHRHBWwRMsvfw7ChGQxFZpwrFTfQan2ciw1I5xOS4NM0RSTMR7SvqECx1R5+fzcKTwzSgijRJoSGs7VnxM5jpWaxIHpjLEeqVVvJv7pBfHKZh3VvZyJNNNUkMXiKONQJ3CWBQyZpETziSGYSGZuh2SEJSbaJFYyoXx/Dv8nHdd2kO3cVivNq2U8RXACTsE5cMAlaIIb0AJtQMAYPIIn8Gw9WC/Wq/W2aC1Yy5lj8AvW+xcDh5Zp</latexit> <latexit sha1_base64="ffiueiebPCrCKMDMy/GagXBHKhw=">AAAB/nicdVDLSsNAFJ3UV62vqks3g0VwFSaxxXZXdOOygn1AG8JkMmmHTiZhZiKUUPAX3Orenbj1V9z6JU4fghY9cOFwzr3ce0+QcqY0Qh9WYW19Y3OruF3a2d3bPygfHnVUkklC2yThiewFWFHOBG1rpjntpZLiOOC0G4yvZ373nkrFEnGnJyn1YjwULGIEayN1Qz8Xvjv1yxVkNxqoWq1BZNeQ67p1Q9CFW2840LHRHBWwRMsvfw7ChGQxFZpwrFTfQan2ciw1I5xOS4NM0RSTMR7SvqECx1R5+fzcKTwzSgijRJoSGs7VnxM5jpWaxIHpjLEeqVVvJv7pBfHKZh3VvZyJNNNUkMXiKONQJ3CWBQyZpETziSGYSGZuh2SEJSbaJFYyoXx/Dv8nHdd2kO3cVivNq2U8RXACTsE5cMAlaIIb0AJtQMAYPIIn8Gw9WC/Wq/W2aC1Yy5lj8AvW+xcDh5Zp</latexit> dn3 <latexit sha1_base64="nSO8qFZKcyDEg6yWfnpy67LEjMY=">AAAB/nicdVDLSsNAFJ34rPVVdelmsAiuwiRtsd0V3bisYB/QhjCZTNqhk0mYmQglFPwFt7p3J279Fbd+idOHoEUPXDiccy/33hOknCmN0Ie1tr6xubVd2Cnu7u0fHJaOjjsqySShbZLwRPYCrChngrY105z2UklxHHDaDcbXM797T6ViibjTk5R6MR4KFjGCtZG6oZ8LvzL1S2VkNxqoWq1BZNeQ67p1Q1DFrTcc6NhojjJYouWXPgdhQrKYCk04VqrvoFR7OZaaEU6nxUGmaIrJGA9p31CBY6q8fH7uFJ4bJYRRIk0JDefqz4kcx0pN4sB0xliP1Ko3E//0gnhls47qXs5EmmkqyGJxlHGoEzjLAoZMUqL5xBBMJDO3QzLCEhNtEiuaUL4/h/+Tjms7yHZuq+Xm1TKeAjgFZ+ACOOASNMENaIE2IGAMHsETeLYerBfr1XpbtK5Zy5kT8AvW+xcFHJZq</latexit> <latexit sha1_base64="nSO8qFZKcyDEg6yWfnpy67LEjMY=">AAAB/nicdVDLSsNAFJ34rPVVdelmsAiuwiRtsd0V3bisYB/QhjCZTNqhk0mYmQglFPwFt7p3J279Fbd+idOHoEUPXDiccy/33hOknCmN0Ie1tr6xubVd2Cnu7u0fHJaOjjsqySShbZLwRPYCrChngrY105z2UklxHHDaDcbXM797T6ViibjTk5R6MR4KFjGCtZG6oZ8LvzL1S2VkNxqoWq1BZNeQ67p1Q1DFrTcc6NhojjJYouWXPgdhQrKYCk04VqrvoFR7OZaaEU6nxUGmaIrJGA9p31CBY6q8fH7uFJ4bJYRRIk0JDefqz4kcx0pN4sB0xliP1Ko3E//0gnhls47qXs5EmmkqyGJxlHGoEzjLAoZMUqL5xBBMJDO3QzLCEhNtEiuaUL4/h/+Tjms7yHZuq+Xm1TKeAjgFZ+ACOOASNMENaIE2IGAMHsETeLYerBfr1XpbtK5Zy5kT8AvW+xcFHJZq</latexit> <latexit sha1_base64="nSO8qFZKcyDEg6yWfnpy67LEjMY=">AAAB/nicdVDLSsNAFJ34rPVVdelmsAiuwiRtsd0V3bisYB/QhjCZTNqhk0mYmQglFPwFt7p3J279Fbd+idOHoEUPXDiccy/33hOknCmN0Ie1tr6xubVd2Cnu7u0fHJaOjjsqySShbZLwRPYCrChngrY105z2UklxHHDaDcbXM797T6ViibjTk5R6MR4KFjGCtZG6oZ8LvzL1S2VkNxqoWq1BZNeQ67p1Q1DFrTcc6NhojjJYouWXPgdhQrKYCk04VqrvoFR7OZaaEU6nxUGmaIrJGA9p31CBY6q8fH7uFJ4bJYRRIk0JDefqz4kcx0pN4sB0xliP1Ko3E//0gnhls47qXs5EmmkqyGJxlHGoEzjLAoZMUqL5xBBMJDO3QzLCEhNtEiuaUL4/h/+Tjms7yHZuq+Xm1TKeAjgFZ+ACOOASNMENaIE2IGAMHsETeLYerBfr1XpbtK5Zy5kT8AvW+xcFHJZq</latexit> <latexit sha1_base64="nSO8qFZKcyDEg6yWfnpy67LEjMY=">AAAB/nicdVDLSsNAFJ34rPVVdelmsAiuwiRtsd0V3bisYB/QhjCZTNqhk0mYmQglFPwFt7p3J279Fbd+idOHoEUPXDiccy/33hOknCmN0Ie1tr6xubVd2Cnu7u0fHJaOjjsqySShbZLwRPYCrChngrY105z2UklxHHDaDcbXM797T6ViibjTk5R6MR4KFjGCtZG6oZ8LvzL1S2VkNxqoWq1BZNeQ67p1Q1DFrTcc6NhojjJYouWXPgdhQrKYCk04VqrvoFR7OZaaEU6nxUGmaIrJGA9p31CBY6q8fH7uFJ4bJYRRIk0JDefqz4kcx0pN4sB0xliP1Ko3E//0gnhls47qXs5EmmkqyGJxlHGoEzjLAoZMUqL5xBBMJDO3QzLCEhNtEiuaUL4/h/+Tjms7yHZuq+Xm1TKeAjgFZ+ACOOASNMENaIE2IGAMHsETeLYerBfr1XpbtK5Zy5kT8AvW+xcFHJZq</latexit> P(y | x) <latexit sha1_base64="UNRPnN0ig3hl+sy9EWTrYW1RcXM=">AAACAXicdZDLSgMxFIYzXmu9VV26CRahbkpGam13RTcuK9gLtkPJpJk2NMkMSUYsQ1e+glvduxO3Polbn8RMW0GL/hD4+c45nJPfjzjTBqEPZ2l5ZXVtPbOR3dza3tnN7e03dRgrQhsk5KFq+1hTziRtGGY4bUeKYuFz2vJHl2m9dUeVZqG8MeOIegIPJAsYwcai23ph3BWsD+9Perk8Kp4ht1ouQ1REyC1VXGuq1YqF0LUkVR7MVe/lPrv9kMSCSkM41rrjosh4CVaGEU4n2W6saYTJCA9ox1qJBdVeMr14Ao8t6cMgVPZJA6f050SChdZj4dtOgc1QL9ZS+GfNFwubTVDxEiaj2FBJZouDmEMTwjQO2GeKEsPH1mCimL0dkiFWmBgbWtaG8v1z+L9pnhZdVHSvS/naxTyeDDgER6AAXHAOauAK1EEDECDBI3gCz86D8+K8Om+z1iVnPnMAfsl5/wJZI5cV</latexit> <latexit sha1_base64="UNRPnN0ig3hl+sy9EWTrYW1RcXM=">AAACAXicdZDLSgMxFIYzXmu9VV26CRahbkpGam13RTcuK9gLtkPJpJk2NMkMSUYsQ1e+glvduxO3Polbn8RMW0GL/hD4+c45nJPfjzjTBqEPZ2l5ZXVtPbOR3dza3tnN7e03dRgrQhsk5KFq+1hTziRtGGY4bUeKYuFz2vJHl2m9dUeVZqG8MeOIegIPJAsYwcai23ph3BWsD+9Perk8Kp4ht1ouQ1REyC1VXGuq1YqF0LUkVR7MVe/lPrv9kMSCSkM41rrjosh4CVaGEU4n2W6saYTJCA9ox1qJBdVeMr14Ao8t6cMgVPZJA6f050SChdZj4dtOgc1QL9ZS+GfNFwubTVDxEiaj2FBJZouDmEMTwjQO2GeKEsPH1mCimL0dkiFWmBgbWtaG8v1z+L9pnhZdVHSvS/naxTyeDDgER6AAXHAOauAK1EEDECDBI3gCz86D8+K8Om+z1iVnPnMAfsl5/wJZI5cV</latexit> <latexit sha1_base64="UNRPnN0ig3hl+sy9EWTrYW1RcXM=">AAACAXicdZDLSgMxFIYzXmu9VV26CRahbkpGam13RTcuK9gLtkPJpJk2NMkMSUYsQ1e+glvduxO3Polbn8RMW0GL/hD4+c45nJPfjzjTBqEPZ2l5ZXVtPbOR3dza3tnN7e03dRgrQhsk5KFq+1hTziRtGGY4bUeKYuFz2vJHl2m9dUeVZqG8MeOIegIPJAsYwcai23ph3BWsD+9Perk8Kp4ht1ouQ1REyC1VXGuq1YqF0LUkVR7MVe/lPrv9kMSCSkM41rrjosh4CVaGEU4n2W6saYTJCA9ox1qJBdVeMr14Ao8t6cMgVPZJA6f050SChdZj4dtOgc1QL9ZS+GfNFwubTVDxEiaj2FBJZouDmEMTwjQO2GeKEsPH1mCimL0dkiFWmBgbWtaG8v1z+L9pnhZdVHSvS/naxTyeDDgER6AAXHAOauAK1EEDECDBI3gCz86D8+K8Om+z1iVnPnMAfsl5/wJZI5cV</latexit> <latexit sha1_base64="UNRPnN0ig3hl+sy9EWTrYW1RcXM=">AAACAXicdZDLSgMxFIYzXmu9VV26CRahbkpGam13RTcuK9gLtkPJpJk2NMkMSUYsQ1e+glvduxO3Polbn8RMW0GL/hD4+c45nJPfjzjTBqEPZ2l5ZXVtPbOR3dza3tnN7e03dRgrQhsk5KFq+1hTziRtGGY4bUeKYuFz2vJHl2m9dUeVZqG8MeOIegIPJAsYwcai23ph3BWsD+9Perk8Kp4ht1ouQ1REyC1VXGuq1YqF0LUkVR7MVe/lPrv9kMSCSkM41rrjosh4CVaGEU4n2W6saYTJCA9ox1qJBdVeMr14Ao8t6cMgVPZJA6f050SChdZj4dtOgc1QL9ZS+GfNFwubTVDxEiaj2FBJZouDmEMTwjQO2GeKEsPH1mCimL0dkiFWmBgbWtaG8v1z+L9pnhZdVHSvS/naxTyeDDgER6AAXHAOauAK1EEDECDBI3gCz86D8+K8Om+z1iVnPnMAfsl5/wJZI5cV</latexit> Region-wise model 0 1 0 0 0 0 1 1 1 1 Edward Pyro Prob Torch BayesFlow ⽣命科学/医・薬・⽣物 化学(量⼦化学・触媒化学・⽣化学・有機化学) 物質・材料科学 最近の関⼼:「機械学習」+「離散構造」for「⾃然科学」
  5. ܾఆ໦ɾܾఆDAG χϡʔϥϧωοτ ֬཰తϓϩάϥϛϯά • ର৅͕ʮ཭ࢄߏ଄ʯΛ࣋ͭ • Ϟσϧ͕ʮ཭ࢄߏ଄ʯΛ࣋ͭ • ର৅ͷؔ܎͕ʮ཭ࢄߏ଄ʯΛ࣋ͭ H

    H H H H H H H O N O O H H H O O H H N O O Cl Cl Cl ࿦ཧɺू߹ɺؔ܎ɺܥྻɺ૊߹ͤɺஔ׵ɺ෼ذ(໦)ɺωοτϫʔΫ(άϥϑ)ɺ୅਺ܥɺ… 「離散構造」を伴う機械学習
  6. Institute for Chemical Reaction Design and Discovery 北海道⼤学 化学反応創成研究拠点 (ICReDD)

    安定状態 1 安定状態 2 遷移状態 θ1 θ2 Schrödinger equation Potential Energy Surface (PES) • ⼊⼝出⼝は"離散組合せ的"対象 化合物 = ⾼々100数種類の元素 (現在118種)がなす膨⼤な組合せ • 化学反応は(⾃然法則が定める) 原⼦や結合の組み替え過程 エネルギーの⾕→峠→⾕の遷移だが このエネルギー⾯ を求めるには 毎点で電⼦に関する⽅程式の求解が必要 アイクレッド エネルギー 2018年10⽉〜 ⽂科省:世界トップレベル研究拠点(WPI)プログラム 物質の変換を司る化学反応の⾃在な設計と制御
  7. 展望:Theory-driven vs Data-drivenの解消と融合 Theory-driven Data-driven • 対象現象の複雑化 • シミュレーション技法も複雑化 •

    "経験的に決める"パラメタや初期値 • 汎関数、交換相関項の設計 • ⼩サンプル・低カウントの問題 • 外挿の不可能性の問題 • 帰納バイアスのモデルエンコード • Blackbox性・解釈性の問題 • 知識ベースと論理推論(記号AI)の限界 • 厳密推論や探索の計算爆発(NP困難性) • ⼤量データの知識化の問題 • 制約プログラミングや組合せ最適化 (⼈⼯知能分野) (⼈⼯知能分野) • Data-Driven⼿法(機械学習)と⼈間の 論理的思考との⼤きなギャップ • Dataがない領域の探索や「ひらめき」 • モデル適⽤範囲と信頼性・安全性 新たな⽅法論へ? データ同化、模倣学習、論理合成、etc モデルベース最適化、強化学習、メタ 学習、ドメイン適応、⽣成モデル、etc 【合理論】 【経験論】 参考) ⼈⼯知能の基本問題に関する総説(Open Access) http://id.nii.ac.jp/1004/00010296/
  8. 化学の分野で⾔うと... Takeaway: We also need 'data-driven' bridges!
 first principles are

    not enough for us to throw away these empirical things; data-driven approaches (ML) play a complementary role! • 理論計算技術と計算機ハードの進歩により理論計算はかなり 実践的な研究でも活⽤されるように。 • しかし主として実験的事実はスキルの⾼い実験化学者が 極めて経験的に発⾒し、理論はその事実の解釈に活⽤される のが現状 • 通常こうした発⾒には実際の化学実験の⻑い「経験」が必要 • 当該分野の論⽂・テキストの経験的知⾒も混合された「勘」 Key Question: 理論や計算は"化学的発⾒"を先導できるのか?
  9. 計算科学・実験科学・情報科学による化学反応設計と探索 "計算化学" ⼈⼯⼒誘起反応(AFIR)法による (第⼀原理)反応経路⾃動探索 (多様な)"実験化学" + ただし理論計算予測だけでは難しい問題がいろいろある... → 「情報科学」への期待 •

    探索空間が組合せ的に巨⼤: 理論的に可能な経路の探索も組合せ爆発を起こす • 計算時間・リソースが⼤きく計算できる系が限られる: 現実の系では何か妥協が必要 • 現実の化学反応の複雑さと不確定さ: 理論計算に⼊らない多様な要因が影響 • 現状の理論モデルの単純な仮定や不完全さ: 多体問題の近似や理論の例外の存在 拠点のコア技術 化学反応経路 ネットワーク (これも組合せ的) (補完的な"第三の⽮"?)
  10. 化学反応の予測 ① Theory-driven (Quantum Chem) ② Knowledge-driven (Knowledge Bases) ③

    Data-driven (Machine Learning) 化学反応をどのような表現・レベルで捉えるか? 量⼦・電⼦系 〜 複雑系・⽣体系 1分⼦レベルでの表現の多様性
  11. 化学反応の予測 ① Theory-driven (Quantum Chem) ② Knowledge-driven (Knowledge Bases) ③

    Data-driven (Machine Learning) 化学反応をどのような表現・レベルで捉えるか? 量⼦・電⼦系 〜 複雑系・⽣体系 1分⼦レベルでの表現の多様性
  12. A traditional topic in chemoinformatics Computer-assisted synthetic planning (path search

    on knowledge bases) or AI-Assisted Synthesis? (with Machine Learning)
  13. 70೥୅͔Βଓ͘௕͍ྺ࢙ 化学反応をデータベース化して反応経路を探索(検索)したい e.g.) 化学反応の表現、化学経路の分類、化学反応の探索、… Corey+ 1972 J Am Chem Soc

    (JACS), 94(2), 1972. 440 Computer-Assisted Synthetic Analysis for Complex Molecules. Methods and Procedures for Machine Generation of Synthetic Intermediates E. J. Corey,* Richard D. Cramer III, and W. Jeffrey Howe Contribution from the Department of Chemistry, Harvard University, Cambridge, Massachusetts 02138. Received January 30, 1971 Abstract: A classification of synthetic reactions is outlined which is suitable for use in a machine program to generate a tree of synthetic intermediates starting from a given target molecule. The generation of a particular intermediate by the program involves the search of appropriate data tables of synthetic processes, the search being driven by the information obtained by machine perception of the parent structure and certain basic strategies. Procedures have been developed for the evaluation of chemical interconversions which allow the effective exclusion of invalid or naive structures. The paper provides a view of the status of computer-assisted synthetic problem solving as of 1970. The communication of chemical structural informa- tion to and from a digital computer by graphical methods has been discussed in detail in a foregoing paper,1 as has the machine representation and percep- tion of key features within structures,2 as for example, functional groups and rings. This paper is concerned with the ways in which the structural information made available by the perception process can be utilized to generate a tree of chemical structures3 which represent possible synthetic intermediates for the construction of a complex target molecule. More specifically, the following topics will be treated: (1) classification of and necessary control strategies, and also for eventual inclusion of a fairly complete collection of families. In the discussion which follows, the degree of imple- mentation of each area of study will be cited. A variety of rational schemes for creating families of synthetic reactions already exists. However, most of these depend on properties of the reactants,5 and as such they are irrelevant to a computer program which analyzes the features of a target or product molecule in order to generate appropriate starting materials. One very general treatment of synthetic reactions in- volves classification on the basis of the structural Computer-Assisted Solution of Chemical Problems- The Historical Development and the Present State of the Art of a New Discipline of Chemistry By Ivar Ugi," Johannes Bauer, Klemens Bley, Alf Dengler, Andreas Dietz, Eric Fontain, Bernhard Gruber, Rainer Herges, Michael Knauer, Klaus Reitsam, and Natalie Stein Dedicated to Projkssor Karl-Heinz Biicliel The topic of this article is the development and the present state of the art of computer chemistry, the computer-assisted solution of chemical problems. Initially the problems in computer chemistry were confined to structure elucidation on the basis of spectroscopic data, then programs for synthesis design based on libraries of reaction data for relatively narrow classes of target compounds were developed, and now computer programs for the solution of a great variety of chemical problems are available or are under development. Previously it was an achievement when any solution of a chemical problem could be generated by computer assistance. Today, the main task is the efficient, transparent, and non-arbitrary selection of meaningful results from the immense set of potential solutions--that also may contain innova- tive proposals. Chemistry has two aspects, constitutional chemistry and stereochemistry, which are interrelated, but still require different approaches. As a result, about twenty years ago, an algebraic model of the logical structure of chemistry was presented that consisted of two parts: the constitution-oriented algebra of be- and r-matrices, and the theory of the Ugi+ 1993 Angew Chem Int Ed Engl. 32, 202-227, 1993.
  14. Gasteigerͷओؔ৺͕Խֶ൓Ԡܦ࿏ͷ༧ଌ΍߹੒ࢧԉ(ͨͿΜ) Analytrcu Chrmlcu Act, 235 (1990) 65-75 Elsevter Sctence Pubhshers

    B.V., Amsterdam - Pnnted m The Netherlands 65 Computer-assisted reaction prediction and synthesis design J. GASTEIGER *, W D. IHLENFELDT, P ROSE and R. WANKE Instwte of Orgunrc Chemrstry, Technlcul Umversrty Munrch, D-8046 Gurchmg (F R G) (Received 18th December 1989) ABSTRACT The design of organic syntheses requires deep msight mto chemical reactivtty. Methods have been developed to calculate important electromc and energy effects and use them for the modellmg of reaction mechanisms The approach 1s tllustrated by the haloform reaction. The procedures have been mcorporated mto different versions of the EROS system. A study of the synthests of fredericamycm tllustrates the use of these EROS procedures m syntheses design and reaction prediction. Recent work on synthesis design for aromatic compounds 1s h&lighted and new deftmtions of the stmtlanty of chemical compounds are discussed. Gasteiger+ 1990 教科書の「反応」関連の章もGasteiger⾃⾝が執筆
  15. 化学反応の予測 ① Theory-driven (Quantum Chem) ② Knowledge-driven (Knowledge Bases) ③

    Data-driven (Machine Learning) 化学反応をどのような表現・レベルで捉えるか? 量⼦・電⼦系 〜 複雑系・⽣体系 1分⼦レベルでの表現の多様性
  16. Automated reaction-path search via GRRM strategy θ1 θ2 O H

    H Energy θ = 104.45° 1 θ = 95.84 pm 2 θ1 Schrödinger equation Potential Energy Surface EQ EQ T ADDF Ohno & Maeda, Chem Phys Lett, 2004 Reaction Path AFIR Maeda & Morokuma, J Chem Phys, 2010 θ2
  17. But computational chemistry has limitations for now... Chemical reactions =

    recombinations of atoms and chemical bonds subjected to the laws of nature • Intractably large chemical space: A intractably large number of "theoretically possible" candidates for reactions and compounds... • Scalability issue: Simulating an Avogadro-constant number of atoms is utterly infeasible... (After all, we need some compromise here) • Complexity and uncertainty of real-world systems: Many uncertain factors and arbitrary parameters are involved... • Known and unknown imperfections of currently established theories: Current theoretical calculations have many exceptions and limitations...
  18. 化学反応の予測 ① Theory-driven (Quantum Chem) ② Knowledge-driven (Knowledge Bases) ③

    Data-driven (Machine Learning) 化学反応をどのような表現・レベルで捉えるか? 量⼦・電⼦系 〜 複雑系・⽣体系 1分⼦レベルでの表現の多様性
  19. Yet another approach: Data-driven Cause-and-Effect
 Relationship Related factors
 (and their

    states) Outcome Reactions Some mechanism [Inputs] [Outputs] Theory-driven methods try to explicitly model the inner workings of a target phenomenon (e.g. through first-principles simulations) Data-driven methods try to precisely approximate its outer behavior (the input-output relationship) observable as "data". 
 (e.g. through machine learning from a large collection of data) based on very different principles and quite complementary! governing equation?
  20. Machine Learning (ML) Generic Object Recognition Speech Recognition Machine Translation

    QSAR/QSPR Prediction AI Game Players “͋Γ͕ͱ͏” J’aime la musique I love music CH 3 N N H N H H 3 C N Growth inhibition 0.739 A new style of programming a technique to reproduce a transformation process (or function) where the underlying principle is unclear and hard to be explicitly modelled 
 just by giving a lot of input-output examples.
  21. How ML works: fitting a function to data Inputs Outputs

    ML model x <latexit sha1_base64="BkOuic6isW1cYY2ZNWiUOdOU/tM=">AAACq3ichVFNLwNRFD3G92eLjcRGNMRG8wYJsWrYWJbqR2jTzIxXHvOVmdcGTf+AlZ1gRWIhfoaNP2DhJ4gliY2FO9NJBFF3MvPOO/ee+86bq7um8CVjT21Ke0dnV3dPb1//wOBQLD48kvOdqmfwrOGYjlfQNZ+bwuZZKaTJC67HNUs3eV4/WA3y+Rr3fOHYm/LI5SVL27VFRRiaJCpX1K36YaMcT7AkC2PiN1AjkEAUaSf+gCJ24MBAFRY4bEjCJjT49GxDBYNLXAl14jxCIsxzNNBH2ipVcarQiD2g7y7ttiPWpn3Q0w/VBp1i0uuRcgJT7JHdslf2wO7YM/v4s1c97BF4OaJVb2q5W46djGXe/1VZtErsfalaepaoYCn0Ksi7GzLBLYymvnZ89ppZ3piqT7Nr9kL+r9gTu6cb2LU342adb1y28KOTl7//WJCPKmiE6s+B/Qa5uaQ6n5xbX0ikVqJh9mAck5ihiS0ihTWkkaUT9nGKc1wos0pG2VKKzVKlLdKM4lso/BN9vpmr</latexit> y <latexit sha1_base64="getvLqfzl+lmP3jVELri0P4Sr2g=">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</latexit> A function best fitted to a given set of example input-output pairs (the training data). (x1, y1), (x2, y2), . . . , (xn, yn) <latexit sha1_base64="l6cITD180CW4htD4CpRHsG+/qlU=">AAAC+3ichVE9T9xAEB1MSMCQcCENUppTTiCQTqdZJwoHFSINJV8HSBidbLMcK/wle++Uw7o/kD9AQQUoBYE2Tdo0/IEUdLRASaQ0FMz6fCCKI2PZ+/bNvNm3Hjt0RSwRL3q03hd9L1/1D+iDQ6/fDOfejqzGQT1yeMUJ3CBat62Yu8LnFSmky9fDiFue7fI1e/eLyq81eBSLwF+RzZBvelbNF9vCsSRR1dyKaYuaayb6hGl7yddWlRUVaBKYLD6QRoc0iDS3AhnrxU7O7+T8SV01i8xWNVfAEiIyxvIKsKnPSGB6umywcp6pFEUBslgIcudgwhYE4EAdPODggyTsggUxPRvAACEkbhMS4iJCIs1zaIFO2jpVcaqwiN2lb412Gxnr0171jFO1Q6e49EakzMMY/sETvMVzPMUrvOvaK0l7KC9NWu22lofV4W+jy//+q/JolbDzqHrWs4RtKKdeBXkPU0bdwmnrG3v7t8szS2PJOB7hDfk/xAv8TTfwG3+d74t86eAZPzZ56f7HVD6roBF25pTvDlaNEvtYMhY/FWbnsmH2w3v4ABM0sSmYhXlYgAqd8Asu4QqutZZ2rP3QztqlWk+meQdPQvt5D2QXt/E=</latexit> f(x; ✓) <latexit sha1_base64="33zlDWOHXmZvZwuGF4JM5OwSths=">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</latexit> x <latexit sha1_base64="BkOuic6isW1cYY2ZNWiUOdOU/tM=">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</latexit> y <latexit sha1_base64="getvLqfzl+lmP3jVELri0P4Sr2g=">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</latexit> ✓ <latexit sha1_base64="lTDMb0MkD19hJd3A01US8Q9hJ/8=">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</latexit> x <latexit sha1_base64="BkOuic6isW1cYY2ZNWiUOdOU/tM=">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</latexit> y <latexit sha1_base64="getvLqfzl+lmP3jVELri0P4Sr2g=">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</latexit> x <latexit sha1_base64="BkOuic6isW1cYY2ZNWiUOdOU/tM=">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</latexit> y <latexit sha1_base64="getvLqfzl+lmP3jVELri0P4Sr2g=">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</latexit> x <latexit sha1_base64="BkOuic6isW1cYY2ZNWiUOdOU/tM=">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</latexit> y <latexit sha1_base64="getvLqfzl+lmP3jVELri0P4Sr2g=">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</latexit> interpolative prediction (High-dimensional) High Low Model Complexity Underfitting (High bias, Low variance) Overfitting (Low bias, High variance) "The bias-variance tradeoff" The training data f(x; ✓) <latexit sha1_base64="33zlDWOHXmZvZwuGF4JM5OwSths=">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</latexit> extrapolative prediction
  22. Multilevel representations of chemical reactions Brc1cncc(Br)c1 C[O-] CN(C)C=O Na+ COc1cncc(Br)c1

    SMILES Structural Formla Steric Structures Electronic States Reactants Reagents Products As pattern languages (e.g. known facts in textbooks/databases) As physical entities (e.g. quantum chemical calculations)
  23. ML-based chemical reaction predictions 3N-MCTS/AlphaChem Segler+ Nature 2018 Molecular Transformer

    Schwaller+ ACS Cent Sci 2019 seq2seq Liu+ ACS Cent Sci 2017 WLDN Jin+ NeurIPS 2017 ELECTRO Bradshaw+ICLR 2019 WLN Coley+ Chem Sci 2019 GPTN Do+ KDD 2019 Graph NN Sequence NN Combined or Other IBM RXN Schwaller+ Chem Sci 2018 Molecule Chef Bradshaw+ DeepGenStruct (ICLR WS) 2019 Neural-Symbolic ML Segler+ Chemistry 2017 Similarity-based Coley+ ACS Cent Sci 2017 Fermionic Neural Network Pfau+ Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks. 
 arXiv:1909.02487, Sep 2019. ML + First-principle simulations Hamiltonian Graph Networks with ODE Integrators Sanchez-Gonzalez+ Hamiltonian Graph Networks with ODE Integrators. 
 arXiv:1909.12790, Sep 2019. Both from GLN Dai+ NeurIPS2019 Transformer Karpov+ ICANN 2019
  24. ࢀߟ̍) GNNs (Graph Neural Networks) • "グラフ構造"を⼊⼒にとるニューラルネットワーク. • 主要な機械学習の国際会議ではほぼこのテーマのWorkshopを開催 •

    2019夏以降論⽂も激増, 様々なタスクで道具に使われている e.g.) Bengio+ Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon. https://arxiv.org/abs/1811.06128 (2018) • 低分⼦化合物は分⼦グラフとして分析されることから、Chemoinformatics/ Materials informatics分野の応⽤論⽂も最近たくさん • 現⾏のGNNは技術的限界もよくわかってきた (NeurIPS2019で複数の分析論⽂) こうしたいくつかの限界の技術的解決が可能なのかが機械学習分野の関⼼
  25. ࢀߟ̎) Sequence Neural Networks (ಛʹTransformers/Attention) • 何らかのSequenceを受け取るニューラルネットワーク • 機械翻訳や⽂章要約などの⾃然⾔語処理(NLP)タスクが主対象 •

    古典的にはLSTM/GRUなどをユニットにしたRecurrent NNで⾏われてきた • Googleの"Transformers"の発表とそれに基づく⾔語モデルBERTの⼤ブレイク で分野が様変わり (⾔語タスクでも事前学習が極めて有効に) • RNNは学習が遅いので(Attentionつきの)CNNが使われるようになったあとに登場 • Transformer構造はマルチヘッドのAttentionをstackするとてもシンプルな構造 (かつAttention Weightsを⾏列積ベースにモデル化することでScalabilityを持つ)
  26. Խֶ൓Ԡ/߹੒ܦ࿏ͷ༧ଌʹؔ܎͢ΔReview Papers • Coley CW, Green WH, Jensen KF. Machine

    Learning in Computer-Aided Synthesis Planning. Acc Chem Res. 2018 May 15;51(5):1281-1289. doi: 10.1021/acs.accounts.8b00087. • Szymkuć S, Gajewska EP, Klucznik T, Molga K, Dittwald P, Startek M, Bajczyk M, Grzybowski BA. Computer-Assisted Synthetic Planning: The End of the Beginning. Angew Chem Int Ed Engl. 2016 May 10;55(20):5904-37. doi: 10.1002/anie.201506101.
  27. REVIEW Inverse molecular design using machine learning: Generative models for

    matter engineering Benjamin Sanchez-Lengeling1 and Alán Aspuru-Guzik2,3,4* The discovery of new materials can bring enormous societal and technological progress. In this context, exploring completely the large space of potential materials is computationally intractable. Here, we review methods for achieving inverse design, which aims to discover tailored materials from the starting point of a particular desired functionality. Recent advances from the rapidly growing field of artificial intelligence, mostly from the subfield of machine learning, have resulted in a fertile exchange of ideas, where approaches to inverse molecular design are being proposed and employed at a rapid pace. Among these, deep generative models have been applied to numerous classes of materials: rational design of prospective drugs, synthetic routes to organic compounds, and optimization of photovoltaics and redox flow batteries, as well as a variety of other solid-state materials. Many of the challenges of the 21st century (1), from personalized health care to energy production and storage, share a common theme: materials are part of the solution (2). In some cases, the solu- tions to these challenges are fundamentally limited by the physics and chemistry of a ma- terial, such as the relationship of a materials bandgap to the thermodynamic limits for the generation of solar energy (3). Several important materials discoveries arose by chance or through a process of trial and error. For example, vulcanized rubber was prepared in the 19th century from random mixtures of com- pounds, based on the observation that heating with additives such as sulfur improved the rubber’s durability. At the molecular level, in- dividual polymer chains cross-linked, forming bridges that enhanced the macroscopic mechan- ical properties (4). Other notable examples in this vein include Teflon, anesthesia, Vaseline, Perkin’s mauve, and penicillin. Furthermore, these materials come from common chemical compounds found in nature. Potential drugs either were prepared by synthesis in a chem- ical laboratory or were isolated from plants, soil bacteria, or fungus. For example, up until 2014, 49% of small-molecule cancer drugs were natural products or their derivatives (5). In the future, disruptive advances in the dis- covery of matter could instead come from unex- plored regions of the set of all possible molecular and solid-state compounds, known as chemical space (6, 7). One of the largest collections of molecules, the chemical space project (8), has mapped 166.4 billion molecules that contain at most 17 heavy atoms. For pharmacologically rele- vant small molecules, the number of structures is estimated to be on the order of 1060 (9). Adding consideration of the hierarchy of scale from sub- nanometer to microscopic and mesoscopic fur- ther complicates exploration of chemical space in its entirety (10). Therefore, any global strategy for covering this space might seem impossible. Simulation offers one way of probing this space without experimentation. The physics and chemistry of these molecules are governed by quantum mechanics, which can be solved via the Schrödinger equation to arrive at their ex- act properties. In practice, approximations are used to lower computational time at the cost of accuracy. Although theory enjoys enormous progress, now routinely modeling molecules, clusters, and perfect as well as defect-laden periodic solids, the size of chemical space is still overwhelming, and smart navigation is required. For this purpose, machine learning (ML), deep learning (DL), and artificial intelligence (AI) have a potential role to play because their computational strategies automatically improve through experience (11). In the context of materials, ML techniques are often used for property prediction, seeking to learn a function that maps a molecular material to the property of choice. Deep generative models are a special class of DL methods that seek to model the underlying probability distribution of both structure and property and relate them in a nonlinear way. By exploiting patterns in massive datasets, these models can distill average and salient features that characterize molecules (12, 13). Inverse design is a component of a more complex materials discovery process. The time scale for deployment of new technologies, from discovery in a laboratory to a commercial pro- duct, historically, is 15 to 20 years (14). The pro- cess (Fig. 1) conventionally involves the following steps: (i) generate a new or improved material concept and simulate its potential suitability; (ii) synthesize the material; (iii) incorporate the ma- terial into a device or system; and (iv) characterize and measure the desired properties. This cycle generates feedback to repeat, improve, and re- fine future cycles of discovery. Each step can take up to several years. In the era of matter engineering, scientists seek to accelerate these cycles, reducing the FRONTIERS IN COMPUTATION 1Department of Chemistry and Chemical Biology, Harvard LOSKI on July 26, 2018 http://science.sciencemag.org/ Downloaded from REVIEW https://doi.org/10.1038/s41586-018-0337-2 Machine learning for molecular and materials science Keith T. Butler1, Daniel W . Davies2, Hugh Cartwright3, Olexandr Isayev4* & Aron Walsh5,6* Here we summarize recent progress in machine learning for the chemical sciences. We outline machine-learning techniques that are suitable for addressing research questions in this domain, as well as future directions for the field. We envisage a future in which the design, synthesis, characterization and application of molecules and materials is accelerated by artificial intelligence. The Schrödinger equation provides a powerful structure– property relationship for molecules and materials. For a given spatial arrangement of chemical elements, the distribution of electrons and a wide range of physical responses can be described. The development of quantum mechanics provided a rigorous theoretical foundation for the chemical bond. In 1929, Paul Dirac famously proclaimed that the underlying physical laws for the whole of chemistry are “completely known”1. John Pople, realizing the importance of rapidly developing computer technologies, created a program—Gaussian 70—that could perform ab initio calculations: predicting the behaviour, for molecules of modest size, purely from the fundamental laws of physics2. In the 1960s, the Quantum Chemistry Program Exchange brought quantum chemistry to the masses in the form of useful practical tools3. Suddenly, experi- mentalists with little or no theoretical training could perform quantum calculations too. Using modern algorithms and supercomputers, systems containing thousands of interacting ions and electrons can now be described using approximations to the physical laws that govern the world on the atomic scale4–6. The field of computational chemistry has become increasingly pre- dictive in the twenty-first century, with activity in applications as wide ranging as catalyst development for greenhouse gas conversion, materials discovery for energy harvesting and storage, and computer-assisted drug design7. The modern chemical-simulation toolkit allows the properties of a compound to be anticipated (with reasonable accuracy) before it has been made in the laboratory. High-throughput computational screening has become routine, giving scientists the ability to calculate the properties of thousands of compounds as part of a single study. In particular, den- sity functional theory (DFT)8,9, now a mature technique for calculating the structure and behaviour of solids10, has enabled the development of extensive databases that cover the calculated properties of known and hypothetical systems, including organic and inorganic crystals, single molecules and metal alloys11–13. The emergence of contemporary artificial-intelligence methods has the potential to substantially alter and enhance the role of computers in science and engineering. The combination of big data and artificial intel- ligence has been referred to as both the “fourth paradigm of science”14 and the “fourth industrial revolution”15, and the number of applications in the chemical domain is growing at an astounding rate. A subfield of artificial intelligence that has evolved rapidly in recent years is machine generating, testing and refining scientific models. Such techniques are suitable for addressing complex problems that involve massive combi- natorial spaces or nonlinear processes, which conventional procedures either cannot solve or can tackle only at great computational cost. As the machinery for artificial intelligence and machine learning matures, important advances are being made not only by those in main- stream artificial-intelligence research, but also by experts in other fields (domain experts) who adopt these approaches for their own purposes. As we detail in Box 1, the resources and tools that facilitate the application of machine-learning techniques mean that the barrier to entry is lower than ever. In the rest of this Review, we discuss progress in the application of machine learning to address challenges in molecular and materials research. We review the basics of machine-learning approaches, iden- tify areas in which existing methods have the potential to accelerate research and consider the developments that are required to enable more wide-ranging impacts. Nuts and bolts of machine learning With machine learning, given enough data and a rule-discovery algo- rithm, a computer has the ability to determine all known physical laws (and potentially those that are currently unknown) without human input. In traditional computational approaches, the computer is little more than a calculator, employing a hard-coded algorithm provided by a human expert. By contrast, machine-learning approaches learn the rules that underlie a dataset by assessing a portion of that data and building a model to make predictions. We consider the basic steps involved in the construction of a model, as illustrated in Fig. 1; this constitutes a blueprint of the generic workflow that is required for the successful application of machine learning in a materials-discovery process. Data collection Machine learning comprises models that learn from existing (train- ing) data. Data may require initial preprocessing, during which miss- ing or spurious elements are identified and handled. For example, the Inorganic Crystal Structure Database (ICSD) currently contains more than 190,000 entries, which have been checked for technical mistakes but are still subject to human and measurement errors. Identifying DNA to be sequences into distinct pieces, parcel out the detailed work of sequencing, and then reassemble these independent ef- forts at the end. It is not quite so simple in the world of genome semantics. Despite the differences between genome se- quencing and genetic network discovery, there are clear parallels that are illustrated in Table 1. In genome sequencing, a physical map is useful to provide scaffolding for assembling the fin- ished sequence. In the case of a genetic regula- tory network, a graphical model can play the same role. A graphical model can represent a high-level view of interconnectivity and help isolate modules that can be studied indepen- dently. Like contigs in a genomic sequencing project, low-level functional models can ex- plore the detailed behavior of a module of genes in a manner that is consistent with the higher level graphical model of the system. With stan- dardized nomenclature and compatible model- ing techniques, independent functional models can be assembled into a complete model of the cell under study. To enable this process, there will need to be standardized forms for model representa- tion. At present, there are many different modeling technologies in use, and although models can be easily placed into a database, they are not useful out of the context of their specific modeling package. The need for a standardized way of communicating compu- tational descriptions of biological systems ex- tends to the literature. Entire conferences have been established to explore ways of mining the biology literature to extract se- mantic information in computational form. Going forward, as a community we need to come to consensus on how to represent what we know about biology in computa- tional form as well as in words. The key to postgenomic biology will be the computa- tional assembly of our collective knowl- edge into a cohesive picture of cellular and organism function. With such a comprehen- sive model, we will be able to explore new types of conservation between organisms and make great strides toward new thera- peutics that function on well-characterized pathways. References 1. S. K. Kim et al., Science 293, 2087 (2001). 2. A. Hartemink et al., paper presented at the Pacific Symposium on Biocomputing 2000, Oahu, Hawaii, 4 to 9 January 2000. 3. D. Pe’er et al., paper presented at the 9th Conference on Intelligent Systems in Molecular Biology (ISMB), Copenhagen, Denmark, 21 to 25 July 2001. 4. H. McAdams, A. Arkin, Proc. Natl. Acad. Sci. U.S.A. 94, 814 ( 1997 ). 5. A. J. Hartemink, thesis, Massachusetts Institute of Technology, Cambridge (2001). V I E W P O I N T Machine Learning for Science: State of the Art and Future Prospects Eric Mjolsness* and Dennis DeCoste Recent advances in machine learning methods, along with successful applications across a wide variety of fields such as planetary science and bioinformatics, promise powerful new tools for practicing scientists. This viewpoint highlights some useful characteristics of modern machine learn- ing methods and their relevance to scientific applications. We conclude with some speculations on near-term progress and promising directions. Machine learning (ML) (1) is the study of computer algorithms capable of learning to im- prove their performance of a task on the basis of their own previous experience. The field is closely related to pattern recognition and statis- tical inference. As an engineering field, ML has become steadily more mathematical and more successful in applications over the past 20 years. Learning approaches such as data clus- tering, neural network classifiers, and nonlinear regression have found surprisingly wide appli- cation in the practice of engineering, business, and science. A generalized version of the stan- dard Hidden Markov Models of ML practice have been used for ab initio prediction of gene structures in genomic DNA (2). The predictions correlate surprisingly well with subsequent gene expression analysis (3). Postgenomic bi- ology prominently features large-scale gene ex- pression data analyzed by clustering methods (4), a standard topic in unsupervised learning. Many other examples can be given of learning and pattern recognition applications in science. Where will this trend lead? We believe it will lead to appropriate, partial automation of every element of scientific method, from hypothesis generation to model construction to decisive experimentation. Thus, ML has the potential to amplify every aspect of a working scientist’s progress to understanding. It will also, for better or worse, endow intelligent computer systems with some of the general analytic power of scientific thinking. Machine Learning at Every Stage of the Scientific Process Each scientific field has its own version of the scientific process. But the cycle of observing, creating hypotheses, testing by decisive exper- iment or observation, and iteratively building up comprehensive testable models or theories is shared across disciplines. For each stage of this abstracted scientific process, there are relevant developments in ML, statistical inference, and pattern recognition that will lead to semiauto- matic support tools of unknown but potentially broad applicability. Increasingly, the early elements of scientific method—observation and hypothesis genera- tion—face high data volumes, high data acqui- sition rates, or requirements for objective anal- ysis that cannot be handled by human percep- tion alone. This has been the situation in exper- imental particle physics for decades. There automatic pattern recognition for significant events is well developed, including Hough transforms, which are foundational in pattern recognition. A recent example is event analysis for Cherenkov detectors (8) used in neutrino oscillation experiments. Microscope imagery in cell biology, pathology, petrology, and other fields has led to image-processing specialties. So has remote sensing from Earth-observing satellites, such as the newly operational Terra spacecraft with its ASTER (a multispectral thermal radiometer), MISR (multiangle imag- ing spectral radiometer), MODIS (imaging Machine Learning Systems Group, Jet Propulsion Lab- oratory/California Institute of Technology, Pasadena, CA, 91109, USA. *To whom correspondence should be addressed. E- mail: [email protected] Table 1. Parallels between genome sequencing and genetic network discovery. Genome sequencing Genome semantics Physical maps Graphical model Contigs Low-level functional models Contig reassembly Module assembly Finished genome sequence Comprehensive model www.sciencemag.org SCIENCE VOL 293 14 SEPTEMBER 2001 2051 C O M P U T E R S A N D S C I E N C E on August 29, 2018 http://science.sciencemag.org/ Downloaded from Nature, 559
 pp. 547–555 (2018) Science, 293 pp. 2051-2055 (2001) Science, 361 pp. 360-365 (2018) Science is changing, the tools of science are changing. And that requires different approaches. ── Erich Bloch, 1925-2016 教訓 "low input, high throughput, no output science." (Sydney Brenner) → 雑な設定・系で網羅的なハイスループット実験をいくらしても何も得られない 「データ利活⽤技術」は科学研究の道具の⼀つに
  28. 観察データだけでは不⼗分 + データの解析のアヤ https://www.chemistryworld.com/news/dispute-over-reaction-prediction-puts-machine-learnings-pitfalls-in-spotlight/ 3009912.article • Science論⽂ "Predicting reaction performance

    in C‒N cross-coupling using machine learning" • Main paper https://doi.org/10.1126/science.aar5169 • Erratum https://doi.org/10.1126/science.aat7648 • Negative comment paper https://doi.org/10.1126/science.aat8603 • Author's response https://doi.org/10.1126/science.aat8763 機械学習は与えられた⾒本データを代表する予測モデルを作る技術で「どのよう なデータで学習したか」が肝. 結果の再現性のなさは機械学習分野でも問題に
  29. (Review) Machine learning for catalysis informatics: 
 recent applications and

    prospects.
 Toyao T, Maeno Z, Takakusagi S, Kamachi T, Takigawa I*, Shimizu K*.
 ACS Catalysis, Accepted. Reviewer: 1 I don't usually recommend that papers should be accepted "as is", but in this case I don't see the need for changes. This review should be accepted and published in ACS Catalysis. ... I will certainly recommend it to my group and my students when it is published. Reviewer: 2 The manuscript gives an excellent over the field of machine learning especially with regard to heterogeneous catalysis and I would highly recommend the article for the publication in ACS Catalysis. Reviewer: 3 This is one of the best reviews for catalyst informatics that the Reviewer has read. In particular, the chapter 2 delivers a very good tutorial, which is concisely and professionally written. Chapter 2が機械学習のユーザガイドになっています!↓査読者からのお薦めの⾔葉
  30. 化学反応の予測 ① Theory-driven (Quantum Chem) ② Knowledge-driven (Knowledge Bases) ③

    Data-driven (Machine Learning) 化学反応をどのような表現・レベルで捉えるか? 量⼦・電⼦系 〜 複雑系・⽣体系 1分⼦レベルでの表現の多様性 技術的融合により化学反応の多⾓性・多因⼦性を捉える
  31. ① Theory-driven (Quantum Chem) ② Knowledge-driven (Knowledge Bases) ③ Data-driven

    (Machine Learning) 計算科学・実験科学・情報科学による化学反応設計と探索
  32. ΞϯϞχΞͷ޻ۀత߹੒
 (ϋʔόʔɾϘογϡ๏) మܥ৮ഔͳͲ NOx CO HC N2 CO2 H2O ഉؾΨε(༗ಟ)

    ແ֐Խ وۚଐ৮ഔͳͲ (Pt, Pd, Rh…) • Τλϯ • ΤνϨϯ • ϝλϊʔϧ • : ϝλϯ ۚଐ৮ഔ (Li, ر౔ྨ, ΞϧΧϦ౔ྨ) ഉؾΨεͷড়Խ ϝλϯస׵ “ਫͱੴ୸ͱۭؾ͔ΒύϯΛ࡞Δํ๏” 20ੈلͷ৯ྐ೉Λղܾͨ͠ਓ޻త஠ૉݻఆ adsorption diffusio desorption dissociati recombinatio kinks terraces adatom vacancy steps 気相 (反応物) 固相 (触媒) 計算での扱いがまだまだ難しい例:不均⼀系触媒 Heterogeneous Catalysis • 固体表⾯での気相反応 (複雑系) • 吸着・乖離・拡散・反応・脱離 など複数の素反応過程の関与 • 多数の因⼦に依存: 触媒組成、 担持⾦属ナノ粒⼦のサイズや形状、 担体表⾯の終端構造、反応温度や ガス圧⼒等の反応条件、...
  33. 1. Predicting the d-band centers by ML
 Takigawa I*, Shimizu

    K, Tsuda K, Takakusagi S
 RSC Advances. 2016; 6: 52587-52595. 2. Predicting the adsorption energy by ML
 Toyao T*, Suzuki K, Kikuchi S, Takakusagi S, Shimizu K, Takigawa I*.
 The Journal of Physical Chemistry C. 2018; 122(15): 8315-8326. 3. Predicting the experimentally-reported catalytic activity by ML
 Suzuki K, Toyao T, Maeno Z, Takakusagi S, Shimizu K*, Takigawa I*.
 ChemCatChem. 2019; 11(18): 4537-4547. (Front Cover) 機械学習に基づく研究3事例を紹介 (with 触媒科学研究所) (Review) Machine learning for catalysis informatics: 
 recent applications and prospects.
 Toyao T, Maeno Z, Takakusagi S, Kamachi T, Takigawa I*, Shimizu K*.
 ACS Catalysis, Accepted.
  34. Heterogeneous Catalysis Haber–Bosch Process Ferrous Metal Catalysis NOx CO HC

    N2 CO2 H2O Exhaust Gas Harmless gas Noble Metal Catalysis (Pt, Pd, Rh…) • Ethane • Ethylene • Methanol • : Methane Various Metallic Catalysts
 (Li, rare earthes, alkaline earths) (industrial synthesis of ammonia) Exhaust Gas Purification Conversion of Methane “Fertilizer from Air” artificial nitrogen fixation • Heterogeneous catalysis is a type of catalysis in which the catalyst occupies a different phase from the reactants and products. • It can be more easily recycled than homogeneous, but characterization of the catalyst and optimization of properties can be more difficult. • It is of paramount importance in many areas of the chemical and energy industries.
  35. Heterogeneous Catalysis Wolfgang Pauli “God made the bulk; 
 the

    surface was invented by the devil.” adsorption diffusio desorption dissociati recombinatio kinks terraces adatom vacancy steps Gas-Phase (Reactants) Sold-Phase (Catalysts) Many hard-to-quantify intertwined factors involved. Too complicated (impossible?) to model everything... • multiple elementary reaction processes • composition, support, surface termination, particle size, particle morphology, atomic coordination environment • reaction conditions Notoriously complex surface reactions between different phases.
  36. Our ML-based case studies 1. Can we predict the d-band

    center? 2. Can we predict the adsorption energy? 3. Can we predict the catalytic activity? predicting DFT-calculated values by machine learning (Takigawa et al, RSC Advances, 2016) predicting DFT-calculated values by machine learning (Toyao et al, JPCC, 2018) predicting values from experiments reported in the literature by machine learning (Suzuki et al, ChemCatChem, 2019)
  37. How to understand the catalytic activities? K. Shimizu et al,

    ACS Catal. 2, 1904 (2012) d-band center (εd − EF ) / eV d-band center (εd − EF ) / eV Hammer‒Nørskov d-band model reaction rates Volcano trends! adsorption energy / eV Brønsted-Evans-Polanyi relation activation energy / eV Linear trends! Traditionally, the computable indexes that well correlate the catalytic activities have been investigated...
  38. Case 1. Predicting the d-band centers Guest Host Ruban, Hammer,

    Stoltze, Skriver, Nørskov, J Mol Catal A, 115:421-429 (1997) J. K. Nørskov, et al., Advances in Catalysis, 2000 Host Guest Two types of models • 1% doped • overlayer [1% doped] The d-band center is one of the established indexes to understand the trends of heterogeneous catalysts (transition metals based).
  39. Simple ML can accurately predict them... •Group (G) •Bulk Wigner‒Seitz

    radius (R) in Å •Atomic number (AN) •Atomic mass (AM) in g mol−1 •Period (P) •Electronegativity (EN) •Ionization energy (IE) in eV •Enthalpy of fusion (∆fusH) in J g−1 •Density at 25 ℃ (ρ) in g cm−3 (1) Group in the periodic table (host) (2) Density at 25 ℃ (host) (3) Enthalpy of fusion (guest) (4) Ionization energy (guest) (5) Enthalpy of fusion (host) (6) Ionization energy (host) We showed that gradient boosted trees with only 6 descriptors below
 can predict the d-band centers without any first-principles calculations. 9 types of readily
 available values pretested
  40. Fe Co Ni Cu Ru Rh Pd Ag Ir Pt

    Au Fe -0.92 -0.96 -0.97 -1.65 -1.64 -2.24 -1.87 -2.4 -3.11 Co -1.37 -1.23 -2.12 -2.82 -2.53 -2.26 -3.56 Ni -0.33 -1.18 -1.92 -2.03 -2.43 -2.15 -2.82 -3.39 Cu -2.42 -2.49 -2.67 -2.89 -2.94 -3.82 -4.63 Ru -1.11 -1.04 -1.12 -1.41 -1.88 -1.81 -1.54 -2.27 Rh -1.42 -1.32 -1.51 -1.7 -1.73 -2.12 -1.81 -1.7 -2.18 -2.3 Pd -1.47 -1.29 -1.29 -1.03 -1.58 -1.83 -1.68 -1.52 -1.79 Ag -3.75 -3.56 -3.62 -3.8 -4.03 -3.5 -3.93 -4.51 Ir -1.78 -1.71 -1.78 -1.55 -2.14 -2.53 -2.2 -2.11 -2.6 -2.7 Pt -1.71 -1.47 -2.13 -2.01 -2.23 -2.06 -1.96 -2.33 Au -3.03 -2.82 -2.85 -2.89 -3.44 -3.56 Fe Co Ni Cu Ru Rh Pd Ag Ir Pt Au Fe -0.78 -1.65 -1.64 -1.87 Co -1.18 -1.17 -1.37 -1.87 -2.12 -2.82 -2.26 Ni -0.33 -1.18 -1.17 -2.61 -2.43 -2.15 -2.82 Cu -2.42 -2.89 -2.94 -3.88 -4.63 Ru -1.11 -1.04 -1.12 -1.11 -1.41 -1.81 -2.27 Rh -1.42 -1.51 -2.12 -1.81 -1.7 Pd -1.29 -1.29 -1.03 -1.58 -1.83 -1.52 -1.79 Ag -3.68 -3.8 -3.63 -4.51 Ir -2.14 -2.11 -2.7 Pt -1.71 -1.47 -2.13 -2.01 -2.23 -2.06 Au -2.86 -3.09 -2.89 -3.44 -3.56 Fe Co Ni Cu Ru Rh Pd Ag Ir Pt Au Fe -2.17 -3.11 Co -1.17 -1.37 -2.12 Ni -0.33 -1.18 -2.61 -2.43 Cu -2.42 -2.29 -2.49 -3.71 -4.63 Ru -2.02 Rh -1.32 -1.73 -2.12 Pd -1.94 -1.83 -1.97 Ag -3.75 -3.68 -4.51 Ir -1.78 -1.71 -2.7 Pt -2.13 Au -3.09 -2.89 training sets (75%) test sets (25%) training sets (50%) test sets (50%) training sets (25%) test sets (75%) gradient boosting w/ 6 descriptors gradient boosting w/ 6 descriptors gradient boosting w/ 6 descriptors 100 times
 mean RMSE: 0.153 / eV 100 times
 mean RMSE: 0.235 / eV 100 times
 mean RMSE: 0.402 / eV ML Prediction (without any quantum calculations)
  41. Descriptor analysis and selection 100 times mean RMSE: 0.204±0.047 /

    eV 100 times mean RMSE: 0.212±0.047 / eV 100 times mean RMSE: 0.214±0.046 / eV      *NQPSUBODFPGEFTDSJQUPS (VFTU      *NQPSUBODFPGEFTDSJQUPS (SPVQ #VML8JHOFS4FJU[SBEJVT "UPNJD/VNCFS "UPNJD.BTT 1FSJPE &OUIBMQZPGGVTJPO *POJ[BUJPOFOFSHZ &MFDUSPOFHBUJWJUZ %FOTJUZBU P$ )PTU       GBR with 18 descriptors GBR with 6 descriptors GBR with 4 descriptors Descriptor Importances Descriptor Selection
 (top-k) training sets (75%) test sets (25%) Analyzing the prediction model trained with the current data also provides some insights on contributing factors, and variable selection.
  42. DFT calculation of adsorption energy • 10 hours with our

    32 cores workstation 
 (CH3 on the Cu monometallic surface) • even longer time (about 34 hours) for the system containing another metal such as Pb Predicting Adsorption energy of CH3 (on 46 Cu-based alloys) ML prediction • < 1 sec with our 1 core laptop • not dependent on target systems, but methods we choose training sets (75%) test sets (25%) Adsorbates: 
 CH3, CH2, CH, C, H Case 2. Predicting the adsorption energy
  43. Case 3. Predicting the experimental catalyst activities For some reactions,

    large datasets from already published results are available. Why not just directly applying ML to them! • Oxidative coupling of methane (OCM) 
 1866 catalysts [Zavyalova+ 2011] • Water gas shift reaction (WGS) 
 4360 catalysts [Odabaşi+ 2014] • CO oxidation 
 5610 catalysts [Günay+ 2013] Collections from various papers published in the past including • catalyst compositions, support types, promotor types • catalyst performance (C2 yields, CO conversion) • experimental conditions (pressure, temperature, etc)
  44. Two big problems we had • Problem 1: Data sparsity

    (Low sample counts for many elements) OCM WGS CO oxidation # Catal: 1866 # Elem: 74 # Catal: 4360 # Elem: 51 # Catal: 5610 # Elem: 31 • For compositions, only a few are non-zero. (very sparse table) • Non-zero elements are very biased, many elements have only a few nonzero samples (low sample counts), and statistically negligible...
  45. Two big problems we had Cat-ABC = (0.90, 0.06, 0.04,

    0.00, 0.00) catalyst with 90% A, 6% B, and 4% C catalyst with 60% D, 30% B, and 10% C catalyst with 60% E, 30% B, and 10% C Cat-BCD = (0.00, 0.30, 0.10, 0.60, 0.00) Cat-BCE = (0.00, 0.30, 0.10, 0.00, 0.60) A B C D E • The similarities for ABC-BCD and ABC-BCE becomes the same... • For large datasets, this composition vectors are very sparse and mostly the overlapped elements are only one or two (or even zero...) • Problem 1: Data sparsity (Less compositional overlaps) OCM OCM WGS WGS CO oxidation CO oxidation # elems in a catalyst # overlapped elems (for a pair)
  46. Catalyst A B C D Exp. conditions Catal-1 0.90 0.06

    0.04 0.00 Catal-2 0.00 0.10 0.00 0.90 • Sparse (many zeros), and less compositional overlaps • low sample count for many elements except a few very widely used elements, and hard to directly compare Element Desc-1 Desc-2 … Desc-p A 2 1.67 103.1 B 21 0.37 0.9 C 16 2.30 40.1 D 69 6.20 23.6 Catalyst Performance Catal-1 20.4 Catal-2 6.8 ML Literature data Prediction All elements appeared in the data (many and diverse elements) Elemental descriptors (features) Catalyst A B C D Primary feat. Secondary feat. Tertiary feat. Exp. conditions Catal-1 0.90 0.06 0.04 0.00 0.90 0.06 0.04 Catal-2 0.00 0.10 0.00 0.90 0.90 0.10 0.00 Desc(A) Desc(B) Desc(C) Desc(B) Desc(D) Features from not contained elements are zero out Proposed (High-dimensionality is addressed by ML methods) Elemental features are considered for catalyst characterization Compositional information … … … • Periodic table • Handbook • Textbook Our solution: Integrating elemental discriptors
  47. • Problem 2: Very strong "selection bias" in existing datasets

    Catalyst research has relied heavily on prior published data, tends to be biased toward catalyst composition that were successful Two big problems we had Example) Oxidative coupling of methane (OCM) • 1868 catalysts in the original dataset [Zavyalova+ 2011] • Composed of 68 different elements: 61 cations and 7 anions (Cl, F, Br, B, S, C, and P) excluding oxygen • only 317 catalysts performed well with C2 yields 15% and 
 C2 selectivity 50%; Occurrences of only a few elements such as La, Ba, Sr, Cl, Mn, and F are very high. • Widely used elements such as Li, Mg, Na, Ca, and La also frequent in the data
  48. An ML model is just representative of the training data

    Highly Inaccurate Model Predictions from Extrapolation (Lohninger 1999) "Beware of the perils of extrapolation, and understand that ML algorithms build models that are representative of the available training samples." "exploitation" "exploration" to obtain new knowledge/data to use the knowledge/data to improve the performane We also need this ML basically for this
  49. No guarantee of data-driven for the outside of given data

    Cause-and-Effect
 Relationship Related factors
 (and their states) Outcome Reactions Some mechanism [Inputs] [Outputs] Data-driven methods try to precisely approximate its outer behavior (the input-output relationship) observable as "data". 
 (e.g. through machine learning from a large collection of data) Keep in mind: Given data DEFINES the data-driven prediction! Theory-driven methods try to explicitly model the inner workings of a target phenomenon (e.g. through first-principles simulations) governing equation?
  50. Empirical optimization: "Edisonian empiricism" 既知の知⾒・ 観測(データ) • 実験 • シミュレーション

    仮説形成 結果の確認と 検証 次の実験計画へ feedback • Genius is 1% inspiration and 99% perspiration. • There is no substitute for hard work. • I have not failed. I've just found 10,000 ways that won't work. : 問題:時間とコストは有限!! 理論的に可能なあらゆる候補を この⽅式で検証することは不可能 よく考えるとブラックなことしか⾔ってない! 仮説検証 "観察と帰納 (empirical/inductive)" "論理と演繹 (rational/deductive)" Thomas Edisonઌੜ
  51. ՊֶతൃݟͱηϨϯσΟϐςΟ 既知の知⾒・ 観測(データ) • 実験 • シミュレーション 仮説形成 結果の確認と 検証

    次の実験計画へ feedback • それゆえ「研究者のセンス・腕の⾒せ所」+「幸運(セレンディピティ)」に依存する 筋の良さそうな候補を選ぶ、今まで試されてない全く新しいやり⽅を思いつく、etc • 候補があまりに膨⼤(実質ほぼ無限)なので(数多く試すのは有利だとは⾔え...) 必ずしも「⼒技とお⾦と⼈海戦術で数多く試した者が勝つ」とは限らない • 仮説形成はふつう完全に⾏き当たりばったりではない。「勘と経験」が⾮常に⼤切。 すばらしい発⾒は...「完全に運」<「幸運は準備された者に降りる」 問題:時間とコストは有限!! 理論的に可能なあらゆる候補を この⽅式で検証することは不可能 仮説検証
  52. ػցֶश/σʔλՊֶͷར༻ʹجͮ͘࠷ద࣮ݧܭըʁ 既知の知⾒・ 観測(データ) 結果の確認と 検証 ⾼速・⾼精度な Data-Driven予測 次の実験計画へ feedback 仮説形成

    (シミュレーション+実験) • 再現性を担保する⾼精度・⾼速実験系 • 仮想化検証が可能な因⼦のシミュレー ション(計算科学)による探索 → 望ましい対象のさらなる絞り込み 仮説検証 (機械学習・データマイニング) • どういう実験・シミュレーションを 次に⾏うかの計画⽴案 • 時間のかかる計算の⾼精度⾼速近似 • 曖昧な因⼦や実験条件の最適化 • Multilevelの情報統合
  53. Model-based optimization Check and validate results predictions Machine Learning or

    any "data- driven" 
 predictions The "Surrogate" model for • Demanding experiments • Time-consuming hi-fidelity simulations Available data and findings Generate hypotheses Grrr, give me any 
 serendipity...
  54. Model-based optimization Check and validate results predictions Machine Learning or

    any "data- driven" 
 predictions The "Surrogate" model for • Demanding experiments • Time-consuming hi-fidelity simulations Available data and findings Generate hypotheses We need a mechanism balancing exploitation and exploration Grrr, give me any 
 serendipity...
  55. Machine Learning͸༩͑ͨσʔλΛ୅ද͢Δ͚ͩ 機械学習 = 訓練データの平均的法則性をとらえる 発⾒ = 訓練データの中にないものを⾒つけたい 予測モデルとの誤差の「期待値」を最⼩化 =

    汎化 ⼊⼒ (⼀般には⾼次元) 出⼒ x <latexit sha1_base64="BLB8K/n7QYAsE73zsDEUiBvCSV8=">AAAB/XicbVDLSgMxFL2pr1pfVZdugkVwVWZE0GXRjcsK9gHtUDJppo1NMkOSEctQ/AW3uncnbv0Wt36JaTsLbT1w4XDOvZzLCRPBjfW8L1RYWV1b3yhulra2d3b3yvsHTROnmrIGjUWs2yExTHDFGpZbwdqJZkSGgrXC0fXUbz0wbXis7uw4YYEkA8UjTol1UrMbyuxx0itXvKo3A14mfk4qkKPeK393+zFNJVOWCmJMx/cSG2REW04Fm5S6qWEJoSMyYB1HFZHMBNns2wk+cUofR7F2oyyeqb8vMiKNGcvQbUpih2bRm4r/eqFcSLbRZZBxlaSWKToPjlKBbYynVeA+14xaMXaEUM3d75gOiSbUusJKrhR/sYJl0jyr+l7Vvz2v1K7yeopwBMdwCj5cQA1uoA4NoHAPz/ACr+gJvaF39DFfLaD85hD+AH3+ADzJlfc=</latexit> <latexit sha1_base64="BLB8K/n7QYAsE73zsDEUiBvCSV8=">AAAB/XicbVDLSgMxFL2pr1pfVZdugkVwVWZE0GXRjcsK9gHtUDJppo1NMkOSEctQ/AW3uncnbv0Wt36JaTsLbT1w4XDOvZzLCRPBjfW8L1RYWV1b3yhulra2d3b3yvsHTROnmrIGjUWs2yExTHDFGpZbwdqJZkSGgrXC0fXUbz0wbXis7uw4YYEkA8UjTol1UrMbyuxx0itXvKo3A14mfk4qkKPeK393+zFNJVOWCmJMx/cSG2REW04Fm5S6qWEJoSMyYB1HFZHMBNns2wk+cUofR7F2oyyeqb8vMiKNGcvQbUpih2bRm4r/eqFcSLbRZZBxlaSWKToPjlKBbYynVeA+14xaMXaEUM3d75gOiSbUusJKrhR/sYJl0jyr+l7Vvz2v1K7yeopwBMdwCj5cQA1uoA4NoHAPz/ACr+gJvaF39DFfLaD85hD+AH3+ADzJlfc=</latexit> <latexit sha1_base64="BLB8K/n7QYAsE73zsDEUiBvCSV8=">AAAB/XicbVDLSgMxFL2pr1pfVZdugkVwVWZE0GXRjcsK9gHtUDJppo1NMkOSEctQ/AW3uncnbv0Wt36JaTsLbT1w4XDOvZzLCRPBjfW8L1RYWV1b3yhulra2d3b3yvsHTROnmrIGjUWs2yExTHDFGpZbwdqJZkSGgrXC0fXUbz0wbXis7uw4YYEkA8UjTol1UrMbyuxx0itXvKo3A14mfk4qkKPeK393+zFNJVOWCmJMx/cSG2REW04Fm5S6qWEJoSMyYB1HFZHMBNns2wk+cUofR7F2oyyeqb8vMiKNGcvQbUpih2bRm4r/eqFcSLbRZZBxlaSWKToPjlKBbYynVeA+14xaMXaEUM3d75gOiSbUusJKrhR/sYJl0jyr+l7Vvz2v1K7yeopwBMdwCj5cQA1uoA4NoHAPz/ACr+gJvaF39DFfLaD85hD+AH3+ADzJlfc=</latexit> <latexit sha1_base64="BLB8K/n7QYAsE73zsDEUiBvCSV8=">AAAB/XicbVDLSgMxFL2pr1pfVZdugkVwVWZE0GXRjcsK9gHtUDJppo1NMkOSEctQ/AW3uncnbv0Wt36JaTsLbT1w4XDOvZzLCRPBjfW8L1RYWV1b3yhulra2d3b3yvsHTROnmrIGjUWs2yExTHDFGpZbwdqJZkSGgrXC0fXUbz0wbXis7uw4YYEkA8UjTol1UrMbyuxx0itXvKo3A14mfk4qkKPeK393+zFNJVOWCmJMx/cSG2REW04Fm5S6qWEJoSMyYB1HFZHMBNns2wk+cUofR7F2oyyeqb8vMiKNGcvQbUpih2bRm4r/eqFcSLbRZZBxlaSWKToPjlKBbYynVeA+14xaMXaEUM3d75gOiSbUusJKrhR/sYJl0jyr+l7Vvz2v1K7yeopwBMdwCj5cQA1uoA4NoHAPz/ACr+gJvaF39DFfLaD85hD+AH3+ADzJlfc=</latexit> 平均的挙動 のモデル 訓練データの最⼤以上の 訓練データの最⼤ (期待誤差最⼩化) ⽬的物が外れ値(外挿的)で 分布の裾に来てしまう ⽬的が 不整合 「外れ値」 平均的(凡庸)なのは よく当たる...
  56. Optimal design of experiments / Active learning • Exploitation: 


    what we already know and get something close to what we expect • Exploration:
 something we aren't sure about and possibly learn more For next experiments, we face a dilemma in choosing between options. x <latexit sha1_base64="BLB8K/n7QYAsE73zsDEUiBvCSV8=">AAAB/XicbVDLSgMxFL2pr1pfVZdugkVwVWZE0GXRjcsK9gHtUDJppo1NMkOSEctQ/AW3uncnbv0Wt36JaTsLbT1w4XDOvZzLCRPBjfW8L1RYWV1b3yhulra2d3b3yvsHTROnmrIGjUWs2yExTHDFGpZbwdqJZkSGgrXC0fXUbz0wbXis7uw4YYEkA8UjTol1UrMbyuxx0itXvKo3A14mfk4qkKPeK393+zFNJVOWCmJMx/cSG2REW04Fm5S6qWEJoSMyYB1HFZHMBNns2wk+cUofR7F2oyyeqb8vMiKNGcvQbUpih2bRm4r/eqFcSLbRZZBxlaSWKToPjlKBbYynVeA+14xaMXaEUM3d75gOiSbUusJKrhR/sYJl0jyr+l7Vvz2v1K7yeopwBMdwCj5cQA1uoA4NoHAPz/ACr+gJvaF39DFfLaD85hD+AH3+ADzJlfc=</latexit> <latexit sha1_base64="BLB8K/n7QYAsE73zsDEUiBvCSV8=">AAAB/XicbVDLSgMxFL2pr1pfVZdugkVwVWZE0GXRjcsK9gHtUDJppo1NMkOSEctQ/AW3uncnbv0Wt36JaTsLbT1w4XDOvZzLCRPBjfW8L1RYWV1b3yhulra2d3b3yvsHTROnmrIGjUWs2yExTHDFGpZbwdqJZkSGgrXC0fXUbz0wbXis7uw4YYEkA8UjTol1UrMbyuxx0itXvKo3A14mfk4qkKPeK393+zFNJVOWCmJMx/cSG2REW04Fm5S6qWEJoSMyYB1HFZHMBNns2wk+cUofR7F2oyyeqb8vMiKNGcvQbUpih2bRm4r/eqFcSLbRZZBxlaSWKToPjlKBbYynVeA+14xaMXaEUM3d75gOiSbUusJKrhR/sYJl0jyr+l7Vvz2v1K7yeopwBMdwCj5cQA1uoA4NoHAPz/ACr+gJvaF39DFfLaD85hD+AH3+ADzJlfc=</latexit> <latexit sha1_base64="BLB8K/n7QYAsE73zsDEUiBvCSV8=">AAAB/XicbVDLSgMxFL2pr1pfVZdugkVwVWZE0GXRjcsK9gHtUDJppo1NMkOSEctQ/AW3uncnbv0Wt36JaTsLbT1w4XDOvZzLCRPBjfW8L1RYWV1b3yhulra2d3b3yvsHTROnmrIGjUWs2yExTHDFGpZbwdqJZkSGgrXC0fXUbz0wbXis7uw4YYEkA8UjTol1UrMbyuxx0itXvKo3A14mfk4qkKPeK393+zFNJVOWCmJMx/cSG2REW04Fm5S6qWEJoSMyYB1HFZHMBNns2wk+cUofR7F2oyyeqb8vMiKNGcvQbUpih2bRm4r/eqFcSLbRZZBxlaSWKToPjlKBbYynVeA+14xaMXaEUM3d75gOiSbUusJKrhR/sYJl0jyr+l7Vvz2v1K7yeopwBMdwCj5cQA1uoA4NoHAPz/ACr+gJvaF39DFfLaD85hD+AH3+ADzJlfc=</latexit> <latexit sha1_base64="BLB8K/n7QYAsE73zsDEUiBvCSV8=">AAAB/XicbVDLSgMxFL2pr1pfVZdugkVwVWZE0GXRjcsK9gHtUDJppo1NMkOSEctQ/AW3uncnbv0Wt36JaTsLbT1w4XDOvZzLCRPBjfW8L1RYWV1b3yhulra2d3b3yvsHTROnmrIGjUWs2yExTHDFGpZbwdqJZkSGgrXC0fXUbz0wbXis7uw4YYEkA8UjTol1UrMbyuxx0itXvKo3A14mfk4qkKPeK393+zFNJVOWCmJMx/cSG2REW04Fm5S6qWEJoSMyYB1HFZHMBNns2wk+cUofR7F2oyyeqb8vMiKNGcvQbUpih2bRm4r/eqFcSLbRZZBxlaSWKToPjlKBbYynVeA+14xaMXaEUM3d75gOiSbUusJKrhR/sYJl0jyr+l7Vvz2v1K7yeopwBMdwCj5cQA1uoA4NoHAPz/ACr+gJvaF39DFfLaD85hD+AH3+ADzJlfc=</latexit> ML༧ଌ <latexit sha1_base64="0VEGB1BS2t8KmbZWf3FuR1QlwM8=">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</latexit> هड़ࢠ(Ұൠʹ͸ߴ࣍ݩ) ׆ੑ
  57. Optimal design of experiments / Active learning • Exploitation: 


    what we already know and get something close to what we expect • Exploration:
 something we aren't sure about and possibly learn more For next experiments, we face a dilemma in choosing between options. x <latexit sha1_base64="BLB8K/n7QYAsE73zsDEUiBvCSV8=">AAAB/XicbVDLSgMxFL2pr1pfVZdugkVwVWZE0GXRjcsK9gHtUDJppo1NMkOSEctQ/AW3uncnbv0Wt36JaTsLbT1w4XDOvZzLCRPBjfW8L1RYWV1b3yhulra2d3b3yvsHTROnmrIGjUWs2yExTHDFGpZbwdqJZkSGgrXC0fXUbz0wbXis7uw4YYEkA8UjTol1UrMbyuxx0itXvKo3A14mfk4qkKPeK393+zFNJVOWCmJMx/cSG2REW04Fm5S6qWEJoSMyYB1HFZHMBNns2wk+cUofR7F2oyyeqb8vMiKNGcvQbUpih2bRm4r/eqFcSLbRZZBxlaSWKToPjlKBbYynVeA+14xaMXaEUM3d75gOiSbUusJKrhR/sYJl0jyr+l7Vvz2v1K7yeopwBMdwCj5cQA1uoA4NoHAPz/ACr+gJvaF39DFfLaD85hD+AH3+ADzJlfc=</latexit> <latexit sha1_base64="BLB8K/n7QYAsE73zsDEUiBvCSV8=">AAAB/XicbVDLSgMxFL2pr1pfVZdugkVwVWZE0GXRjcsK9gHtUDJppo1NMkOSEctQ/AW3uncnbv0Wt36JaTsLbT1w4XDOvZzLCRPBjfW8L1RYWV1b3yhulra2d3b3yvsHTROnmrIGjUWs2yExTHDFGpZbwdqJZkSGgrXC0fXUbz0wbXis7uw4YYEkA8UjTol1UrMbyuxx0itXvKo3A14mfk4qkKPeK393+zFNJVOWCmJMx/cSG2REW04Fm5S6qWEJoSMyYB1HFZHMBNns2wk+cUofR7F2oyyeqb8vMiKNGcvQbUpih2bRm4r/eqFcSLbRZZBxlaSWKToPjlKBbYynVeA+14xaMXaEUM3d75gOiSbUusJKrhR/sYJl0jyr+l7Vvz2v1K7yeopwBMdwCj5cQA1uoA4NoHAPz/ACr+gJvaF39DFfLaD85hD+AH3+ADzJlfc=</latexit> <latexit sha1_base64="BLB8K/n7QYAsE73zsDEUiBvCSV8=">AAAB/XicbVDLSgMxFL2pr1pfVZdugkVwVWZE0GXRjcsK9gHtUDJppo1NMkOSEctQ/AW3uncnbv0Wt36JaTsLbT1w4XDOvZzLCRPBjfW8L1RYWV1b3yhulra2d3b3yvsHTROnmrIGjUWs2yExTHDFGpZbwdqJZkSGgrXC0fXUbz0wbXis7uw4YYEkA8UjTol1UrMbyuxx0itXvKo3A14mfk4qkKPeK393+zFNJVOWCmJMx/cSG2REW04Fm5S6qWEJoSMyYB1HFZHMBNns2wk+cUofR7F2oyyeqb8vMiKNGcvQbUpih2bRm4r/eqFcSLbRZZBxlaSWKToPjlKBbYynVeA+14xaMXaEUM3d75gOiSbUusJKrhR/sYJl0jyr+l7Vvz2v1K7yeopwBMdwCj5cQA1uoA4NoHAPz/ACr+gJvaF39DFfLaD85hD+AH3+ADzJlfc=</latexit> <latexit sha1_base64="BLB8K/n7QYAsE73zsDEUiBvCSV8=">AAAB/XicbVDLSgMxFL2pr1pfVZdugkVwVWZE0GXRjcsK9gHtUDJppo1NMkOSEctQ/AW3uncnbv0Wt36JaTsLbT1w4XDOvZzLCRPBjfW8L1RYWV1b3yhulra2d3b3yvsHTROnmrIGjUWs2yExTHDFGpZbwdqJZkSGgrXC0fXUbz0wbXis7uw4YYEkA8UjTol1UrMbyuxx0itXvKo3A14mfk4qkKPeK393+zFNJVOWCmJMx/cSG2REW04Fm5S6qWEJoSMyYB1HFZHMBNns2wk+cUofR7F2oyyeqb8vMiKNGcvQbUpih2bRm4r/eqFcSLbRZZBxlaSWKToPjlKBbYynVeA+14xaMXaEUM3d75gOiSbUusJKrhR/sYJl0jyr+l7Vvz2v1K7yeopwBMdwCj5cQA1uoA4NoHAPz/ACr+gJvaF39DFfLaD85hD+AH3+ADzJlfc=</latexit> ML༧ଌ <latexit sha1_base64="0VEGB1BS2t8KmbZWf3FuR1QlwM8=">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</latexit> ༧ଌͷʮෆ࣮֬͞ʯ ྫ) ༧ଌ෼ࢄ, ༧ଌ෼෍ هड़ࢠ(Ұൠʹ͸ߴ࣍ݩ) ׆ੑ
  58. Optimal design of experiments / Active learning • Exploitation: 


    what we already know and get something close to what we expect • Exploration:
 something we aren't sure about and possibly learn more For next experiments, we face a dilemma in choosing between options. x <latexit sha1_base64="BLB8K/n7QYAsE73zsDEUiBvCSV8=">AAAB/XicbVDLSgMxFL2pr1pfVZdugkVwVWZE0GXRjcsK9gHtUDJppo1NMkOSEctQ/AW3uncnbv0Wt36JaTsLbT1w4XDOvZzLCRPBjfW8L1RYWV1b3yhulra2d3b3yvsHTROnmrIGjUWs2yExTHDFGpZbwdqJZkSGgrXC0fXUbz0wbXis7uw4YYEkA8UjTol1UrMbyuxx0itXvKo3A14mfk4qkKPeK393+zFNJVOWCmJMx/cSG2REW04Fm5S6qWEJoSMyYB1HFZHMBNns2wk+cUofR7F2oyyeqb8vMiKNGcvQbUpih2bRm4r/eqFcSLbRZZBxlaSWKToPjlKBbYynVeA+14xaMXaEUM3d75gOiSbUusJKrhR/sYJl0jyr+l7Vvz2v1K7yeopwBMdwCj5cQA1uoA4NoHAPz/ACr+gJvaF39DFfLaD85hD+AH3+ADzJlfc=</latexit> <latexit sha1_base64="BLB8K/n7QYAsE73zsDEUiBvCSV8=">AAAB/XicbVDLSgMxFL2pr1pfVZdugkVwVWZE0GXRjcsK9gHtUDJppo1NMkOSEctQ/AW3uncnbv0Wt36JaTsLbT1w4XDOvZzLCRPBjfW8L1RYWV1b3yhulra2d3b3yvsHTROnmrIGjUWs2yExTHDFGpZbwdqJZkSGgrXC0fXUbz0wbXis7uw4YYEkA8UjTol1UrMbyuxx0itXvKo3A14mfk4qkKPeK393+zFNJVOWCmJMx/cSG2REW04Fm5S6qWEJoSMyYB1HFZHMBNns2wk+cUofR7F2oyyeqb8vMiKNGcvQbUpih2bRm4r/eqFcSLbRZZBxlaSWKToPjlKBbYynVeA+14xaMXaEUM3d75gOiSbUusJKrhR/sYJl0jyr+l7Vvz2v1K7yeopwBMdwCj5cQA1uoA4NoHAPz/ACr+gJvaF39DFfLaD85hD+AH3+ADzJlfc=</latexit> <latexit sha1_base64="BLB8K/n7QYAsE73zsDEUiBvCSV8=">AAAB/XicbVDLSgMxFL2pr1pfVZdugkVwVWZE0GXRjcsK9gHtUDJppo1NMkOSEctQ/AW3uncnbv0Wt36JaTsLbT1w4XDOvZzLCRPBjfW8L1RYWV1b3yhulra2d3b3yvsHTROnmrIGjUWs2yExTHDFGpZbwdqJZkSGgrXC0fXUbz0wbXis7uw4YYEkA8UjTol1UrMbyuxx0itXvKo3A14mfk4qkKPeK393+zFNJVOWCmJMx/cSG2REW04Fm5S6qWEJoSMyYB1HFZHMBNns2wk+cUofR7F2oyyeqb8vMiKNGcvQbUpih2bRm4r/eqFcSLbRZZBxlaSWKToPjlKBbYynVeA+14xaMXaEUM3d75gOiSbUusJKrhR/sYJl0jyr+l7Vvz2v1K7yeopwBMdwCj5cQA1uoA4NoHAPz/ACr+gJvaF39DFfLaD85hD+AH3+ADzJlfc=</latexit> <latexit sha1_base64="BLB8K/n7QYAsE73zsDEUiBvCSV8=">AAAB/XicbVDLSgMxFL2pr1pfVZdugkVwVWZE0GXRjcsK9gHtUDJppo1NMkOSEctQ/AW3uncnbv0Wt36JaTsLbT1w4XDOvZzLCRPBjfW8L1RYWV1b3yhulra2d3b3yvsHTROnmrIGjUWs2yExTHDFGpZbwdqJZkSGgrXC0fXUbz0wbXis7uw4YYEkA8UjTol1UrMbyuxx0itXvKo3A14mfk4qkKPeK393+zFNJVOWCmJMx/cSG2REW04Fm5S6qWEJoSMyYB1HFZHMBNns2wk+cUofR7F2oyyeqb8vMiKNGcvQbUpih2bRm4r/eqFcSLbRZZBxlaSWKToPjlKBbYynVeA+14xaMXaEUM3d75gOiSbUusJKrhR/sYJl0jyr+l7Vvz2v1K7yeopwBMdwCj5cQA1uoA4NoHAPz/ACr+gJvaF39DFfLaD85hD+AH3+ADzJlfc=</latexit> ML༧ଌ <latexit sha1_base64="0VEGB1BS2t8KmbZWf3FuR1QlwM8=">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</latexit> ༧ଌͷʮෆ࣮֬͞ʯ ྫ) ༧ଌ෼ࢄ, ༧ଌ෼෍ e.g.
 "expected improvement" هड़ࢠ(Ұൠʹ͸ߴ࣍ݩ) ׆ੑ
  59. Model-based optimization 1. Initial Sampling (DoE) 2. Loop: 1. Construct

    a Surrogate Model. 2. Search the Infill Criterion. 3. Add new samples. • Optimal design of experiments (DoE) • Active learning • Bayesian optimization • Blackbox optimization • Reinforcement learning • Multi-armed bandit • Evolutional computation • Game-theoretic approaches An Open Research Topic in ML Use ML to guide the balance between "exploitation" and "exploration"! Our solution: Model-based optimization • Representation: Our elemental-descriptor based vectors • Surrogate: Tree ensembles with prediction variance • Optimization: Extending SMAC algorithm (Hutter+ 2011) to • Constrained search (e.g. sum to 1, [0,1]-valued, one-hot encodings) • Sparsity constraint (otherwise it always suggests dense vectors..) • Discrete local search for nominal value updating • Multiple suggestion at one time (batched optimization) • Infill criterion: Expected improvement (EI) + small explicit exploration
  60. • Oxidative coupling of methane (OCM) 
 [Zavyalova+ 2011] •

    Water gas shift (WGS) 
 [Odabaşi+ 2014] • CO oxidation [Günay+ 2013] Test on 3 Datasets Our model GPR-based BO Random • Our model finds high-performance catalysts more quickly than other alternatives • Our models can suggest a list of promising candidate catalysts with experimental conditions from the entire available data Suggested exp conditions are omitted in this figure Results
  61. ػցֶश෼໺ͷࢀߟࣄྫ AlphaGo
 (Nature, Jan 2016) "VUP.- શࣗಈػցֶश AlphaGo Zero
 (Nature,

    Oct 2017) AlphaZero
 (Science, Dec 2018) w "MHPSJUIN$POpHVSBUJPO w )ZQFSQBSBNFUFS0QUJNJ[BUJPO )10  w /FVSBM"SDIJUFDUVSF4FBSDI /"4  w .FUB-FBSOJOH-FBSOJOHUP-FBSO Amazon SageMaker MuZero
 (arXiv, Nov 2019) ϞσϧϕʔεͷڧԽֶश
  62. ஝ੵ͞Εͨʮܭࢉɾ࣮ݧɾ஌ࣝσʔλʯͷར׆༻ (機械学習・データマイニング) 仮説形成 検証 (シミュレーション+実験) • 再現性を担保する⾼精度・⾼速実験系 • 仮想化検証が可能な因⼦のシミュレー ション(計算科学)による探索

    → 望ましい対象のさらなる絞り込み 実験データ・計算データ・ファクトの蓄積 In-Houseデータ + Publicデータ + 知識ベース + そのQuality Control / Annotations) • どういう実験・シミュレーションを 次に⾏うかの計画⽴案 • 時間のかかる計算の⾼精度⾼速近似 • 曖昧な因⼦や実験条件の最適化 • Multilevelの情報統合
  63. Next expanded to materials science Little human intervention for highly

    reproducible large-scale production lines Automation, monitoring with IoT, and big-data management are also the key to manufacturing. Now these focuses shifted to the R & D phases. (very experimental and empirical traditionally)
  64. Next expanded to materials science Little human intervention for highly

    reproducible large-scale production lines Automation, monitoring with IoT, and big-data management are also the key to manufacturing. Now these focuses shifted to the R & D phases. (very experimental and empirical traditionally)
  65. Effective use of data is another key in natural sciences

    REVIEW Inverse molecular design using machine learning: Generative models for matter engineering Benjamin Sanchez-Lengeling1 and Alán Aspuru-Guzik2,3,4* The discovery of new materials can bring enormous societal and technological progress. In this context, exploring completely the large space of potential materials is computationally intractable. Here, we review methods for achieving inverse design, which aims to discover tailored materials from the starting point of a particular desired functionality. Recent advances from the rapidly growing field of artificial intelligence, mostly from the subfield of machine learning, have resulted in a fertile exchange of ideas, where approaches to inverse molecular design are being proposed and employed at a rapid pace. Among these, deep generative models have been applied to numerous classes of materials: rational design of prospective drugs, synthetic routes to organic compounds, and optimization of photovoltaics and redox flow batteries, as well as a variety of other solid-state materials. Many of the challenges of the 21st century (1), from personalized health care to energy production and storage, share a common theme: materials are part of the solution (2). In some cases, the solu- mapped 166.4 billion molecules that contain at most 17 heavy atoms. For pharmacologically rele- vant small molecules, the number of structures is estimated to be on the order of 1060 (9). Adding consideration of the hierarchy of scale from sub- act properties. In practice, approximations are used to lower computational time at the cost of accuracy. Although theory enjoys enormous progress, now routinely modeling molecules, clusters, and perfect as well as defect-laden periodic solids, the size of chemical space is still overwhelming, and smart navigation is required. For this purpose, machine learning (ML), deep learning (DL), and artificial intelligence (AI) have a potential role to play because their computational strategies automatically improve through experience (11). In the context of materials, ML techniques are often used for property prediction, seeking to learn a function that maps a molecular material to the property of choice. Deep generative models are a special class of DL methods that seek to model the underlying probability distribution of both structure and property and relate them in a nonlinear way. By exploiting patterns in massive datasets, these models can distill average and salient features that characterize molecules (12, 13). Inverse design is a component of a more complex materials discovery process. The time scale for deployment of new technologies, from discovery in a laboratory to a commercial pro- duct, historically, is 15 to 20 years (14). The pro- cess (Fig. 1) conventionally involves the following steps: (i) generate a new or improved material FRONTIERS IN COMPUTATION http Downloaded from REVIEW https://doi.org/10.1038/s41586-018-0337-2 Machine learning for molecular and materials science Keith T. Butler1, Daniel W . Davies2, Hugh Cartwright3, Olexandr Isayev4* & Aron Walsh5,6* Here we summarize recent progress in machine learning for the chemical sciences. We outline machine-learning techniques that are suitable for addressing research questions in this domain, as well as future directions for the field. We envisage a future in which the design, synthesis, characterization and application of molecules and materials is accelerated by artificial intelligence. The Schrödinger equation provides a powerful structure– property relationship for molecules and materials. For a given spatial arrangement of chemical elements, the distribution of electrons and a wide range of physical responses can be described. The development of quantum mechanics provided a rigorous theoretical foundation for the chemical bond. In 1929, Paul Dirac famously proclaimed that the underlying physical laws for the whole of chemistry are “completely known”1. John Pople, realizing the importance of rapidly developing generating, testing and refining scientific models. Such techniques are suitable for addressing complex problems that involve massive combi- natorial spaces or nonlinear processes, which conventional procedures either cannot solve or can tackle only at great computational cost. As the machinery for artificial intelligence and machine learning matures, important advances are being made not only by those in main- stream artificial-intelligence research, but also by experts in other fields (domain experts) who adopt these approaches for their own purposes. As DNA to be sequences into distinct pieces, parcel out the detailed work of sequencing, and then reassemble these independent ef- forts at the end. It is not quite so simple in the world of genome semantics. Despite the differences between genome se- quencing and genetic network discovery, there are clear parallels that are illustrated in Table 1. In genome sequencing, a physical map is useful to provide scaffolding for assembling the fin- ished sequence. In the case of a genetic regula- tory network, a graphical model can play the same role. A graphical model can represent a high-level view of interconnectivity and help isolate modules that can be studied indepen- dently. Like contigs in a genomic sequencing project, low-level functional models can ex- plore the detailed behavior of a module of genes in a manner that is consistent with the higher level graphical model of the system. With stan- dardized nomenclature and compatible model- ing techniques, independent functional models can be assembled into a complete model of the cell under study. To enable this process, there will need to be standardized forms for model representa- tion. At present, there are many different modeling technologies in use, and although models can be easily placed into a database, they are not useful out of the context of their specific modeling package. The need for a standardized way of communicating compu- tational descriptions of biological systems ex- tends to the literature. Entire conferences have been established to explore ways of mining the biology literature to extract se- mantic information in computational form. Going forward, as a community we need to come to consensus on how to represent what we know about biology in computa- tional form as well as in words. The key to postgenomic biology will be the computa- tional assembly of our collective knowl- edge into a cohesive picture of cellular and organism function. With such a comprehen- sive model, we will be able to explore new types of conservation between organisms and make great strides toward new thera- peutics that function on well-characterized pathways. References 1. S. K. Kim et al., Science 293, 2087 (2001). 2. A. Hartemink et al., paper presented at the Pacific Symposium on Biocomputing 2000, Oahu, Hawaii, 4 to 9 January 2000. 3. D. Pe’er et al., paper presented at the 9th Conference on Intelligent Systems in Molecular Biology (ISMB), Copenhagen, Denmark, 21 to 25 July 2001. 4. H. McAdams, A. Arkin, Proc. Natl. Acad. Sci. U.S.A. 94, 814 ( 1997 ). 5. A. J. Hartemink, thesis, Massachusetts Institute of Technology, Cambridge (2001). V I E W P O I N T Machine Learning for Science: State of the Art and Future Prospects Eric Mjolsness* and Dennis DeCoste Recent advances in machine learning methods, along with successful applications across a wide variety of fields such as planetary science and bioinformatics, promise powerful new tools for practicing scientists. This viewpoint highlights some useful characteristics of modern machine learn- ing methods and their relevance to scientific applications. We conclude with some speculations on near-term progress and promising directions. Machine learning (ML) (1) is the study of computer algorithms capable of learning to im- prove their performance of a task on the basis of their own previous experience. The field is closely related to pattern recognition and statis- tical inference. As an engineering field, ML has become steadily more mathematical and more successful in applications over the past 20 years. Learning approaches such as data clus- tering, neural network classifiers, and nonlinear regression have found surprisingly wide appli- cation in the practice of engineering, business, and science. A generalized version of the stan- dard Hidden Markov Models of ML practice have been used for ab initio prediction of gene structures in genomic DNA (2). The predictions correlate surprisingly well with subsequent gene expression analysis (3). Postgenomic bi- ology prominently features large-scale gene ex- pression data analyzed by clustering methods (4), a standard topic in unsupervised learning. Many other examples can be given of learning and pattern recognition applications in science. Where will this trend lead? We believe it will lead to appropriate, partial automation of every element of scientific method, from hypothesis generation to model construction to decisive experimentation. Thus, ML has the potential to amplify every aspect of a working scientist’s progress to understanding. It will also, for better or worse, endow intelligent computer systems with some of the general analytic power of scientific thinking. creating hypotheses, testing by decisive exper- iment or observation, and iteratively building up comprehensive testable models or theories is shared across disciplines. For each stage of this abstracted scientific process, there are relevant developments in ML, statistical inference, and pattern recognition that will lead to semiauto- matic support tools of unknown but potentially broad applicability. Increasingly, the early elements of scientific method—observation and hypothesis genera- tion—face high data volumes, high data acqui- sition rates, or requirements for objective anal- ysis that cannot be handled by human percep- tion alone. This has been the situation in exper- imental particle physics for decades. There automatic pattern recognition for significant events is well developed, including Hough transforms, which are foundational in pattern recognition. A recent example is event analysis for Cherenkov detectors (8) used in neutrino oscillation experiments. Microscope imagery in cell biology, pathology, petrology, and other fields has led to image-processing specialties. So has remote sensing from Earth-observing Machine Learning Systems Group, Jet Propulsion Lab- Table 1. Parallels between genome sequencing and genetic network discovery. Genome sequencing Genome semantics Physical maps Graphical model Contigs Low-level functional models Contig reassembly Module assembly Finished genome sequence Comprehensive model C O M P U T E R S A N D S C I E N C E on August 29, 2018 http://science.sciencemag.org/ Downloaded from Nature, 559
 pp. 547–555 (2018) Science, 293 pp. 2051-2055 (2001) Science, 361 pp. 360-365 (2018) Science is changing, the tools of science are changing. And that requires different approaches. ── Erich Bloch, 1925-2016 (In addition to experiments and simulations) And please keep in mind that unplanned data collection is dangerous. We need right designs for data collection and right tools to analyze. A bitter lesson: "low input, high throughput, no output science." (Sydney Brenner)
  66. 現象の理解・原理 (理論科学・計算科学) 現象の観察・ファクト (実験科学) 伝統的 な⽅法 仮説形成 仮説形成 説明 より合理的・効率的な探索の確⽴

    (新規な触媒・反応の発⾒へ) ボトルネックの⼀つは「(筋の良い)仮説形成」 どのターゲット・条件・パラメタを試すか? 予測 Data-driven Theory-driven Theory-driven vs Data-drivenͷ༥߹ʹΉ͚ͯ
  67. 現象の理解・原理 (理論科学・計算科学) 現象の観察・ファクト (実験科学) 伝統的 な⽅法 仮説形成 仮説形成 説明 より合理的・効率的な探索の確⽴

    (新規な触媒・反応の発⾒へ) ボトルネックの⼀つは「(筋の良い)仮説形成」 どのターゲット・条件・パラメタを試すか? 蓄積される知⾒(データ) の利活⽤ (情報科学) • 予測モデリング • 不確定因⼦の最適化 • マルチレベル情報の統合 • 候補集合を第⼀原理で提⽰/制約 • 仮想的検証・計算データの提供 • 明⽰的ドメイン知識 根拠・データ・ 経験的ファクト 予測 Data-driven Theory-driven Theory-driven vs Data-drivenͷ༥߹ʹΉ͚ͯ
  68. Summary Takeaways: 
 first principles are not enough for us

    to throw away empirical things; data-driven approaches (such as ML) play a complementary role! 1. Takigawa I, Shimizu K, Tsuda K, Takakusagi S
 RSC Advances. 2016; 6: 52587-52595. 2. Toyao T, Suzuki K, Kikuchi S, Takakusagi S, Shimizu K, Takigawa I.
 The Journal of Physical Chemistry C. 2018; 122(15): 8315-8326. 3. Suzuki K, Toyao T, Maeno Z, Takakusagi S, Shimizu K, Takigawa I.
 ChemCatChem. 2019; 11(18): 4537-4547. Ken-ichi SHIMIZU
 (ICAT) Satoru TAKAKUSAGI
 (ICAT) Takashi TOYAO
 (ICAT) Keisuke
 SUZUKI
 (DENSO)