(2021.10) 機械学習と機械発見データ中心型の化学・材料科学の教訓とこれから

/ 166 1 堣唒㷕统ה堣唒涪鋅 ر٦ة⚥䗰㘗ך⻉㷕٥勞俱猰㷕ך侄鎮הֿ׸ַ׵ 戣䊛♧㷕 [email protected] 椚⻉㷕灇瑔䨽ꬠ倜濼腉窟さ灇瑔إٝة٦ J14稢脄鸬䵿⼔㷕涸ٔأؙ㔐鼘ث٦ي 2021䎃10剢26傈

/ 166 㼔Ꟍ堣唒㷕统ה堣唒涪鋅 խխխ暴חꨄ侔圓鸡׾⠵ֲ堣唒㷕统 ر٦ة⚥䗰涸ז荈搫猰㷕灇瑔 խխխ植㖈ך⚺噟⹡䎌稢脄欰暟㷕椚灇⻉㷕⻌㣐
荈䊹稱➜戣䊛♧㷕 ׋ָֹ׻ְ׍ָֻ 2 䎃⻌㣐 ։ 䎃❨㣐 ։ 䎃⻌㣐 ։ 䊨㷕灇瑔猰ءأذي䞔㜠䊨㷕㼔余⽆㡦铬玎⥜✪ ⸋寸㹀⥋〾彁ⴓꨄך-ظٕي剑㼭鍑ך椚锷ⴓ匿⻉㷕灇瑔䨽غ؎ؔ؎ٝؿؓوذ؍ؙأإٝة٦ 讒㷕灇瑔猰⼔讒ⶼ䧭䞔㜠猰㷕㼔余 Ⱟ⹡ 䞔㜠猰㷕灇瑔猰䞔㜠椚䊨㷕㼔余 +45ָֹֽׁ勞俱؎ٝؿؓوذ؍ؙأ걄㚖 Ⱟ⹡ 䎃椚灇 ❨鿪 ։ "*1إٝة٦J14稢脄鸬䵿⼔㷕涸ٔأؙ㔐鼘ث٦ي ⻌㣐⻉㷕⿾䘔ⶼ䧭灇瑔䬿挿 ؙٗأ،ه؎ٝز ⸔侄 Ⲥ侄䱇灇瑔㆞

/ 166 ꨄ侔圓鸡׾⠵ֲ堣唒㷕统 3 ܾఆ໦ɾܾఆDAG χϡʔϥϧωοτϫʔΫ ֬཰తϓϩάϥϛϯά ˖ 㼎韋ָչꨄ侔圓鸡պ׾䭯א ˖
ٌرָٕչꨄ侔圓鸡պ׾䭯א ˖ 㼎韋ךꟼ⤘ָչꨄ侔圓鸡պ׾䭯א ꧊さծ锷椚ծꟼ⤘ծ穈さׇծ禸⴨ծ加ծؚٓؿծ➿侧禸ծ鎉铂ծ˘ CH 3 N N H N H H 3 C N

/ 166 ➙傈ךذ٦و 4 ˖ 荈䊹稱➜ 堣唒㷕统ה荈搫猰㷕ך㞮歲 ˖ 堣唒㷕统הכ倜׃ְفؚٗٓىؚٝך倯岀
˖ 堣唒㷕统㾊כ♧⡤⡦ָ嚂׃ְךַ ˖ ⴓ㶨ך邌植ה堣唒㷕统 ˖ ؚٖ؎نحؙأ剑黝⻉怴糊䌓秛锷椚䱿锷ה窟鎘涸✮庠 ך窟さ ˖ 荈搫猰㷕灇瑔ד堣唒㷕统׾⢪ֲֶהׅ׷ה䗳׆עאַ׷劤䔲חꨇ׃ְ㉏겗 ˖ 5IF5XP$VMUVSFTر٦ةٌرؚٔٝה✮庠،ٕ؞ٔؤي ˖ ✮庠ַ椚鍑ַ3BTIPNPO⸬卓 6OEFSTQFDJDBUJPO 鍑ꅸ㢳圫䚍 ˖ ➂꟦ך钠濼غ؎،أח歋勻ׅ׷㉏겗⟎铡ծ㣟侁ծ䧭⸆غ؎،أծFUD ˖ 堣唒㷕统ַ׵堣唒涪鋅פ ˖ չ涪鋅պչ椚鍑պך麣瘡כさ椚⻉דֹ׷ךַ荈⹛⻉דֹ׷ךַ

/ 166 鯄耵䎃剢傈։ 5 ⻌嵲麣㣐㷕䞔㜠猰㷕灇瑔猰ך灇瑔㹓׾DMPTF׃♴鎸穈籼ך չؙٗأ،ه؎ٝزًٝزպפ ˖ 椚⻉㷕灇瑔䨽 ꬠ倜濼腉窟さ灇瑔إٝة٦ "*1
J14稢脄鸬䵿⼔㷕涸ٔأؙ㔐鼘ث٦ي灇瑔㆞ ˖ ⻌嵲麣㣐㷕⻉㷕⿾䘔ⶼ䧭灇瑔䬿挿 81**$3F%% 暴⟣Ⲥ侄䱇

/ 166 俑猰満⚅歲زحفٖكٕ䬿挿䕎䧭فؚٗٓي 81* 6 https://www.mext.go.jp/a_menu/kagaku/toplevel/

/ 166 ⚅歲زحفٖكٕ䬿挿䕎䧭فؚٗٓي 81* ה䞔㜠猰㷕 7 ر٦ة٥䞔㜠猰㷕חꅾז׷ 81*䬿挿כ✳䬿挿ך׫ صُ٦ٗ؎ٝذٔآؑٝأ㕂ꥷ灇瑔堣圓

/ 166 ⻌嵲麣㣐㷕⻉㷕⿾䘔ⶼ䧭灇瑔䬿挿 81**$3F%% 8 ⻉㷕⿾䘔ה䞔㜠猰㷕

/ 166 ⻌嵲麣㣐㷕⻉㷕⿾䘔ⶼ䧭灇瑔䬿挿 81**$3F%% 9 https://www.icredd.hokudai.ac.jp

/ 166 ظ٦كٕ⻉㷕颣 10

/ 166 https://www.youtube.com/watch?v=clvA49BobsI 11

/ 166 椚⻉㷕灇瑔䨽ꬠ倜濼腉窟さ灇瑔إٝة٦ 12 https://aip.riken.jp/

/ 166 椚⻉㷕灇瑔䨽ꬠ倜濼腉窟さ灇瑔إٝة٦ 13 東京駅理研AIP 皇居

/ 166 椚⻉㷕灇瑔䨽ꬠ倜濼腉窟さ灇瑔إٝة٦ 14 $03&%0傈劤堀'

/ 166 15 https://www.kobe.riken.jp/about/map/keihanna/ ⹶⹡㖑❨ꢻ㣽㖑⼒ ❨鿪䏍湱嚂龾礵螟歕

/ 166 ⹶⹡㖑❨ꢻ㣽㖑⼒ ❨鿪䏍湱嚂龾礵螟歕 16

/ 166 ⹶⹡㖑❨ꢻ㣽㖑⼒ ❨鿪䏍湱嚂龾礵螟歕 17 ࠃཱࠃձਤॻؗؔ੢ؗ

/ 166 㕂ꥷꨵ孡鸐⥋㛇燉䪮遭灇瑔䨽"53 18 瀖랲暴灇ך ،ٝسٗ؎س չؒٔؕպָꔨ䏟㹋暟כ乆䕦犜姺 ˖ 椚⻉㷕灇瑔䨽
ꬠ倜濼腉窟さ灇瑔إٝة٦"*1 ؖ٦ر؍،ٝٗنحزفٗآؙؑز(31 ˖ "53膷䞔㜠鸐⥋筨さ灇瑔䨽膷䞔㜠灇瑔䨽钠濼堣圓灇瑔䨽膷䞔㜠鍑匿灇瑔䨽 https://www.atr.jp ˖ 帾㾴؎ٝةؙٓءّٝ ؎ٝةؙٓءّٝ䪮遭غؙٝ ؎ٝةؙٓءّٝ猰㷕灇瑔䨽瀖랲嵞暴ⴽ灇瑔䨽蠗歊秀⽆暴ⴽ灇瑔䨽 ˖ 搀简٥鸐⥋ 黝䘔؝ىُص؛٦ءّٝ灇瑔䨽岚⹛䊨㷕灇瑔䨽 ˖ 欰ㄏ猰㷕 ⡟谏⻟䗗暴ⴽ灇瑔䨽

/ 166 19 ˖ 膷䞔㜠灇瑔䨽 $/4 ˖ 钠濼堣圓灇瑔䨽 $.$
˖ 膷䞔㜠鍑匿灇瑔䨽 /*" ˖ 鎘皾膷؎ً٦آؚٝ灇瑔㹓 $#* ͑椚灇"*1鎘皾膷ت؎شىؙأث٦ي 㿊♴5 ˖ ⹛涸膷؎ً٦آؚٝ灇瑔㹓 %#* ͑椚灇"*1膷䞔㜠窟さ鍑匿ث٦ي 䊛ꑚ5 ˖ 膷䞔㜠鸐⥋筨さ灇瑔䨽㕂ꥷꨵ孡鸐⥋㛇燉䪮遭灇瑔䨽"53

/ 166 椚灇"*1!"53 20 ˖ ꣇拄猰㷕ث٦ي ♳歊⥜⸆ ˖ 膷䞔㜠窟さ鍑匿ث٦ي
䊛ꑚ♧儙 ˖ 鎘皾膷ت؎شىؙأث٦ي 㿊♴㸾➂ ˖ J14稢脄鸬䵿⼔㷕涸ٔأؙ㔐鼘ث٦ي ♳歊⥜⸆ 椚灇"*1ה❨㣐J14稢脄灇ך鸬䵿ٓن

/ 166 植㖈ךꟼ䗰 21 ˖ ⻌嵲麣㣐㷕⻉㷕⿾䘔ⶼ䧭灇瑔䬿挿 81**$3F%% ˖ 椚⻉㷕灇瑔䨽ꬠ倜濼腉窟さ灇瑔إٝة٦ "*1
˖ ꨄ侔圓鸡٥穈さׇ圓鸡׾⠵ֲ堣唒㷕统 ˖ 䎌稢脄欰暟㷕ך׋׭ך堣唒㷕统稢脄歗⫷ 帾㾴㷕统 ˖ 倜׃ְ،ٕ؞ٔؤي٥剑黝⻉ך㹀䒭⻉ה実鍑岀 ˖ 鷲麓㘗ꨵ㶨겥䗍ꖎ 堣唒㷕统ח״׷⹛涸錁㻊 ˖ 堣唒㷕统ך㹋騧灇瑔 ˖ ⻉㷕⿾䘔ךرؠ؎ٝה涪鋅ך׋׭ך堣唒㷕统 ˖ ⴓ㶨ךؚٓؿ邌植ך㷕统ה欰䧭 ˖ ꆀ㶨⻉㷕鎘皾堣唒㷕统ך輐さ ˖ 堣唒涪鋅䱱稊ծ㹋꿀鎘歗ծ濼陎涪鋅

˖ 堣唒㷕统㾊כ♧⡤⡦ָ嚂׃ְךַ ˖ ⴓ㶨ך邌植ה堣唒㷕统 ˖ ؚٖ؎نحؙأ剑黝⻉怴糊䌓秛 锷椚㷕ה窟鎘㷕ך輐さ ˖ 荈搫猰㷕灇瑔ד堣唒㷕统׾⢪ֲֶהׅ׷ה䗳׆עאַ׷劤䔲חꨇ׃ְ㉏겗 ˖ ر٦ةٌرؚٔٝה✮庠،ٕ؞ٔؤي 5IF5XP$VMUVSFT ˖ ✮庠ַ椚鍑ַ3BTIPNPO⸬卓 6OEFSTQFDJDBUJPO 鍑ꅸ㢳圫䚍 ˖ ➂꟦ך钠濼غ؎،أח歋勻ׅ׷㉏겗⟎铡ծ㣟侁ծ䧭⸆غ؎،أծFUD ˖ 堣唒㷕统ַ׵堣唒涪鋅פ ˖ չ涪鋅պכさ椚⻉דֹ׷ךַׁ׵ח荈⹛⻉דֹ׷ךַ

/ 166 堣唒㷕统הכ倜䩛ך ꧟ז فؚٗٓىؚٝך倯岀 23 ؝ٝؾُ٦ةفؚٗٓي <latexit sha1_base64="DuksIrWdNAsvY6hvC/3omgtTDqo=">AAACq3ichVFNLwNRFD3G93exkdiIpmKjuYOEWAkbS1Q/om2amfEwzFdmpg0af8DKTrAisRA/w8YfsPATxLISGwt3ppMITetOZt55595z33lzVcfQPZ/otU1q7+js6u7p7esfGBwajo2MZjy77GoirdmG7eZUxROGbom0r/uGyDmuUEzVEFn1aC3IZyvC9XTb2vZPHFE0lX1L39M1xWcqU1DN6vFZKRanJIUx2QjkCMQRxYYde0YBu7ChoQwTAhZ8xgYUePzkIYPgMFdElTmXkR7mBc7Qx9oyVwmuUJg94u8+7/IRa/E+6OmFao1PMfh1WTmJBL3QA9XomR7pjb6a9qqGPQIvJ7yqda1wSsPn46nPf1Umrz4OflQtPfvYw1LoVWfvTsgEt9Dq+srpZS21vJWoTtMdvbP/W3qlJ76BVfnQ7jfF1k0LPyp7af7HgnxUwSOU/w6sEWTmkvJ8kjYX4iur0TB7MIEpzPDEFrGCdWwgzScc4gJXuJZmpZS0IxXqpVJbpBnDr5DEN30amak=</latexit> <latexit
sha1_base64="aabjZM6SNm3NlwPbE7sqkAWyXzk=">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</latexit> ♷ִ׵׸׋㣐ꆀךⰅ⳿⸂ך鋅劤⢽׾ⱄ植דֹ׷״ֲזⰅ⸂ַ׵⳿⸂פ ך㢌䳔فؚٗٓي׾ꬊ僇爙涸ח欰䧭ׅ׷׋׭ך害欽涸倯岀 ♧菙暟⡤钠陎 갈㡮钠陎堣唒缺鏬馄鍑⫷؎ً٦آؚٝ ⴓ㶨ך嫩䚍✮庠 ˑ֮׶ָהֲ˒ J’aime la musique I love music CH3 N H 3 C H N S N O CH3 N OH 1.394

/ 166 堣唒㷕统הכ倜䩛ך ꧟ז فؚٗٓىؚٝך倯岀 24 ⠗窟涸זفؚٗٓىؚٝ 怴糊涸ծSBUJPOBM ءىُٖ٦ءّٝ 鎘皾ך׋׭ךٗآحؙכ
ׅץג➂꟦ָ罋ִ׷ Ⰵ⸂ ⳿⸂ 倜׃ְفؚٗٓىؚٝ 䌓秛涸ծFNQJSJDBM 堣唒㷕统 Ⰵ⳿⸂ךꟼ⤘כ״ֻⴓַ ׵זְךד镘׭׷ Ⰵ⸂ ⳿⸂ չػًٓةד䮙⹛׾荈歋ח㢌ִ׵׸׷害欽䕎պד ꧵䕎׾欽䠐׃ծ׋ֻׁ׿ךⰅ⳿⸂ך鋅劤⢽׾♷ִג 鋅劤⢽׾ⱄ植ׅ׷״ֲػًٓةך⦼׾锃侭ׅ׷

/ 166 堣唒㷕统剣ꣲך挿פךꟼ侧ؿ؍حذ؍ؚٝ 25 x1 x2 y p1 p2 p3
p5 p4 Variable 1 Variable 2 <latexit sha1_base64="Ill3Als4zZd947f5Xm9sW99d0QA=">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</latexit> x1 <latexit sha1_base64="QFtMwnKe2I12XGZu0bNJbdnDaaE=">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</latexit> x2 <latexit sha1_base64="Ill3Als4zZd947f5Xm9sW99d0QA=">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</latexit> x1 <latexit sha1_base64="QFtMwnKe2I12XGZu0bNJbdnDaaE=">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</latexit> x2 x1 x2 y ML 5 params Random Forest Neural Networks SVR Kernel Ridge

/ 166 ⴓ겲 DMBTTJDBUJPO BTؿ؍حذ؍ؚٝ 26

/ 166 ⴓ겲 DMBTTJDBUJPO BTؿ؍حذ؍ؚٝ 26 ך然桦⦼׾⳿⸂ QSFEJDU@QSPCB P(class=red) P(class=blue)
= 1 - P(class=red)

/ 166 ⴓ겲 DMBTTJDBUJPO BTؿ؍حذ؍ؚٝ 26 Random Forest Gaussian Process
Classiﬁer Logistic Regression ך然桦⦼׾⳿⸂ QSFEJDU@QSPCB P(class=red) P(class=blue) = 1 - P(class=red)

/ 166 #PSJOH"* BLB.BDIJOF-FBSOJOH 27 https://www.forbes.com/sites/forbestechcouncil/2020/02/19/ in-praise-of-boring-ai-a-k-a-machine-learning/ ʜ “Let’s face
it: So far, the artificial intelligence plastered all over PowerPoint slides hasn’t lived up to its hype.” The AI frenzy: hope & hype

/ 166 #PSJOH"* BLB.BDIJOF-FBSOJOH 27 From AAAI-20 Oxford-Style Debate https://www.forbes.com/sites/forbestechcouncil/2020/02/19/
in-praise-of-boring-ai-a-k-a-machine-learning/ ʜ “Let’s face it: So far, the artificial intelligence plastered all over PowerPoint slides hasn’t lived up to its hype.” The AI frenzy: hope & hype

/ 166 ꟼ侧ؿ؍حذ؍ؚٝה׃גך堣唒㷕统 28 Prediction Input variables Classiﬁer or Regressor
<latexit sha1_base64="Ill3Als4zZd947f5Xm9sW99d0QA=">AAAChnichVHLTsJAFD3UF+ID1I2JGyLBuCJTomJcEd245CGPBAlp64gNpW3aQkTiD5i4lYUrTVwYP8APcOMPuOATjEtM3LjwUpoYJeJtpnPmzD13zsyVTU21Hca6PmFsfGJyyj8dmJmdmw+GFhbzttGwFJ5TDM2wirJkc03Vec5RHY0XTYtLdVnjBbm2198vNLllq4Z+4LRMXq5LVV09VhXJISp7WhEroQiLMTfCw0D0QARepIzQIw5xBAMKGqiDQ4dDWIMEm74SRDCYxJXRJs4ipLr7HOcIkLZBWZwyJGJr9K/SquSxOq37NW1XrdApGg2LlGFE2Qu7Zz32zB7YK/v8s1bbrdH30qJZHmi5WQleLGc//lXVaXZw8q0a6dnBMbZdryp5N12mfwtloG+edXrZnUy0vcZu2Rv5v2Fd9kQ30Jvvyl2aZ65H+JHJC70YNUj83Y5hkI/HxK1YPL0RSe56rfJjBatYp34kkMQ+UshR/SoucYWO4BdiwqaQGKQKPk+zhB8hJL8AVA6Qmg==</latexit> x1 <latexit sha1_base64="QFtMwnKe2I12XGZu0bNJbdnDaaE=">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</latexit> x2 <latexit sha1_base64="lFhRrRrVTrFR31ebbMgRp5myJpc=">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</latexit> x3 <latexit sha1_base64="0IPXcU0UIDvzZlYURjV2A/THv9U=">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</latexit> . . . Function model 垥彊涸ז堣唒㷕统ٌرٕ

/ 166 邌植㷕统葺ְ悵㖈暴䗙ꆀךر٦ةַ׵ך䬄⳿ 29 Prediction Input variables Function model
<latexit sha1_base64="QFtMwnKe2I12XGZu0bNJbdnDaaE=">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</latexit> x2 <latexit sha1_base64="lFhRrRrVTrFR31ebbMgRp5myJpc=">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</latexit> x3 <latexit sha1_base64="0IPXcU0UIDvzZlYURjV2A/THv9U=">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</latexit> . . . Latent variables Learnable variable transformation Representation learning Classiﬁer or Regressor <latexit sha1_base64="Ill3Als4zZd947f5Xm9sW99d0QA=">AAAChnichVHLTsJAFD3UF+ID1I2JGyLBuCJTomJcEd245CGPBAlp64gNpW3aQkTiD5i4lYUrTVwYP8APcOMPuOATjEtM3LjwUpoYJeJtpnPmzD13zsyVTU21Hca6PmFsfGJyyj8dmJmdmw+GFhbzttGwFJ5TDM2wirJkc03Vec5RHY0XTYtLdVnjBbm2198vNLllq4Z+4LRMXq5LVV09VhXJISp7WhEroQiLMTfCw0D0QARepIzQIw5xBAMKGqiDQ4dDWIMEm74SRDCYxJXRJs4ipLr7HOcIkLZBWZwyJGJr9K/SquSxOq37NW1XrdApGg2LlGFE2Qu7Zz32zB7YK/v8s1bbrdH30qJZHmi5WQleLGc//lXVaXZw8q0a6dnBMbZdryp5N12mfwtloG+edXrZnUy0vcZu2Rv5v2Fd9kQ30Jvvyl2aZ65H+JHJC70YNUj83Y5hkI/HxK1YPL0RSe56rfJjBatYp34kkMQ+UshR/SoucYWO4BdiwqaQGKQKPk+zhB8hJL8AVA6Qmg==</latexit> x1 剑鵚ך帾㾴㷕统דכ㔐䌓٥ⴓ겲ך⵸ח葺ְ悵㖈㢌侧邌植פך㢌䳔׾遤ֲ אךـٗحؙךさ䧭׾ꟼ侧ؿ؍حذ؍ؚٝה׃ג♧孡鸐顐ד剑黝⻉ׅ׷

/ 166 邌植㷕统葺ְ悵㖈暴䗙ꆀךر٦ةַ׵ך䬄⳿ 29 Prediction Input variables Function model
<latexit sha1_base64="QFtMwnKe2I12XGZu0bNJbdnDaaE=">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</latexit> x2 <latexit sha1_base64="lFhRrRrVTrFR31ebbMgRp5myJpc=">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</latexit> x3 <latexit sha1_base64="0IPXcU0UIDvzZlYURjV2A/THv9U=">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</latexit> . . . Latent variables Learnable variable transformation Representation learning Classiﬁer or Regressor Linear <latexit sha1_base64="Ill3Als4zZd947f5Xm9sW99d0QA=">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</latexit> x1 Simple model is enough when we have good features. 剑鵚ך帾㾴㷕统דכ㔐䌓٥ⴓ겲ך⵸ח葺ְ悵㖈㢌侧邌植פך㢌䳔׾遤ֲ אךـٗحؙךさ䧭׾ꟼ侧ؿ؍حذ؍ؚٝה׃ג♧孡鸐顐ד剑黝⻉ׅ׷

/ 166 邌植㷕统葺ְ悵㖈暴䗙ꆀךر٦ةַ׵ך䬄⳿ 30 https://colah.github.io/posts/2014-03-NN-Manifolds-Topology/ 简䕎ⴓꨄ〳腉ז邌植פך㢌䳔׾㷕统 ֿךةأؙכ㹋騧涸חכ⣛搫׬׆ַ׃ֻ ꟦麩ִ׷ה⯋״׶ꃎֻז׶ֲ׷

/ 166 31 https://towardsdatascience.com/a-comprehensive-guide-to-convolutional-neural-networks-the-eli5-way-3bd2b1164a53 ... ... 葺ְ悵㖈㢌侧邌植פך㢌䳔׾ر٦ةַ׵㷕统 ةأؙ׀הח㔐䌓٥ⴓ겲 ֿך鿇ⴓכ✼ְח湱ꟼך֮׷醱侧ך ⴽةأؙדⵃ欽דֹ׷
鯄獳㷕统邌植㷕统葺ְ悵㖈暴䗙ꆀ ךⴽך♴崧ةأؙפך鯄獳

/ 166 32 ... ... 葺ְ悵㖈㢌侧邌植פך㢌䳔׾ر٦ةַ׵㷕统 ةأؙ׀הח㔐䌓٥ⴓ겲 Ԩ ر٦ة挿׾Ⰵ⸂邌植דכזֻ悵㖈㢌侧邌植חְֶגⰻ䯏ׅ׷ֿהחז׷կ Ԩ
Ⱏ鸐ךչ葺ְ悵㖈㢌侧邌植պ׾䭯אةأؙדչ邌植㷕统ـٗحؙպ׌ֽ׾㷕统 דֹ׷〳腉䚍׾䭯אկ 㣐鋉垷ر٦ةדך✲⵸㷕统̔㼭鋉垷⢽פ鯄獳㷕统邌植㷕统葺ְ悵㖈暴䗙ꆀ ךⴽך♴崧ةأؙפך鯄獳

/ 166 堣唒㷕统ך植➿涸ז⩎꬗ 33 ˖ ٌرٕػًٓة侧ָה׿ד׮זֻ㢳ְ ˖ 荈⹛䗍ⴓ禸ך涪㾜ח״׶فؚٗٓيה׃ג剅ֽ׸ל⡦ד׮堣唒㷕统〳腉ח ResNet50: 26
million params ResNet101: 45 million params EﬃcientNet-B7: 66 million params VGG19: 144 million params 12-layer, 12-heads BERT: 110 million params 24-layer, 16-heads BERT: 336 million params GPT-2 XL: 1558 million params GPT-3: 175 billion params 植➿ך堣唒㷕统כ ⭙⦐ךػًٓة 荈歋䏝 ׾䭯אٌرٕ׾侧⼧♰ך如⯋׾䭯א 侧⼪♰⦐ךر٦ةחؿ؍حذ؍ؚٝ׃גְג湫䠬ָ⸬ַזְꬊ荈僇ז朐屣

˖ 堣唒㷕统㾊כ♧⡤⡦ָ嚂׃ְךַ ˖ ⴓ㶨ך邌植ה堣唒㷕统 ˖ ؚٖ؎نحؙأ剑黝⻉怴糊䌓秛 锷椚㷕ה窟鎘㷕ך輐さ ˖ 荈搫猰㷕灇瑔ד堣唒㷕统׾⢪ֲֶהׅ׷ה䗳׆עאַ׷劤䔲חꨇ׃ְ㉏겗 ˖ ر٦ةٌرؚٔٝה✮庠،ٕ؞ٔؤي 5IF5XP$VMUVSFT ˖ ✮庠ַ椚鍑ַ3BTIPNPO⸬卓 6OEFSTQFDJDBUJPO 鍑ꅸ㢳圫䚍 ˖ ➂꟦ך钠濼غ؎،أח歋勻ׅ׷㉏겗⟎铡ծ㣟侁ծ䧭⸆غ؎،أծFUD ˖ 堣唒㷕统ַ׵堣唒涪鋅פ ˖ չ涪鋅պכさ椚⻉דֹ׷ךַׁ׵ח荈⹛⻉דֹ׷ךַ

/ 166 ⴓ㶨כչ穈さׇ涸պז⩎꬗׾׮א 35 https://cen.acs.org/physical-chemistry/computational-chemistry/Exploring-chemical-space-AI-take/98/i13

/ 166 ⴓ㶨鎸鶢㶨 36 NPSFUIBO EFTDSJQUPST ˖ %鎸鶢㶨 ˖ DPOTUJUVUJPOBMEFTDSJQUPST
˖ DPVOUEFTDSJQUPST ˖ %鎸鶢㶨 ˖ MJTUPGTUSVDUVSBMGSBHNFOUT ˖ GJOHFSQSJOUT ˖ %鎸鶢㶨 ˖ HSBQIJOWBSJBOUT ˖ %鎸鶢㶨 ˖ %.P34& 8)*. (&5"8": ˖ RVBOUVNDIFNJDBMEFTDSJQUPST ˖ TJ[F TUFSJD TVSGBDF WPMVNF FUD ˖ %鎸鶢㶨 ˖ (3*% $P.'" 7PMTVSG %3"(0/ EFTDSJQUPST ㉀欽ך鎸鶢㶨اؿزؐؑ، ˖ 㹋꿀涸ז鎘庠ꆀ ˖ 鎘皾涸ז鎸鶢㶨 Quantitative Structure–Property Relationship Modeling of Diverse Materials Properties. Chem Rev, 2012, 112 (5), pp 2889–2919 ؔ٦فٝا٦أؿٖ٦يٙ٦ؙ • Descriptors • Descriptors3D • GraphDescriptors • Fingerprints • ChemicalFeatures • ChemicalForceFields rdkit.Chem rdkit.ML.Descriptors Todeschini and Consonni, Molecular Descriptors for Chemoinformatics. Wiley‐VCH, 2009. https://doi.org/10.1002/9783527628766

/ 166 ⴓ㶨ךչ葺ְ害欽涸邌植պך㷕统 37 Reactions Materials Molecules CC1CCNO1 NCc1ccoc1.S=(Cl)Cl>>[RX_5]S=C=NCc1ccoc1 悵㖈㢌侧邌植
زهٗآ 갥挿暴䗙鴟暴䗙 Representation Learning … ˖ ⴓ겲 ˖ 㔐䌓 ˖ 欰䧭圫ղז ♴崧ةأؙ ⴓ㶨ך橆㞮勴⟝垥涸湱✼⡲欽瘝ך䞔㜠 ؚٓؿ邌植 Task-Speciﬁc Head

/ 166 6TF$BTF7JSUVBM4DSFFOJOH 24"32413 38 • Mutagenic potency • Carcinogenic
potency • Endocrine disruption • Growth inhibition • Aqueous solubility N NH O O H H H H H H H H H H H H H H H H H H H H H H H H H O O O O O O Cl H H H H H H H H H H H H H H H H H Br Br O P O O Br Br O Br Br H H H H H H H H H H H H H H H N S N N H H H H H H H 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 H H H H H H H N O O H H H H H H H H H N O O H H H H H H H N H N O O N O O H H H H H H H H N CH3 O O H N Cl Cl Cl Cl Cl H 3 C O O O O O O H 3 C CH3 CH2 O HN O O NH CH3 HO OH CH 3 N O O CH 3 N N H N H H 3 C N H 3 C H 3 C NH O N O N O CH3 O N NH 2 O CH3 Br CH3 N H 3 C H N S N O CH3 N OH CH3 CH3 N N N CH3 H 3 C H2 N NH2 H OH O HO CH 3 H H O CH 3 H O O H 3 C H H H O H 3 C S CH3 O H H O CH3 CH3 O O HO H 3 C H HO F H O H 3 C NH 2 O N HO H O O H H O O O H 3 C O O O CH 3 O CH 3 H O CH 3 H O O CH 3 H H N H N O H 3 C O O O

/ 166 6TF$BTF7JSUVBM4DSFFOJOH 24"32413 39 https://pubchem.ncbi.nlm.nih.gov/bioassay/1

/ 166 6TF$BTF7JSUVBM4DSFFOJOH 24"32413 40 input output ML activity: “Active”
LogGI50: -7.8811 CID 11978790 GI50: concentration required for 50% inhibition of growth

/ 166 .PMFDVMBS(SBQITⴓ㶨ךؚٓؿ邌植 41 Input representation (molecular graph) 1 2
1 3 explicit Hs 4 5 6 7 8 9 10 11 12 13 14 15 16 17 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Any permutation of this numbering should not change the results. ❗ CID 204 atoms → nodes bonds → edges 1. permutation equivariance 2. permutation invariance

1 3 explicit Hs 4 5 6 7 8 9 10 11 12 13 14 15 16 17 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Any permutation of this numbering should not change the results. ❗ CID 204 • atomic_num (one-hot, 101) • total_degree (one-hot, 7) • formal_charge (one-hot, 6) • chiral_tag (one-hot, 5) • num_Hs (one-hot, 6) • hybridization (one-hot, 6) • is_aromatic (binary, 1) • atomic_mass (real, 1) 17 edge(bond) features • no_bond (binary, 1) • is_single (binary, 1) • is_double (binary, 1) • is_triple (binary, 1) • is_aromatic (binary, 1) • is_connjugated (binary, 1) • is_in_ring (binary, 1) • stereo (one-hot, 7) 17 14 133 node(atom) features 133 features 14 features e.g. Features for ChemProp (Yang et al, 2019) atoms → nodes bonds → edges 1. permutation equivariance 2. permutation invariance

1 3 explicit Hs 4 5 6 7 8 9 10 11 12 13 14 15 16 17 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Any permutation of this numbering should not change the results. ❗ atom features bond features topology Molecular Graph read out graph-level output • sum, mean or max • attentive pooling CID 204 • atomic_num (one-hot, 101) • total_degree (one-hot, 7) • formal_charge (one-hot, 6) • chiral_tag (one-hot, 5) • num_Hs (one-hot, 6) • hybridization (one-hot, 6) • is_aromatic (binary, 1) • atomic_mass (real, 1) 17 edge(bond) features • no_bond (binary, 1) • is_single (binary, 1) • is_double (binary, 1) • is_triple (binary, 1) • is_aromatic (binary, 1) • is_connjugated (binary, 1) • is_in_ring (binary, 1) • stereo (one-hot, 7) 17 14 133 node(atom) features 133 features 14 features e.g. Features for ChemProp (Yang et al, 2019) atoms → nodes bonds → edges 1. permutation equivariance 2. permutation invariance

/ 166 (SBQI/FVSBM/FUXPSLT (//T 42 N O C C C
C H H H H H N O C C C C H H H H H GNN Layer GNN updates features

C H H H H H N O C C C C H H H H H GNN Layer GNN updates features <latexit sha1_base64="+I1ZH8a510AHL/VRK05INyOdDHc=">AAACi3ichVHLSsNAFL2Nr1qtrboR3BRLxVWZaFEpLooiuOzDPqAtJYnTdmheJGmhhv6ASzcu6kbBhfgBfoAbf8BFP0FcVnDjwps0IFqsN0zmzJl77pyZK+oyMy1CBj5uanpmds4/H1hYDC6FwssrBVNrGxLNS5qsGSVRMKnMVJq3mCXTkm5QQRFlWhRbR85+sUMNk2nqqdXVaVURGiqrM0mwkCpVRMVu9mqsFo6SOHEjMg54D0TBi7QWfoQKnIEGErRBAQoqWIhlEMDErww8ENCRq4KNnIGIufsUehBAbRuzKGYIyLbw38BV2WNVXDs1TVct4SkyDgOVEYiRF3JPhuSZPJBX8vlnLdut4Xjp4iyOtFSvhS7Wch//qhScLWh+qyZ6tqAO+65Xht51l3FuIY30nfOrYS6Zjdmb5Ja8of8bMiBPeAO18y7dZWi2P8GPiF7wxbBB/O92jIPCdpzfjScyiWjq0GuVH9ZhA7awH3uQghNIQ97twyX04ZoLcjtckjsYpXI+T7MKP4I7/gL6JJMZ</latexit> hi <latexit sha1_base64="iVE2zwSrY7uMFp5lULN8y4s7ZXg=">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</latexit> eij atom features bond features

C H H H H H N O C C C C H H H H H GNN Layer GNN updates features <latexit sha1_base64="rQGx6XMOvsCjXRp7b9gbmKjgm1M=">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</latexit> hi 0 @hi, M j2Ni (hi, hj, eij) 1 A Update by “Message Passing” <latexit sha1_base64="+I1ZH8a510AHL/VRK05INyOdDHc=">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</latexit> hi <latexit sha1_base64="iVE2zwSrY7uMFp5lULN8y4s7ZXg=">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</latexit> eij atom features bond features

C H H H H H N O C C C C H H H H H GNN Layer GNN updates features Ԯ ԮMessage Permutation equivariant operations • nn.Linear Bond features can be used (typically in Ԯ) <latexit sha1_base64="rQGx6XMOvsCjXRp7b9gbmKjgm1M=">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</latexit> hi 0 @hi, M j2Ni (hi, hj, eij) 1 A Update by “Message Passing” <latexit sha1_base64="+I1ZH8a510AHL/VRK05INyOdDHc=">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</latexit> hi <latexit sha1_base64="iVE2zwSrY7uMFp5lULN8y4s7ZXg=">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</latexit> eij atom features bond features

C H H H H H N O C C C C H H H H H GNN Layer GNN updates features • sum, mean or max • attentive pooling ԯ ԯAggregate Permutation invariant operations Ԯ ԮMessage Permutation equivariant operations • nn.Linear Bond features can be used (typically in Ԯ) <latexit sha1_base64="rQGx6XMOvsCjXRp7b9gbmKjgm1M=">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</latexit> hi 0 @hi, M j2Ni (hi, hj, eij) 1 A Update by “Message Passing” <latexit sha1_base64="+I1ZH8a510AHL/VRK05INyOdDHc=">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</latexit> hi <latexit sha1_base64="iVE2zwSrY7uMFp5lULN8y4s7ZXg=">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</latexit> eij atom features bond features

C H H H H H N O C C C C H H H H H GNN Layer GNN updates features • sum, mean or max • attentive pooling ԯ ԯAggregate Permutation invariant operations ԰ ԰Update Any • nn.Linear Ԯ ԮMessage Permutation equivariant operations • nn.Linear Bond features can be used (typically in Ԯ) <latexit sha1_base64="rQGx6XMOvsCjXRp7b9gbmKjgm1M=">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</latexit> hi 0 @hi, M j2Ni (hi, hj, eij) 1 A Update by “Message Passing” <latexit sha1_base64="+I1ZH8a510AHL/VRK05INyOdDHc=">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</latexit> hi <latexit sha1_base64="iVE2zwSrY7uMFp5lULN8y4s7ZXg=">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</latexit> eij atom features bond features

/ 166 6TF$BTF7JSUVBM4DSFFOJOH 24"32413 43 ChemProp (Directed MPNN) ExtraTrees w/
ECFP6(1024) Performance for unseen (test) data: Standard ML GNN Stokes et al, Cell (2020) https://doi.org/10.1016/j.cell.2020.01.021 Marchant, Nature (2020) https://doi.org/10.1038/d41586-020-00018-3 ChemProp (Yang et al, 2019) from MIT MLPDS (Machine Learning for Pharmaceutical Discovery and Synthesis) Consortium Disclaimer: This is just for a toy demo. This should be taken as classification for ACTIVITY_OUTCOME (Active or Inactive) 95.079% (Active/Inactive) 95.604% (Active/Inactive) • Regression for LogGI50 • Regression for LogGI50 • Classification accuracy • Classification accuracy RMSE 0.6076 RMSE 0.7970 Activie/Inactive (Classification), LogGI50 (Regression)

/ 166 &$'1ה/FVSBM(SBQI'JOHFSQSJOU 44 ˖ /FVSBM(SBQI'JOHFSQSJOU剑ⴱ劍ח䲿周ׁ׸׋(//ך♧א ˖ (SBQI$POWPMVUJPO׾欽ְ׋(//ך♧珏ה׫זׇ׷ ˖ &$'1
$JSDVMBS'JOHFSQSJOU ך'JOHFSQSJOU鎘皾׾ػًٓة׾䭯א䗍ⴓ〳腉ז 怴皾ד剅ֹ湫ֿׅהד䖤׵׸׷㷕统〳腉ז'JOHFSQSJOUהְֲ⡘縧בֽ Duvenaud, Maclaurin, Aguilera-Iparraguirre, Gómez-Bombarell, Hirzel, Aspuru-Guzik, Adams, Convolutional networks on graphs for learning molecular ﬁngerprints. NIPS (2015)

/ 166 ("5ה5SBOTGPSNFS㘗(// 45 (Multihead) Self-attention Feed-forward NN Add +
LayerNorm Add + LayerNorm ˖ ぐ갥挿ך暴䗙كؙزٕ׾刿倜ׅ׷ꥷח"UUFOUJPO׾Ⰵ׸׋ְ ˖ 5SBOTGPSNFSכزهٗآⵖ秈ךזְ(SBQI"UUFOUJPO/FUXPSL ("5 㢌珏ה׫זׇ׷ ˖ 鷞ח׮׍׹׿5SBOTGPSNFS㘗ך4FMG"UUFOUJPO׾(//ח׮׍ֿ׬ֿה׮דֹ׷ Transformer GNN Layer ⡂גְ׷˘ Embedding + Pos Encoding A Generalization of Transformer Networks to Graphs Dwivedi & Bresson (2020) https://arxiv.org/abs/2012.09699 Do Transformers Really Perform Bad for Graph Representation? Ying et al (2021) https://arxiv.org/abs/2106.05234 Communicative Representation Learning on Attributed Molecular Graphs Song et al (2020) https://www.ijcai.org/proceedings/2020/0392.pdf Graph-BERT: Only Attention is Needed for Learning Graph Representations Zhang et al (2020) https://arxiv.org/abs/2001.05140 Veličković, Cucurull, Casanova, Romero, Liò, Bengio, Graph Attention Networks (ICLR 2018) https://arxiv.org/abs/1710.10903 Joshi, Transformers are Graph Neural Networks. (2020) https://graphdeeplearning.github.io/post/transformers-are-gnns/ Ying et al (2021) ͷGraphormer͸ KDDCup 2021ͷOpen Graph Benchmark Large-Scale Challenge(ޙड़)ͷGraph-level λεΫͷ༏উϞσϧͰ࢖ΘΕͨ େن໛σʔλͳΒάϥϑͰ΋ Transformer͸༗ޮ…!?

/ 166 ⴓ㶨邌植ך✲⵸㷕统ה鯄獳㷕统 46 ˖ 5SBOTGPSNFSפךꟼ䗰כ 4FMG4VQFSWJTFEז 㣐鋉垷✲⵸㷕统ה鯄獳פך劍䖉ך植׸ ˖ ⴓ㶨ةأؙ׮植㹋ך⦐ⴽ朐屣דכ㼭؟ٝفٕד֮׷ֿהָקה׿ו
˖ ׮׃害欽ךⴓ㶨邌植׾㣐鋉垷✲⵸㷕统ח״׶栻䖤׃'FXTIPU;FSPTIPU鯄獳ָדֹ׷ ךז׵岚⿹⸬卓כ鎘׶濼׸זְ DG$7ך*NBHF/FUQSFUSBJOFE$// /-1ך#&35瘝 Strategies for Pre-training Graph Neural Networks Hu, Liu, Gomes, Zitnik, Liang, Pande, Leskovec (ICLR 2020) https://arxiv.org/abs/1905.12265 Self-Supervised Graph Transformer on Large-Scale Molecular Data Rong, Bian, Xu, Xie, Wei, Huang, Huang (NeurIPS 2020) https://arxiv.org/abs/2007.02835

/ 166 ⴓ㶨邌植ך欰䧭 47 ˖ ׮ֲמהאךⴓ㶨ך邌植㷕统פך劍䖉כⴓ㶨ؚٓؿװⴓ㶨圓鸡ך欰䧭 ˖ ⴓ㶨欰䧭ך㜥さכ暴ח%FDPEFSָꬊ荈僇ד圓鸡涸זⳢ椚׾㹋植ׅ׷䗳銲ָ֮׷ ˖ 圓䧭䚍ٌآُ٦ٕ䚍װ⻉㷕涸ٕ٦ٕ׮罋䣁׃זְה䠐㄂ךזְ⳿⸂חז׶䖤׷
˖ 俑㶵⴨邌植 4.*-&4鎸岀 ַ׵ך欰䧭כ湫䱸涸זךדؚٓؿ邌植ך⮚⡘䚍׮銲嗚鏾 https://arxiv.org/abs/2012.15544

/ 166 6TF$BTF2VBOUVNDIFNJTUSZ 48 https://qcarchive.molssi.org/apps/ml_datasets/

/ 166 6TF$BTF2VBOUVNDIFNJTUSZ 49 input output gdb_21014 1000 sec
Density Functional Theory (DFT) B3LYP/6-31G(2df, p) <latexit sha1_base64="JI//afsBt1AdIhSgVUbVSGVXtww=">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</latexit> ˆ H = E ⢽ ♧ꨵ㶨晛ך4DISµEJOHFS倯玎䒭 ,PIOˊ4IBN倯玎䒭 ך実鍑 QMܭࢉ

/ 166 6TF$BTF2VBOUVNDIFNJTUSZ 49 input output gdb_21014 1000 sec
Density Functional Theory (DFT) B3LYP/6-31G(2df, p) <latexit sha1_base64="JI//afsBt1AdIhSgVUbVSGVXtww=">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</latexit> ˆ H = E ⢽ ♧ꨵ㶨晛ך4DISµEJOHFS倯玎䒭 ,PIOˊ4IBN倯玎䒭 ך実鍑 ML 0.01 sec ≈ 100,000 times faster! QMܭࢉ

/ 166 6TF$BTF2VBOUVNDIFNJTUSZ 50 ICML 2017 https://arxiv.org/abs/1704.01212 JCTC 2017 https://doi.org/10.1021/acs.jctc.7b00577
˖ (PPHMFָ葿ղז(//ךغٔؒ٦ءّٝ׾չ.1// .FTTBHF1BTTJOH// պה׃ג 窟♧涸ח鋅湫׃׋ꥷחة٦؜حزחׁ׸׋ךָֿךꆀ㶨⻉㷕鎘皾鵚⡂ةأؙ

/ 166 6TF$BTF2VBOUVNDIFNJTUSZ 51 ؔٔآشٕך'$'1⾱㶨♶㢌ꆀ ؔٔآشٕך&$'1⾱㶨♶㢌ꆀ • the number of
immediate neighbors who are “heavy” (non-hydrogen) atoms • the valence minus the number of hydrogens • the atomic number • the atomic mass • the atomic charge • the number of attached hydrogens • whether the atom is contained in at least one ring %BZMJHIU ⾱㶨♶㢌ꆀ • hydrogen-bond acceptor or not? • hydrogen-bond donor or not? • negatively ionizable or not? • positively ionizable or not? • aromatic or not? • halogen or not? Rogers and Hahn, JCIM (2005) https://doi.org/10.1021/ci100050t Faber et al, JCTC (2017) https://doi.org/10.1021/acs.jctc.7b00577 .1//ח״׷ꆀ㶨⻉㷕鎘皾鵚⡂ד欽ְ׵׸׋갥挿٥鴟暴䗙鸬竲ꆀٓكٕ

/ 166 4DI/FU 52 input molecule H2O gdb_3 0 1
2 graph (SchNet) 0 1 atom features 0 1 2 2 edges w/ cutoff (10Å) 0 bond features 0 1 1 0 2 2 1 2 edge_index 0.9620 0.9622 1.5133 <latexit sha1_base64="WhwbZjIo+PbaHz7kU/YZBO38PiQ=">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</latexit> rij := kri rj k <latexit sha1_base64="kMmroSd0z/qeaFfqTkrtDbgltFg=">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</latexit> Z0 = 8 <latexit sha1_base64="QxdA1PVsyCLNE23CpTjm2APprYs=">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</latexit> Z1 = 1 <latexit sha1_base64="PJMbQqlxF/BaTgtbHwfwEQN8SrI=">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</latexit> Z2 = 1 <latexit sha1_base64="A/aHUcWCUQde6WVY9Df1h30Gjpk=">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</latexit> r0 = [ 0.0344, 0.9775, 0.0076] <latexit sha1_base64="2hhG9gKLK2JIb9w0aH6ObiinRms=">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</latexit> r1 = [0.0648, 0.0206, 0.0015] <latexit sha1_base64="FqaYo7zlBtUvxlEmhgyAfxy/v8k=">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</latexit> r2 = [0.8718, 1.3008, 0.0007] SchNet (Schütt et al, 2017) <latexit sha1_base64="tzvRXqv2dAYIROlG6uwbJPf0mrw=">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</latexit> xi xi + 0 @ X j2Ni (xj) !ij 1 A Message Passing with residual connections <latexit sha1_base64="4oqceeOsg0RegmHmCOLOjG0SaOU=">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</latexit> x0 <latexit sha1_base64="jqQfQ7TB6F1UPH31OFoS1eerzNw=">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</latexit> x1 <latexit sha1_base64="fLMd1ywDpT0cBkzaL9hTb77jq/8=">AAACi3ichVHLSsNAFL2Nr1qtrboR3BRLxVWZ1KJSXBRFcNmHfUBbShLHGpoXybRYQ3/ApRsXdaPgQvwAP8CNP+CinyAuK7hx4U0aEC3WGyZz5sw9d87MFQ1FthghfR83MTk1PeOfDczNBxdC4cWloqW3TIkWJF3RzbIoWFSRNVpgMlNo2TCpoIoKLYnNfWe/1KamJevaEesYtKYKDU0+kSWBIVWuiqp91q0n6uEoiRM3IqOA90AUvMjo4UeowjHoIEELVKCgAUOsgAAWfhXggYCBXA1s5ExEsrtPoQsB1LYwi2KGgGwT/w1cVTxWw7VT03LVEp6i4DBRGYEYeSH3ZECeyQN5JZ9/1rLdGo6XDs7iUEuNeuhiJf/xr0rFmcHpt2qsZwYnsON6ldG74TLOLaShvn1+NcincjF7ndySN/R/Q/rkCW+gtd+luyzN9cb4EdELvhg2iP/djlFQTMT5rXgym4ym97xW+WEV1mAD+7ENaTiEDBTcPlxCD665ILfJpbjdYSrn8zTL8CO4gy+ndJLy</latexit> x2 <latexit sha1_base64="YVJW2X9s34FCmpunsQgR00z8vXY=">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</latexit> w01 <latexit sha1_base64="tYR7XnwyhyUSVK/6XFo1uz/tDtI=">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</latexit> w02 <latexit sha1_base64="Ak3wjfcp94hUo7DAHdEjDzlDdm0=">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</latexit> w12

2 graph (SchNet) 0 1 atom features 0 1 2 2 edges w/ cutoff (10Å) 0 bond features 0 1 1 0 2 2 1 2 edge_index 0.9620 0.9622 1.5133 <latexit sha1_base64="WhwbZjIo+PbaHz7kU/YZBO38PiQ=">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</latexit> rij := kri rj k <latexit sha1_base64="kMmroSd0z/qeaFfqTkrtDbgltFg=">AAACinichVHLSsNAFL2Nr1qrrboR3ARLxVW5LUWrIhR14bIP+8BaShKnNTRNQpIWavEH3LkS7ErBhfgBfoAbf8BFP0FcVnDjwps0IFqsN0zmzJl77pyZK+qKbFqIPQ83Nj4xOeWd9s34Z+cCwfmFvKk1DYnlJE3RjKIomEyRVZazZEthRd1gQkNUWEGs79n7hRYzTFlTD622zsoNoabKVVkSLKIKRxXkd/hEJRjCCDrBD4OoC0LgRkoLPsIxnIAGEjShAQxUsAgrIIBJXwmigKATV4YOcQYh2dlncA4+0jYpi1GGQGyd/jValVxWpbVd03TUEp2i0DBIyUMYX/Ae+/iMD/iKn3/W6jg1bC9tmsWBlumVwMVS9uNfVYNmC06/VSM9W1CFhONVJu+6w9i3kAb61tlVP7uVCXdW8RbfyP8N9vCJbqC23qW7NMt0R/gRyQu9GDUo+rsdwyAfi0TXI/F0PJTcdVvlhWVYgTXqxwYk4QBSkHPqX8I1dDk/F+M2ue1BKudxNYvwI7j9Ly4OkVo=</latexit> Z0 = 8 <latexit sha1_base64="QxdA1PVsyCLNE23CpTjm2APprYs=">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</latexit> Z1 = 1 <latexit sha1_base64="PJMbQqlxF/BaTgtbHwfwEQN8SrI=">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</latexit> Z2 = 1 <latexit sha1_base64="A/aHUcWCUQde6WVY9Df1h30Gjpk=">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</latexit> r0 = [ 0.0344, 0.9775, 0.0076] <latexit sha1_base64="2hhG9gKLK2JIb9w0aH6ObiinRms=">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</latexit> r1 = [0.0648, 0.0206, 0.0015] <latexit sha1_base64="FqaYo7zlBtUvxlEmhgyAfxy/v8k=">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</latexit> r2 = [0.8718, 1.3008, 0.0007] nn.Embedding 128 -1.249 1.6278 -0.1370 ⋮ -0.9488 0.3105 -1.6185 0.1960 ⋮ -0.5310 0.3105 -1.6185 0.1960 ⋮ -0.5310 <latexit sha1_base64="4oqceeOsg0RegmHmCOLOjG0SaOU=">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</latexit> x0 <latexit sha1_base64="jqQfQ7TB6F1UPH31OFoS1eerzNw=">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</latexit> x1 <latexit sha1_base64="fLMd1ywDpT0cBkzaL9hTb77jq/8=">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</latexit> x2 SchNet (Schütt et al, 2017) <latexit sha1_base64="tzvRXqv2dAYIROlG6uwbJPf0mrw=">AAAC9XichVHNShxBEK6d+BeNuiaXgJchi7IiLL0iieQk5pKT+Lcq2DL0jL27vfZMDz29a3SYF8gL5BByiKgQcvDoA3jxBRLwEYJHBS8erJ0dEqKoNcz011/VV/N1lxtKERlCznPWs67unt6+5/0DLwaHhvMjL1cj1dQer3hKKr3usohLEfCKEUby9VBz5ruSr7nbH9r5tRbXkVDBitkN+abPaoGoCo8ZpJx8SF0//pQ4wqaSVw3TWu3Yf7lJm4aRSDNFGjV9J27YVAQ29Zmpe0zG81iVYFFdFDNRY8KmakuZtAlVPq+xxIlFI6Fa1OpmwskXSImkYd8H5QwUIIsFlT8BClugwIMm+MAhAINYAoMInw0oA4EQuU2IkdOIRJrnkEA/aptYxbGCIbuN3xruNjI2wH27Z5SqPfyLxFej0oYx8ov8IJfkjPwkf8jNg73itEfbyy6ubkfLQ2f48+vl6ydVPq4G6v9Uj3o2UIWZ1KtA72HKtE/hdfStvS+Xy++XxuJxsk8u0P93ck5O8QRB68o7XORLXx/x46IXvDEcUPnuOO6D1alS+W1penG6MDuXjaoPRuENFHEe72AWPsICVLD/b7jJded6rB3rm3VgHXVKrVymeQX/hXV8C560vMU=</latexit> xi xi + 0 @ X j2Ni (xj) !ij 1 A Message Passing with residual connections <latexit sha1_base64="YVJW2X9s34FCmpunsQgR00z8vXY=">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</latexit> w01 <latexit sha1_base64="tYR7XnwyhyUSVK/6XFo1uz/tDtI=">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</latexit> w02 <latexit sha1_base64="Ak3wjfcp94hUo7DAHdEjDzlDdm0=">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</latexit> w12

2 graph (SchNet) 0 1 atom features 0 1 2 2 edges w/ cutoff (10Å) 0 bond features 0 1 1 0 2 2 1 2 edge_index 0.9620 0.9622 1.5133 <latexit sha1_base64="WhwbZjIo+PbaHz7kU/YZBO38PiQ=">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</latexit> rij := kri rj k 50 MLP 50 →128 0.1803 0.0826 0.3349 ⋮ -0.474 0.0403 -0.003 0.0802 ⋮ -0.061 0.1803 0.0826 0.3349 ⋮ -0.474 128 <latexit sha1_base64="zybc8bdG60pci39izd8WqLQ5/Rk=">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</latexit> exp( ↵(rij µ↵)2) <latexit sha1_base64="kMmroSd0z/qeaFfqTkrtDbgltFg=">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</latexit> Z0 = 8 <latexit sha1_base64="QxdA1PVsyCLNE23CpTjm2APprYs=">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</latexit> Z1 = 1 <latexit sha1_base64="PJMbQqlxF/BaTgtbHwfwEQN8SrI=">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</latexit> Z2 = 1 <latexit sha1_base64="A/aHUcWCUQde6WVY9Df1h30Gjpk=">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</latexit> r0 = [ 0.0344, 0.9775, 0.0076] <latexit sha1_base64="2hhG9gKLK2JIb9w0aH6ObiinRms=">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</latexit> r1 = [0.0648, 0.0206, 0.0015] <latexit sha1_base64="FqaYo7zlBtUvxlEmhgyAfxy/v8k=">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</latexit> r2 = [0.8718, 1.3008, 0.0007] nn.Embedding 128 -1.249 1.6278 -0.1370 ⋮ -0.9488 0.3105 -1.6185 0.1960 ⋮ -0.5310 0.3105 -1.6185 0.1960 ⋮ -0.5310 <latexit sha1_base64="4oqceeOsg0RegmHmCOLOjG0SaOU=">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</latexit> x0 <latexit sha1_base64="jqQfQ7TB6F1UPH31OFoS1eerzNw=">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</latexit> x1 <latexit sha1_base64="fLMd1ywDpT0cBkzaL9hTb77jq/8=">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</latexit> x2 Weighted ACSFs (ACSFs = atom- centered symmetry functions) for Behler-Parrinello potentials <latexit sha1_base64="bbWlQHipawsZwudry4/MYk1A7nU=">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</latexit> 1 2 ✓ cos ✓ ⇡rij rc ◆ + 1 ◆ cutoff function element-wise product <latexit sha1_base64="YVJW2X9s34FCmpunsQgR00z8vXY=">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</latexit> w01 <latexit sha1_base64="tYR7XnwyhyUSVK/6XFo1uz/tDtI=">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</latexit> w02 <latexit sha1_base64="Ak3wjfcp94hUo7DAHdEjDzlDdm0=">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</latexit> w12 SchNet (Schütt et al, 2017) <latexit sha1_base64="tzvRXqv2dAYIROlG6uwbJPf0mrw=">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</latexit> xi xi + 0 @ X j2Ni (xj) !ij 1 A Message Passing with residual connections

/ 166 6TF$BTF2VBOUVNDIFNJTUSZ 53 pred vs true for SchNet (Schütt
et al, 2017) pred vs true for DimeNet (Klicpera et al, 2020) Dipole Moment Energy U HOMO LUMO Heat Capacity Enthalpy H Dipole Moment Energy U HOMO LUMO Heat Capacity Enthalpy H

/ 166 6TF$BTF2VBOUVNDIFNJTUSZ 53 pred vs true for SchNet (Schütt
et al, 2017) pred vs true for DimeNet (Klicpera et al, 2020) Dipole Moment Energy U HOMO LUMO Heat Capacity Enthalpy H Dipole Moment Energy U HOMO LUMO Heat Capacity Enthalpy H ⦓鸞ְז׵ ⼧ⴓ鏩㺁דֹ׷✮庠铎䊴 ֿ׸כذأزر٦ة 鎮箺儗ח 鋅ׇגזְر٦ة ך穠卓

/ 166 6TF$BTF2VBOUVNDIFNJTUSZ 54 SchNet (Schütt et al, 2017) DimeNet
(Klicpera et al, 2020) Free Energy Free Energy y_true y_true y_pred y_pred ExtraTrees w/ ECFP6 LightGBM w/ ECFP6 3-Layer MLP w/ ECFP6 (without 3D geometry) (without 3D geometry) (without 3D geometry) Free Energy Free Energy Free Energy

/ 166 4DI/0SC岚⹛ꟼ侧荈⡤׾堣唒㷕统 55

/ 166 (//TGPS(FPNFUSJD%FFQ-FBSOJOH 56 https://arxiv.org/abs/2104.13478 https://youtu.be/uF53xsT7mjc https://youtu.be/w6Pw4MOzMuo ICLR 2021 Keynote
(Michael Bronstein) Seminar Talk (Petar Veličković) (//כ䌴䎢ְ䎗⡦圓鸡׾窟♧涸ח䪔ִ׷単穈׫ 堣唒㷕统ךٕؒٓٝ؜ٝ٥فؚٗٓي (T(SJET (SPVQT (SBQIT (FPEFTJDT(BVHFT

/ 166 ِ٦ؙٔحسך麊⹛纇חꟼׅ׷♶㢌䚍٥ず㢌䚍 57 ˖ ِ٦ؙٔحس纇& %ך⚛鹌٥㔐鯄㼎獥䚍 ˖ 暴婊ِ٦ؙٔحس纇4&
%ך⚛鹌٥㔐鯄٥ꖎ⫷㼎獥䚍 Schütt et al, SchNet. (2017) https://arxiv.org/abs/1706.08566 Satorras et al, E(n) Equivariant Graph Neural Networks. (2021) https://arxiv.org/abs/2102.09844 Anderson et al, Cormorant. (2019) https://arxiv.org/abs/1906.04015 Unke et al, PhysNet. (2019) https://arxiv.org/abs/1902.08408 Klicpera et al, DimeNet++. (2020) https://arxiv.org/abs/2011.14115 Fuchs et al, SE(3)-Transformers. (2021) https://arxiv.org/abs/2006.10503 Köhler et al, Equivariant Flows (Radial Field). (2020) https://arxiv.org/abs/2006.02425 Thomas et al, Tensor Field Networks. (2018) https://arxiv.org/abs/1802.08219 ⱖ⫷ָ㢌䳔חꟼ׃ג ♶㢌 JOWBSJBU ず㢌 FRVJWBSJBOU <latexit sha1_base64="NH4UQ68bqmsH0AzQM//vHVYIu40=">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</latexit> f(g · x) = g · f(x) <latexit sha1_base64="z65vGkIR8AznuZeRro+w9TcH+xY=">AAACl3ichVHLSsNAFD3Gd3206kZxEyyVuilTFRVBLAri0qqtQislSac1mCYhmZZq8Qf8AReCoCAqfoAf4MYfcOEniMsKblx4mwZEi3rDZM6cuefOmbmqbeiuYOy5TWrv6Ozq7ukN9PUPDAZDQ8Np1yo7Gk9plmE5u6rickM3eUrowuC7tsOVkmrwHfVgtbG/U+GOq1vmtji0+V5JKZp6QdcUQVQuNFyIFrNa3hJydUpekgvR6lQuFGYx5oXcCuI+CMOPDSt0jyzysKChjBI4TAjCBhS49GUQB4NN3B5qxDmEdG+f4xgB0pYpi1OGQuwB/Yu0yvisSetGTddTa3SKQcMhpYwIe2K3rM4e2R17YR+/1qp5NRpeDmlWm1pu54Ino1vv/6pKNAvsf6n+9CxQwILnVSfvtsc0bqE19ZWj0/rW4makNsku2Sv5v2DP7IFuYFbetKsk3zz7w49KXujFqEHxn+1oBenpWHwuNpOcDSdW/Fb1YBwTiFI/5pHAOjaQovpVnOMaN9KYtCytSevNVKnN14zgW0jJT5AOlcI=</latexit> f(g · x) = f(x) 㢌䳔׃ג׮׃זְהֹה㢌׻׵זְ 㢌䳔׃גַ׵ⱖ⫷׃ג׮ⱖ⫷׃גַ׵㢌䳔׃ג׮㢌׻׵זְ <latexit sha1_base64="h5Nu57LzNEgsKVoc7SjFgDOfXxQ=">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</latexit> g 2 G <latexit sha1_base64="98i0QCpyFbQuYbP7ylFU0FuKpWo=">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</latexit> f : X ! Y 䎗⡦涸(//דכ㛇劤涸ז銲锜暴חꆀ㶨⻉㷕鎘皾鵚⡂ך㜥さ & ず㢌 & ♶㢌 4& ず㢌⾱㶨ךYZ[䏟垥⦼׾׉ךתת갥挿暴䗙ꆀחׅ׷ךכ ➿周ך⢽⾱㶨꟦騃ꨄ׾鴟暴䗙ח 䎂遤獳⹛װ㔐鯄דYZ[כ㢌׻׷ָ⢽ִל׉ךⴓ㶨ךؒطؘٕ٦כ㢌׻׵זְ 갥挿װ鴟ך暴䗙ꆀװ(// ⱖ⫷ ךرؠ؎ٝד㹋植ׅ׷

/ 166 ⴓ㶨邌植ך窟♧涸倯岀锷חז׶ִ׷ַ 58 ػة٦ٝ鎉铂ה׃ג ⻉㷕ך侄猰剅٥ر٦ةك٦أח֮׷濼陎邌植 Brc1cncc(Br)c1 C[O-] CN(C)C=O Na+
COc1cncc(Br)c1 SMILES Structural Formla Steric Structures Electronic States Reactants Reagents Products 暟椚涸㼎韋ה׃ג ꆀ㶨⻉㷕ח㛇בֻꨵ㶨朐䡾鎘皾俑㶵⴨ ؚٓؿ %挿꧊さ ⴓ䋒PS 7PMVNF

/ 166 0(#-BSHF4DBMF$IBMMFOHF ,%%$VQ 59 1st place: 10 GNNs (12-Layer
Graphormer) + 8 ExpC*s (5-Layer ExpandingConv) 73 GNNs (11-Layer LiteGEMConv with Self-Supervised Pretraining) 20 GNNs (32-Layer GNN with Noisy Nodes) Test MAE 0.1200 (eV) 2nd place:Test MAE 0.1204 (eV) 3rd place: Test MAE 0.1205 (eV) %ךⴓ㶨ؚٓؿַ׵ꆀ㶨⻉㷕鎘皾 %'5鎘皾 ד実׭׋)0.0-6.0ٍؘحف׾✮庠ׅ׷ةأؙ ر٦ةإحز1VC$IFN2$ַ׵ ؚٓؿ DG2.כ ؚٓؿ Results: https://ogb.stanford.edu/kddcup2021/results/#awardees_pcqm4m https://ogb.stanford.edu/kddcup2021/

/ 166 *$3F%%⻉㷕⿾䘔ךرؠ؎ٝה涪鋅 60 "'*3 (33. "SUJDJBM'PSDF*OEVDFE3FBDUJPO ➂䊨⸂钷饯⿾䘔岀 (MPCBM3FBDUJPO3PVUF.BQQJOH ؚٗ٦غٕ⿾䘔穗騟وحؾؚٝ
⚥呌䪮遭כ䬿挿ꞿ٥⵸歊椚侄䱇ָꟚ涪׃׋ꆀ㶨⻉㷕鎘皾ח㛇בֻ ⻉㷕⿾䘔穗騟荈⹛䱱稊،ٕ؞ٔؤي S. Maeda, Y. Harabuchi, Exploring paths of chemical transformations in molecular and periodic systems: An approach utilizing force., WIREs Comput. Mol. Sci., 2021, 11, e1538. https://doi.org/10.1002/wcms.1538 ㉀欽晛اؿزؐؑ،ךせ⵸ח׮

/ 166 䞔㜠猰㷕ַ׵鋅׋⿾䘔穗騟ך荈⹛䱱稊 61 㸜㹀朐䡾 &2 㸜㹀朐䡾 &2 鼂獳朐䡾 54
θ 1 θ 2 鍑ֻץֹ㉏겗 㢳䂼䚍ך㢳㢌侧ꟼ侧ך 噰㼭鍑הꭓ挿ךչⰋ⴨䮙պ ׉ך⾱㶨ꂁ縧Ăח֮׷הֹך Ⰻؒطؘٕ٦& Ă ך⦼

/ 166 ⵖ秈 ꟼ侧䕎כꤿחכ剅ֽ׆ծ ぐ挿ךꟼ侧⦼G Y כ 䭷㹀׃׋Y׀הח鎘皾儗꟦׾ 銲ׅ׷㉏ְさ׻ׇד䖤׷ 䞔㜠猰㷕ַ׵鋅׋⿾䘔穗騟ך荈⹛䱱稊
62 㸜㹀朐䡾 &2 㸜㹀朐䡾 &2 鼂獳朐䡾 54 θ 1 θ 2 鍑ֻץֹ㉏겗 㢳䂼䚍ך㢳㢌侧ꟼ侧ך 噰㼭鍑הꭓ挿ךչⰋ⴨䮙պ ׉ך⾱㶨ꂁ縧Ăח֮׷הֹך Ⰻؒطؘٕ٦& Ă ך⦼  

θ 1 θ 2 鍑ֻץֹ㉏겗 㢳䂼䚍ך㢳㢌侧ꟼ侧ך 噰㼭鍑הꭓ挿ךչⰋ⴨䮙պ ׉ך⾱㶨ꂁ縧Ăח֮׷הֹך Ⰻؒطؘٕ٦& Ă ך⦼   ⾱㶨ꂁ縧 HFPNFUSZ 1PUFOUJBM FOFSHZ ꨵ㶨朐䡾岚⹛ꟼ侧 ꆀ㶨⻉㷕鎘皾 ˖ (BVTTJBO ˖ 03$" ˖ HBNFTT

θ 1 θ 2 鍑ֻץֹ㉏겗 㢳䂼䚍ך㢳㢌侧ꟼ侧ך 噰㼭鍑הꭓ挿ךչⰋ⴨䮙պ ׉ך⾱㶨ꂁ縧Ăח֮׷הֹך Ⰻؒطؘٕ٦& Ă ך⦼   ⾱㶨ꂁ縧 HFPNFUSZ 1PUFOUJBM FOFSHZ ꨵ㶨朐䡾岚⹛ꟼ侧

θ 1 θ 2 鍑ֻץֹ㉏겗 㢳䂼䚍ך㢳㢌侧ꟼ侧ך 噰㼭鍑הꭓ挿ךչⰋ⴨䮙պ ׉ך⾱㶨ꂁ縧Ăח֮׷הֹך Ⰻؒطؘٕ٦& Ă ך⦼   ⾱㶨ꂁ縧 HFPNFUSZ 1PUFOUJBM FOFSHZ ꨵ㶨朐䡾岚⹛ꟼ侧 ꆀ㶨⻉㷕鎘皾 ˖ (BVTTJBO ˖ 03$" ˖ HBNFTT

θ 1 θ 2 鍑ֻץֹ㉏겗 㢳䂼䚍ך㢳㢌侧ꟼ侧ך 噰㼭鍑הꭓ挿ךչⰋ⴨䮙պ ׉ך⾱㶨ꂁ縧Ăח֮׷הֹך Ⰻؒطؘٕ٦& Ă ך⦼ ׉׿זך搀椚דכ 䎃ծ剣せז鎘皾⻉㷕ך侄猰剅 ד'SBOL+FOTFOכչ㢌侧ך侧ָ זְ׃׾馄ִ׷ה⻉㷕⿾䘔ך鼂獳朐䡾׾ׅץג実׭׷ֿהכ♶〳腉ד֮׷պה鶢ץ׋կ

θ 1 θ 2 鍑ֻץֹ㉏겗 㢳䂼䚍ך㢳㢌侧ꟼ侧ך 噰㼭鍑הꭓ挿ךչⰋ⴨䮙պ ˖ 噰㼭鍑 &2 ֶ״ןꭓ挿 54 ׾ 実׭׷̔չ"'*3պ ˖ Ⰻ⴨䮙٥ⵖ秈➰ֹ穗騟䱱稊̔ չ(33.պ 'SBOL+FOTFOך侄猰剅כ䎃ח չ㣐ꅿ٥⵸歊׵ך倯岀ד〳腉חז׏׋պ ה剅ֹ䳔ִ׵׸׋

/ 166 噰㼭鍑 &2 ֶ״ןꭓ挿 54 ׾実׭׷̔չ"'*3պ 66 ׉׮׉׮չ1&4պך㢳䂼䚍ָז׈欰ׄ׷ַ׾罋ִג׫׷ אך⾱㶨"ה#ָ⿾䘔׃גⴓ㶨"#ח
ז׷הֹؒطؘٕ٦ꥺ㠖ָ植׸׷ַ׵ " # S "# "# &2 54 騃ꨄח䘔ׄ׋؜ة׾כַׇ׷ה וַֿד⽃锃幾㼰ꟼ侧חז׶ ꨇ׃ְ)JMM$MJNCJOHָ♶銲ח 騃ꨄח䘔ׄ׋ؒطؘٕ٦ ⸂ ׾ ➂䊨涸ח⸇ִ׷ֿהח湱䔲鵚⡂54

/ 166 噰㼭鍑 &2 ֶ״ןꭓ挿 54 ׾実׭׷̔չ"'*3պ 67 ぐ⾱㶨׾⾱㶨꟦ך騃ꨄָ㼭ֻׁז׷倯ぢפ➂䊨⸂'ד䬃ׅ PS䒷ֻ
"SUJDJBM'PSDF*OEVDFE3FBDUJPO ➂䊨⸂钷饯⿾䘔岀⾱㶨꧊さ4ה4ך꟦ך"'*3ꟼ侧騃ꨄ ˖ ꦄ䱸&2ה穗歋54ָ 䖤׵׸׷ ˖ '׾禸窟涸ח㢌ִג ꦄ䱸&2׾笨繎涸ח䱱稊 ꦄ䱸&2 穗歋ׅ׷54 Ⱏ剣穠さ⼱䖇 <latexit sha1_base64="il4EkNHP/gYCGb84oy5/wv0yFmI=">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</latexit> rij <latexit sha1_base64="PN3QcQcJmm7HtMHQLSyUIZzGGr8=">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</latexit> Ri <latexit sha1_base64="5Ry5Nejqv0ra6NvgYtpsdE5/iAs=">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</latexit> ػًٓة ⸂'ך䓼ׁ <latexit sha1_base64="CjZ7YXJc2lmcGBfDn4BHNa0/pUs=">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</latexit> ↵ = Ⰵ⸂&2 4 4 ֿך鵚⡂涸ז♳歲⦼⟃♴ ך⿾䘔ꥺ㠖ד鼂獳דֹ׷ ⿾䘔穗騟׾笨繎涸ח䱱稊

/ 166 噰㼭鍑 &2 ֶ״ןꭓ挿 54 ׾実׭׷̔չ"'*3պ 68 ⳿涪暟颵ה欵暟ָ ♷ִ׵׸׷✳畭挿穗騟
׾実׭׷㜥さח⢪ֲ " #̔9 さ⢘㘗さ䧭 " #̔9 : 穈剏㘗さ䧭 "̔9 殯䚍⻉ "̔9 : ⴓ鍑٥⛣ꨄ .$"'*3 4$"'*3 %4"'*3 ⸂ ⸂ "%%' 4$"'*3הずׄ湡涸׌ָ "'*3ה殯ז׷䩛岀㢳䧭ⴓך꟦ח⸂׾ַֽ׷ ⽃♧䧭ⴓךⰻך⾱㶨㔚ך ꟦ח⸂׾ַֽ׷ ぐ⾱㶨׾⾱㶨꟦ך騃ꨄָ㼭ֻׁז׷倯ぢפ➂䊨⸂'ד䬃ׅ PS䒷ֻ "SUJDJBM'PSDF*OEVDFE3FBDUJPO ➂䊨⸂钷饯⿾䘔岀

/ 166 Ⰻ⴨䮙٥ⵖ秈➰ֹ穗騟䱱稊̔չ(33.պ 69 ⳿涪朐䡾ַ׵鼂獳〳腉ז&2׾"'*3ד⴨䮙׃ծ倜׋ז&2ָ⳿זֻז׷תד ⱄ䌓涸חֿךⳢ椚׾黝欽 (MPCBM3FBDUJPO3PVUF.BQQJOH ؚٗ٦غٕ⿾䘔穗騟وحؾؚٝ EQ 㹋ꥷחכ⾱㶨玎䏝ך禸דזְהⰋ⴨䮙כ
侧ָ㢳ֺׅג搀椚זךד黝㹅䗳銲ח䘔ׄגⵖ秈 ̔(333.דכ鸞䏝㹀侧遤⴨　簭岀 3$.$ ָⵃ欽〳腉 EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ

/ 166 *$3F%%⻉㷕⿾䘔ךرؠ؎ٝה涪鋅 70 EQ1 EQ2 Chemical Reaction How we
can have this?

/ 166 *$3F%%⻉㷕⿾䘔ךرؠ؎ٝה涪鋅 70 EQ1 EQ2 Chemical Reaction

/ 166 *$3F%%⻉㷕⿾䘔ךرؠ؎ٝה涪鋅 70 EQ1 EQ2 Chemical Reaction ML Retrosynthesis
prediction Forward Reaction prediction

/ 166 *$3F%%⻉㷕⿾䘔ךرؠ؎ٝה涪鋅 70 EQ1 EQ2 Chemical Reaction

/ 166 *$3F%%⻉㷕⿾䘔ךرؠ؎ٝה涪鋅 70 Potential Energy Surface <latexit sha1_base64="Wyp4gB8RxRsto5OIPkBWRdHaY3U=">AAAChHichVG7SgNBFD1ZNcZ31EawCQbFQsJE4wMLCYpgaRIThSiyu07i4GZ32Z0EYvAHtFUsrBQsxA/wA2z8AYt8glhGsLHwZrMgGtS7zM6ZM/fcOTNXsw3hSsbqAaWjsyvYHerp7esfGBwKD4/kXKvs6DyrW4bl7Giqyw1h8qwU0uA7tsPVkmbwbe1orbm/XeGOKyxzS1ZtvldSi6YoCF2VRKXW98NRFmNeRNpB3AdR+LFphR+wiwNY0FFGCRwmJGEDKlz68oiDwSZuDzXiHELC2+c4QS9py5TFKUMl9oj+RVrlfdakdbOm66l1OsWg4ZAygkn2zO5Ygz2xe/bCPn6tVfNqNL1UadZaWm7vD52OZd7/VZVoljj8Uv3pWaKAJc+rIO+2xzRvobf0lePLRmY5PVmbYjfslfxfszp7pBuYlTf9NsXTV3/40cgLvRg1KP6zHe0gNxuLL8QSqUQ0ueq3KoRxTGCa+rGIJDawiSzV5zjDOS6UoDKjzCnzrVQl4GtG8S2UlU9p44/F</latexit> E
<latexit sha1_base64="VQOOvVSP0lW6m0gNVQ8zA5pNsEc=">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</latexit> ri <latexit sha1_base64="kTQzD4iiA9afGMFuEz1PlDAJN4Y=">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</latexit> rj EQ1 EQ2 Chemical Reaction

<latexit sha1_base64="VQOOvVSP0lW6m0gNVQ8zA5pNsEc=">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</latexit> ri <latexit sha1_base64="kTQzD4iiA9afGMFuEz1PlDAJN4Y=">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</latexit> rj EQ1 EQ2 TS Chemical Reaction

<latexit sha1_base64="VQOOvVSP0lW6m0gNVQ8zA5pNsEc=">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</latexit> ri <latexit sha1_base64="kTQzD4iiA9afGMFuEz1PlDAJN4Y=">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</latexit> rj EQ1 EQ2 TS Chemical Reaction Energy <latexit sha1_base64="Wyp4gB8RxRsto5OIPkBWRdHaY3U=">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</latexit> E ML • Acceleration by ML potential? • Artiﬁcial force learning? ML Forces • Scope/network expansion? ML • Fill any gap between theory and experiments (reality) by data?

/ 166 71 ⴓ㶨ך䕎׾鋅ג⿾䘔ָ饯ֿ׷״ֲחֲתֻ䬃׃׋׶䒷ְ׋׶כ㷕统דֹ׷˘

/ 166 ꆀ㶨⻉㷕堣唒㷕统ך輐さ׾湡䭷׃ג 72

/ 166 ׮׃ֻכծءىُٖ٦ءّٝ堣唒㷕统ך輐さ 73 Annu. Rev. Phys. Chem. 71:361–90 (2020)
Nat. Rev. Chem. 4: 347–358 (2020) PNAS (2020)

/ 166 䩛竲ֹ涸٥鎸〾涸乼⡲ך堣唒㷕统䪮遭׮굲鬨涸ח涪㾜 74 https://uclnlp.github.io/nampi/ Machine intelligence capable of learning
complex procedural behavior, inducing (latent) programs, and reasoning with these programs is a key to solving artiﬁcial intelligence. Recently, there have been a lot of success stories in the deep learning community related to learning neural networks capable of using trainable memory abstractions. Neural Abstract Machines & Program Induction • Differentiable Neural Computers / Neural Turing Machines (Graves+ 2014) • Memory Networks (Weston+ 2014) • Pointer Networks (Vinyals+ 2015) • Neural Stacks (Grefenstette+ 2015, Joulin+ 2015) • Hierarchical Attentive Memory (Andrychowicz+ 2016) • Neural Program Interpreters (Reed+ 2016) • Neural Programmer (Neelakantan+ 2016) • DeepCoder (Balog+ 2016) : 䩛竲ֹ涸٥鎸〾涸乼⡲׮㷕统דֹ׷فؚٗٓيה׃ג䪔ִ׷״ֲחז׏גֹ׋

/ 166 䌓秛غ؎،أךرؠ؎ٝ僇爙涸濼陎堣唒㷕统ך輐さ 75 Variable 1 Variable 2 <latexit sha1_base64="Ill3Als4zZd947f5Xm9sW99d0QA=">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</latexit>
x1 <latexit sha1_base64="QFtMwnKe2I12XGZu0bNJbdnDaaE=">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</latexit> x2 <latexit sha1_base64="Ill3Als4zZd947f5Xm9sW99d0QA=">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</latexit> x1 <latexit sha1_base64="QFtMwnKe2I12XGZu0bNJbdnDaaE=">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</latexit> x2 x1 x2 y ML 椚锷⻉㷕זו傀濼ך濼陎׾筨⹛㆞׃גչ搀䠐㄂זؿ؍حذ؍ؚٝ穠卓חꤒ׵זְ״ֲחպ ٌرٕך荈歋䏝׾✮׭♳䩛חⵖ秈׃גֶֻ 害欽ך.-ٌرٕדכؿ؍حذ؍ؚٝח⢪ֲ ٌرٕך荈歋䏝ָ넝ֺׅג 6OEFSTQFDJDBUJPOךٔأָؙ넝ֺׅ׷ 植韋׾椚鍑׃׋ְ荈搫猰㷕ⴓꅿדכ㣐㉏겗 Ԩ 堣唒㷕统ٌرٕך䧭⸆ך׋׭חכ㢳ַ׸㼰זַ׸ ٌرٕך䌓秛غ؎،أָ湡⵸ך㉏겗ח黝さ׃גְ ׷䗳銲ָ֮׷ 傀濼זֿהכ㷕统ׅ׷䗳銲ָזְ Ԩ 害欽䚍ך넝ְٌرٕ׾넝ְ然䏝ד㷕统ׅ׷חכ 湱䘔ך花㣐זر٦ةָ䗳銲㢳ֻך㜥さծꨇ׃ְ 植➿涸.-דכ Ⰵ⸂㢌侧ך㟓㣐 ؗحثٝءؙٝ⻉ הػًٓةٌرٕ侧ך肍㣐⻉ח״׶ ٌرٕך荈歋䏝ָ넝ֺׅ׷˘

/ 166 ؚٖ؎نحؙأ剑黝⻉锷椚䱿锷ה窟鎘涸✮庠ך輐さ 76 5IFPSZESJWFO %BUBESJWFO ˖ 㼎韋植韋ך醱꧟⻉ ˖ ءىُٖ٦ءّٝ䪮岀׮醱꧟⻉
˖ 穗꿀涸ח寸׭׷ػًٓةװⴱ劍⦼ ˖ 害ꟼ侧ծ❛䳔湱ꟼ갪ך鏣鎘 ˖ 㼭؟ٝفٕ٥⡚ؕؐٝزך㉏겗 ˖ 䌓秛غ؎،أךٌرٕؒٝ؝٦س ˖ 㢩䯏ך⡚⥋걾䚍ה䱱稊 ˖ #MBDLCPY䚍٥鍑ꅸ䚍ך㉏겗 ˖ 濼陎ك٦أה锷椚䱿锷鎸〾"* ךꣲ歲 ˖ ⿑㺘䱿锷װ䱱稊ך鎘皾旗涪 /1㔭ꨇ䚍 ˖ 㣐ꆀر٦ةך濼陎⻉ך㉏겗 ˖ ⵖ秈فؚٗٓىؚٝװ穈さׇ剑黝⻉ ➂䊨濼腉ⴓꅿ ➂䊨濼腉ⴓꅿ ˖ %BUB%SJWFO䩛岀堣唒㷕统 ה➂꟦ך 锷椚涸䙼罋הך㣐ֹזٍؘحف ˖ %BUBָזְ걄㚖ך䱱稊װչמ׵׭ֹպ ˖ ٌرٕ黝欽眔㔲ה⥋걾䚍٥㸜Ⰻ䚍倜׋ז倯岀锷פ ر٦ةず⻉ծ垷⦺㷕统ծ锷椚さ䧭ծFUD 邌植㷕统ծٌرٕك٦أ剑黝⻉٥䓼⻉㷕统ծًة㷕统ծ欰䧭ٌرٕծFUD ս怴糊٥さ椚锷վ ս䌓秛٥穗꿀锷վ

/ 166 Ⰻ⴨䮙٥ⵖ秈➰ֹ穗騟䱱稊̔չ(33.պ 77 ⳿涪朐䡾ַ׵鼂獳〳腉ז&2׾"'*3ד⴨䮙׃ծ倜׋ז&2ָ⳿זֻז׷תד ⱄ䌓涸חֿךⳢ椚׾黝欽 (MPCBM3FBDUJPO3PVUF.BQQJOH ؚٗ٦غٕ⿾䘔穗騟وحؾؚٝ EQ 㹋ꥷחכ⾱㶨玎䏝ך禸דזְהⰋ⴨䮙כ
侧ָ㢳ֺׅג搀椚זךד黝㹅䗳銲ח䘔ׄגⵖ秈 ̔(333.דכ鸞䏝㹀侧遤⴨　簭岀 3$.$ ָⵃ欽〳腉 EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ EQ

/ 166 ⿾䘔穗騟طحزٙ٦ؙ 78

/ 166 ⿾䘔穗騟طحزٙ٦ؙכ#JPJOGPד侔ղ灇瑔׃גֹ׋㼎韋79 IUUQCJPDIFNJDBMQBUIXBZTDPNNBQ

/ 166 ⻉㷕ךمحززؾحؙד֮׷׌ֽדזֻ˘ 80

/ 166 ⻉㷕ךمحززؾحؙד֮׷׌ֽדזֻ˘ 81

/ 166 堣唒㷕统ⴓꅿךمحززؾحؙד׮֮׷ 82 NeurIPS 2020 ICML 2020, 2021 ICLR
2020, 2021 • Self-Supervised Graph Transformer on Large-Scale Molecular Data • RetroXpert: Decompose Retrosynthesis Prediction Like A Chemist • Reinforced Molecular Optimization with Neighborhood- Controlled Grammars • Autofocused Oracles for Model-based Design • Barking Up the Right Tree: an Approach to Search over Molecule Synthesis DAGs • On the Equivalence of Molecular Graph Convolution and Molecular Wave Function with Poor Basis Set • CogMol: Target-Speciﬁc and Selective Drug Design for COVID-19 Using Deep Generative Models • A Graph to Graphs Framework for Retrosynthesis Prediction • Hierarchical Generation of Molecular Graphs using Structural Motifs • Learning to Navigate in Synthetically Accessible Chemical Space Using Reinforcement Learning • Reinforcement Learning for Molecular Design Guided by Quantum Mechanics • Multi-Objective Molecule Generation using Interpretable Substructures • Improving Molecular Design by Stochastic Iterative Target Augmentation • A Generative Model for Molecular Distance Geometry • GraphDF: A Discrete Flow Model for Molecular Graph Generation • An End-to-End Framework for Molecular Conformation Generation via Bilevel Programming • Equivariant message passing for the prediction of tensorial properties and molecular spectra • Learning Gradient Fields for Molecular Conformation Generation • Self-Improved Retrosynthetic Planning • Directional Message Passing for Molecular Graphs • GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation • Augmenting Genetic Algorithms with Deep Neural Networks for Exploring the Chemical Space • A Fair Comparison of Graph Neural Networks for Graph Classiﬁcation • MARS: Markov Molecular Sampling for Multi-objective Drug Discovery • Practical Massively Parallel Monte-Carlo Tree Search Applied to Molecular Design • Learning Neural Generative Dynamics for Molecular Conformation Generation • Conformation-Guided Molecular Representation with Hamiltonian Neural Networks • Symmetry-Aware Actor-Critic for 3D Molecular Design

˖ 堣唒㷕统㾊כ♧⡤⡦ָ嚂׃ְךַ ˖ ⴓ㶨ך邌植ה堣唒㷕统 ˖ ؚٖ؎نحؙأ剑黝⻉怴糊䌓秛 锷椚㷕ה窟鎘㷕ך輐さ ˖ 荈搫猰㷕灇瑔ד堣唒㷕统׾⢪ֲֶהׅ׷ה䗳׆עאַ׷劤䔲חꨇ׃ְ㉏겗 ˖ ر٦ةٌرؚٔٝה✮庠،ٕ؞ٔؤي 5IF5XP$VMUVSFT ˖ ✮庠ַ椚鍑ַ3BTIPNPO⸬卓 6OEFSTQFDJDBUJPO 鍑ꅸ㢳圫䚍 ˖ ➂꟦ך钠濼غ؎،أח歋勻ׅ׷㉏겗⟎铡ծ㣟侁ծ䧭⸆غ؎،أծFUD ˖ 堣唒㷕统ַ׵堣唒涪鋅פ ˖ չ涪鋅պչ椚鍑պך麣瘡כさ椚⻉דֹ׷ךַ荈⹛⻉דֹ׷ךַ

/ 166 ت٦ؙ؟؎سפ״ֲֿ׉ 84 Ԩ ֿ׸תדך鑧כ⚺חչꆀ㶨⻉㷕鎘皾ח״׷ر٦ةպדؙٔ٦ٝז⚅歲 錁庠ظ؎ؤָזְ٥⳿⸂׾䖤׷ךח䗳銲⼧ⴓזⰅ⸂䞔㜠ָⴓַ׏גְ׷٥ ְ׹ְ׹זؔ٦فٝر٦ةָⵃ欽דֹ׷٥FUD Ԩ 植㹋כא׵ְ˘
˖ 錁庠ظ؎ؤָ֮׶暟椚涸醱醡ָ䗳銲 ✳䏝庠׷ה⦼ָ殯ז׷倯ָ兛鸐 ˖ 椚锷鎘皾ח《׶Ⰵ׸׵׸גזְ搀侧ך❛窃㔓㶨װ㢩✉㔓㶨ך䕦갟 ˖ 醱꧟禸דכⰅ⸂㢌侧ח⡦׾Ⰵ׸׷ץֹזךַָ♶僇הְֲآٖٝو ̔Ⰵ⳿⸂ꟼ⤘ך堣䎷ָⴓַ׵זְַ׵堣唒㷕统׾⢪ְ׋ְךח խ䗳銲ז䞔㜠׾Ⰵ⸂חⰅ׸זְה堣唒㷕统חכ亻⡂湱ꟼ׃ַ鋅ִזְ ˖ ׉׮׉׮鎘庠٥ⵖ䖴דֹזְ׋ֻׁ׿ךغحؙؚٓؐٝس㔓㶨ָ֮׷ ˖ ➂꟦ָ㹋꿀׾鎘歗ׅ׷ה䖤׵׸׷ر٦ةכ䌢חغ؎،أ׾ろ׬ ̔չ葺ְㅷ颵ךպ䗳銲⼧ⴓז鋅劤⢽׾⡲׷ךכ劤䔲חꨇ׃ְ

/ 166 ت٦ؙ؟؎سַ׵ך5BLF)PNFًحإ٦آ 85 荈搫猰㷕ⴓꅿדךⵃ崞欽כ.-ך䪮遭灇熊׌ֽדכ䧭⸆׃זְկ ⴓꅿ㼔Ꟍ㹺הך⼿⫴ָ䗳銲♶〳妀

/ 166 ت٦ؙ؟؎سַ׵ך5BLF)PNFًحإ٦آ 85 ˖ .-ָוְֲֲ䪮遭זךַ.-ך暴䚍הꣲ歲׾姻׃ֻ䪾䳢ׅ׷ 荈搫猰㷕ⴓꅿדךⵃ崞欽כ.-ך䪮遭灇熊׌ֽדכ䧭⸆׃זְկ ⴓꅿ㼔Ꟍ㹺הך⼿⫴ָ䗳銲♶〳妀

/ 166 ت٦ؙ؟؎سַ׵ך5BLF)PNFًحإ٦آ 85 ˖ .-ָוְֲֲ䪮遭זךַ.-ך暴䚍הꣲ歲׾姻׃ֻ䪾䳢ׅ׷ ˖ չر٦ةך　꧊鎘歗㹋꿀鎘歗 הㅷ颵⥂鏾ծ黝欽眔㔲ך椚鍑պ
ָˑEBUBESJWFO˒ך䗰茖ד֮׷ֿה׾ְא׮䗰ח 荈搫猰㷕ⴓꅿדךⵃ崞欽כ.-ך䪮遭灇熊׌ֽדכ䧭⸆׃זְկ ⴓꅿ㼔Ꟍ㹺הך⼿⫴ָ䗳銲♶〳妀

/ 166 ت٦ؙ؟؎سַ׵ך5BLF)PNFًحإ٦آ 85 ˖ .-ָוְֲֲ䪮遭זךַ.-ך暴䚍הꣲ歲׾姻׃ֻ䪾䳢ׅ׷ ˖ չر٦ةך　꧊鎘歗㹋꿀鎘歗 הㅷ颵⥂鏾ծ黝欽眔㔲ך椚鍑պ
ָˑEBUBESJWFO˒ך䗰茖ד֮׷ֿה׾ְא׮䗰ח ˖ չ䱱稊պָ湡涸ז׵.-ך卓׋ׅ䕵ⶴכֻ֮תד♧鿇ה䗰䖤׷ " 㼔Ꟍ㹺הך⼿⫴ծⴓꅿך㼔Ꟍ濼陎ח撑׵׃׋嗚鏾٥鍑ꅸ " ءىُٖ٦ءّٝ٥㹋꿀荈⹛⻉٥锷椚䱿锷הך輐さ荈搫猰㷕ⴓꅿדךⵃ崞欽כ.-ך䪮遭灇熊׌ֽדכ䧭⸆׃זְկ ⴓꅿ㼔Ꟍ㹺הך⼿⫴ָ䗳銲♶〳妀

/ 166 5IF5XP$VMUVSFT 86 https://projecteuclid.org/euclid.ss/1009213726 (Open Access)

/ 166 -FP#SFJNBO ָ㥨ֹ 87 ˖ $"35 $MBTTJDBUJPOBOE3FHSFTTJPO5SFFT 1*.1-&
˖ 3BOEPN'PSFTU ˖ "SDJOH BLB#PPTUJOH ˖ #BHHJOH 1BTUJOH ˖ "$& "MUFSOBUJWF$POEJUJPOBM&YQFDUBUJPOT ˖ 4UBDLFE(FOFSBMJ[BUJPO BLB4UBDLJOH#MFOEJOH ˖ /POOFHBUJWF(BSSPUF -"440ך⵸魦GPS4VCTFU㔐䌓 ˖ *OTUBCJMJUZ4UBCJMJ[BUJPOJO.PEFM4FMFDUJPO ˖ 4IBOOPO.D.JMMBO#SFJNBO5IFPSFN 恷鵚瘝ⴓⶴ䚍 ˖ ,FMMZ#SFJNBO4USBUFHZ 剑黝ז㹀嫰⢽䨌殛 ˖ 6$#FSLFMFZせ钙侄䱇 ˖ 4*(,%%*OOPWBUJPO"XBSE ˖ 1SPCBCJMJUZ5IFPSJTU̔$POTVMUBOU̔4UBUJTUJUJBO *GTUBUJTUJDTJTBOBQQMJFEFMEBOEOPUBNJOPSCSBODIPGNBUIFNBUJDT UIFOPGUIFQVCMJTIFEQBQFSTBSFVTFMFTTFYFSDJTFT 3FFDUJPOTBGUFSSFGFSFFJOHQBQFSTGPS/*14˒ 5IF.BUIFNBUJDTPG(FOFSBMJ[BUJPO &E%)8PMQFSU https://en.wikipedia.org/wiki/File:Leo_Breiman.jpg 侧㷕ך1I% 6$#FSLFMFZ ̔侧㷕猰UFOVSF侄㆞ 6$-" ̔窟鎘؝ٝ؟ٕةٝز 䎃 ̔窟鎘㷕猰侄䱇 6$#FSLFMFZ

/ 166 -FP#SFJNBO ָ㥨ֹ 88 "OOBMTPG"QQMJFE4UBUJTUJDT 7PM /P
%FDFNCFS ח#SFJNBOך 鷄䞄暴꧊ָ֮׶ծ葿ղזꟼ⤘罏ָ䙼ְ⳿ װ娖〷׾铂׏גְתׅ ؿ؋ٝ䗳鋅 ׮׍׹׿'SJFENBO 0MTIFO 4UPOF׮

/ 166 89

/ 166 90

/ 166 91

/ 166 5IF5XP$VMUVSFT 92

/ 166 5IF5XP$VMUVSFT窟鎘㷕WT堣唒㷕统 93 The Data Modeling Culture The Algorithmic
Modeling Culture ⠗窟涸ז 窟鎘㷕堣唒㷕统 "Generative Models" "Discriminative Models" vs vs "Explanatory Modeling" "Predictive Modeling" vs

/ 166 -FP#SFJNBOךٖحأٝ 94

/ 166 -FP#SFJNBOךٖحأٝ 95 ➙ד׮ֿך挿כת׌葿ղה0QFOז㉏겗׾㶱׿ד灇瑔ׁ׸גְ׷ Ӎ "Rashomon"葺ְٌرٕך㢳ꅾ䚍 ꬊ♧䠐䚍ず玎䏝ך葺ְ✮庠礵䏝׾䭯אⰋֻ殯ז׷ٌرָٕ׋ֻׁ׿㶷㖈ׅ׷
Ӎ "Occam"ٌرٕך鍑ꅸ䚍ה✮庠礵䏝ך؝ٝؿؙٔز ٌرٕךءٝفׁٕ 鍑ꅸ䚍 ה✮庠礵䏝ך⚕甧כהג׮ꨇ׃ְ Ӎ "Bellman"넝如⯋ر٦ةָ䒷ֹ饯ֿًׅٔحزהرًٔحز 넝如⯋ז邌植 ꟼ⤘׃׉ֲזדֹ׷׌ֽ㢳ֻך㢌ꆀ ׾䪔ֲץֹזךַ ⠗窟涸ז窟鎘㷕ך״ֲח佄ꂁ涸ז㼰侧ך㢌ꆀ׾嗚鎢׃ⴓ匿ׅץֹזךַ ̔ؗحثٝءؙٝ㔐䌓䙼ְאֻ㢌侧Ⰻ鿇Ⰵ׶ٌرٕ ٥暴䗙ꆀ ؒٝآٔ،ؚٔٝה亻⡂湱ꟼ٥3BTIPNPO⸬卓ך㟓㣐ٔأؙ 3BTIPNPO 0DDBN #FMMNBO

/ 166 猘׋׍ך蕱ꡙ♶㖱♧禸鍗㯭ךرؠ؎ٝה䱱稊 96 https://en.wikipedia.org/wiki/Heterogeneous_catalysis 㼎韋䊨噟さ䧭٥䱖ؖأ崭⻉٥ًةٝ鯄䳔זו㔿⡤鍗㯭邌꬗♳ך孡湱⿾䘔

/ 166 ♶㖱♧禸鍗㯭灇瑔דך堣唒㷕统ך崞欽 97 • Mine+ ChemCatChem. 2021. • Toyao+,
ACS Catalysis. 2020. (Review) • Liu+, The Journal of Physical Chemistry C. 2020. • Suzuki+ ChemCatChem. 2019. (Front Cover) • Kamachi+ The Journal of Physical Chemistry C. 2019. • Hinuma+ The Journal of Physical Chemistry C. 2018. • Toyao+, The Journal of Physical Chemistry C. 2018 • Takigawa+ RSC Advances. 2016. +45$3&45ꬠ倜勞俱Ꟛ涪稢ꅿ걄㚖鍗㯭؎ٝؿؓوذ؍ؙأךⶼ䧭ך׋׭ך㹋꿀٥椚锷٥ر٦ة猰㷕灇瑔幠宏灇♧ 넝虊加麦 둷㾊㽵ꥐ ⵸ꅿ犣 넝㽵㛇〷䂹溪⛲ ꈿ加䣒➜ ֿך竲ֹ暟ך 灇瑔׾稱➜

/ 166 ⿫罋5PZBP "$4$BUBMZTJT 3FWJFX 98 • This is an
excellent review on a very timely subject, which is highly suitable for ACS Catalysis. … I don't usually recommend that papers should be accepted "as is", but in this case I don't see the need for changes. • I will certainly recommend it to my group and my students when it is published. • The manuscript gives an excellent overview in the ﬁeld of machine learning especially with regard to heterogeneous catalysis and I would highly recommend the article for the publication in ACS Catalysis. • 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. Review Comments 畍ָ堣唒㷕统ךِ٦ؠؖ؎س 侧䒭ז׃ חז׏גְתׅ

/ 166 ㉏겗ךꨇ׃ׁך然钠 99 孡湱 ⿾䘔暟㔿湱鍗㯭 չ㔿⡤鍗㯭邌꬗♳ך孡湱⿾䘔醱꧟禸
պך椚鍑כ׉׮׉׮慧يؤ 䬐䭯ꆃ㾩شظ磛㶨ך邌꬗

պך椚鍑כ׉׮׉׮慧يؤ ェ滠䬐䭯ꆃ㾩شظ磛㶨ך邌꬗

պך椚鍑כ׉׮׉׮慧يؤ ェ滠䭁侔䬐䭯ꆃ㾩شظ磛㶨ך邌꬗

պך椚鍑כ׉׮׉׮慧يؤ ェ滠䭁侔鍑ꨄ 䬐䭯ꆃ㾩شظ磛㶨ך邌꬗

պך椚鍑כ׉׮׉׮慧يؤ ェ滠䭁侔鍑ꨄ ⿾䘔䬐䭯ꆃ㾩شظ磛㶨ך邌꬗

պך椚鍑כ׉׮׉׮慧يؤ ェ滠䭁侔鍑ꨄ ⿾䘔膴ꨄ 䬐䭯ꆃ㾩شظ磛㶨ך邌꬗

պך椚鍑כ׉׮׉׮慧يؤ ェ滠䭁侔鍑ꨄ ⿾䘔膴ꨄ 䬐䭯ꆃ㾩شظ磛㶨ך邌꬗ ˖ 鍗㯭穈䧭 ˖ ؟؎ؤװ䕎朐磛㶨ך⡲׶倯 ˖ 邌꬗ך⳽⳻ ˖ 庛䏝װ㖇⸂ 㢳㔓㶨ָꟼ׻׷

պך椚鍑כ׉׮׉׮慧يؤ ˑ邌꬗猰㷕˒ ׉׮׉׮չ邌꬗պָ䝤눤涸זꨇ׃ׁ God made the bulk; the surface was invented by the devil ύ΢Ϧେઌੜ ェ滠䭁侔鍑ꨄ ⿾䘔膴ꨄ 䬐䭯ꆃ㾩شظ磛㶨ך邌꬗ ˖ 鍗㯭穈䧭 ˖ ؟؎ؤװ䕎朐磛㶨ך⡲׶倯 ˖ 邌꬗ך⳽⳻ ˖ 庛䏝װ㖇⸂ 㢳㔓㶨ָꟼ׻׷

/ 166 㹋꿀ָ⚺㼪׃ג葺ְ鍗㯭ָ鋅אַ׏גֹ׋ֿהכ끅殯涸 100 ְתתדך 濼鋅װر٦ة ⡲噟⟎铡̔㹋꿀 椚锷ٌرٕ̔鎘皾穠卓ך然钠ה 怴糊涸ז嗚鏾
ˑ穗꿀ה⹞˒ ٗإٓؕءؚٝؗٝ ⟎铡怴糊岀

ˑ穗꿀ה⹞˒ ٗإٓؕءؚٝؗٝ ⟎铡怴糊岀 • 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. Τδιϯେઌੜ PSˑؒآاٝ涸ז˒穗꿀锷

ˑ穗꿀ה⹞˒ ٗإٓؕءؚٝؗٝ ⟎铡怴糊岀銲秈ׅ׷הչ⸕⸂֮׷ך׫החַֻ׋ֻׁ׿ָ׿ל׸պה鎉׏גְ׷կ ֶ̔ꆃך䫎Ⰵ➂嵲䨌遭 هأسؙװ㷕欰ך麓ꃎז⸤⫴ ד(0 • 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. Τδιϯେઌੜ PSˑؒآاٝ涸ז˒穗꿀锷

/ 166 ׉׸ד׮չ涪鋅պכ׮ךׅ׀ֻٖ،؎كٝزד֮׷ 101 䟝㹀דֹ׷չ鍗㯭㹋꿀勴⟝倯岀պך侧כ㣓俑㷕涸ח䊬㣐 # 剣ꣲך儗꟦٥؝أز׾欰ֹ׷猘׋׍ָ鑐ׇ׷ךכק׿ך♧鿇 # 醱꧟⻉ׅ׷ص٦ؤ׾⿾僥׃׋稆兦׵׃ְ歗劍涸ז鍗㯭ָ 鋅אַ׷然桦כ椚㾄♳כ窫劄涸ח⡚ְ˘כ׆
ˑ"OFFEMFJOBIBZTUBDL˒

/ 166 את׶չإٖٝر؍ؾذ؍͒⩐搫ך䎊麊պ 102 䎊麊כ彊⪒ׁ׸׋׮ךח׌ֽ꣬׶׷ ˖ ⡦׾㹋꿀ׅ׷ַ ⟎铡䕎䧭 כסאֲ㸣Ⰻחٓٝتي ְֹ֮׋׶
ל׏׋׶ דכזְկ ˖ 穗꿀ה⹞չ灇瑔罏ךإٝأպװչ臾ך鋅ׇ䨽պ ˖ ⮚׸׋㹋꿀猰㷕罏ךչ⹞ؾُ٦ة 穗꿀ה⹞ պכٓٝتيדכ זֻ⡦׵ַך䭷ぢ䚍׾䭯א

/ 166 את׶չإٖٝر؍ؾذ؍͒⩐搫ך䎊麊պ 102 䎊麊כ彊⪒ׁ׸׋׮ךח׌ֽ꣬׶׷ ˖ ⡦׾㹋꿀ׅ׷ַ ⟎铡䕎䧭 כסאֲ㸣Ⰻחٓٝتي ְֹ֮׋׶
ל׏׋׶ דכזְկ ˖ 穗꿀ה⹞չ灇瑔罏ךإٝأպװչ臾ך鋅ׇ䨽պ ˖ ⮚׸׋㹋꿀猰㷕罏ךչ⹞ؾُ٦ة 穗꿀ה⹞ պכٓٝتيדכ זֻ⡦׵ַך䭷ぢ䚍׾䭯א ֿך֮׋׶חˑEBUBESJWFO˒ָ顀柃דֹ׷⡭㖑ָ֮׷ ㉏겗㹋ꥷחכر٦ة⻉דֹזְ䞔㜠ָקה׿וזךד ر٦ة⻉דֹ׷䞔㜠ך⚥ךչוְֲֲر٦ةדESJWFׅ׷ךַպ

/ 166 וְֲֲر٦ةד⟎铡䕎䧭٥㹋꿀鎘歗׾ESJWFדֹ׷ַ 103 ˖ ⮚׸׋㹋꿀猰㷕罏ח➙תדךⰋ➂欰דⰅ⸂ׁ׸׋䞔㜠כ花㣐 ر٦ة⻉ׁ׸זְ䞔㜠ָקה׿ו ˖ ر٦ة꽀⹛䩛חⰅ׷ر٦ةַ׵鵚⡂涸ח鶕׷׃ַזְָ
➂꟦ך钠濼ꣲ歲ךⵖ秈װ䙼ְ鴥׫ח״׷勲簂ַ׵荈歋חז׷ ְתתדך 濼鋅װر٦ة ⡲噟⟎铡̔㹋꿀 椚锷ٌرٕ̔鎘皾穠卓ך然钠ה 怴糊涸ז嗚鏾 ⟎铡䕎䧭٥㹋꿀鎘歗ח 堣唒㷕统׾⢪ֲֶ ٗإٓؕءؚٝؗٝ ̞➂꟦כ㢳侧ך㔓㶨ך醱꧟ז㢳如⯋湱ꟼ׾䪾䳢דֹזְ

/ 166 堣唒㷕统׾וֲ崞欽ׅ׷ַ 104 堣唒㷕统׾崞欽ׅ׷׋׭חכ 堣唒㷕统ٌرٕ׾鎮箺ׅ׷׋׭ךչر٦ةպ׾וֲׅ׷ַָ꒲ ˖ 俑柃ַ׵꧊׭׋㹋ꥷך㹋꿀ر٦ة㜠デ׾⢪ֲ ˖ ٓنד㹋꿀׃ג襳琎׃׋ر٦ة׾⢪ֲ
˖ ءىُٖ٦ءّٝ 鎘皾⻉㷕 ד襳琎׃׋ر٦ة׾⢪ֲ ˖ ♳鎸אⰋ鿇⢪ֲ ˖ 㹋꿀鎘庠堣㐻חإٝ؟٦׾אֽתֻ׶ծ㹋꿀׃גְ׷הֿ׹׮ ؽرؔꐮ歗׃ծ㹋꿀罏ך걧ח׮ًؕٓאֽג㹋꿀罏鋔ꅿ׮ؽر ؔꐮ歗׃ծ㹋꿀罏ך⡤ח⹛⡲إٝ؟אֽג鎸ꐮ׃ծ㹋꿀ظ٦ز ׮أٍؗٝ׃ծ֮׵ײ׷ꟼ鸬锷俑װ侄猰剅׮Ⰻ鿇ꨵ㶨⻉׃ծ˘

/ 166 俑柃ַ׵꧊׭׋㹋ꥷך㹋꿀ر٦ة㜠デ׾⢪ֲ 105 鎘皾⻉㷕כ굲鬨涸涪㾜׾鹴־גְ׷ָ椚锷ה植㹋ךٍؘحفכ ְאתד׮㶷㖈ׅ׷կ ˖ 㹋꿀勴⟝װفٗإأ勴⟝זוך㔓㶨 ˖ 椚锷ךꥷח镘׭׋
PSׂ׏ֻ׶鵚⡂׃׋ 稢ַֺׅ׷搀侧ך銲㔓 ˖ ٌٕחכ،نؖسٗ㹀侧 ⦐ך銲稆ָ劤䔲כ֮׷ 俑柃ַ׵꧊׭׋㹋ꥷך㹋꿀ر٦ة㜠デ׾⢪ֲ չ麓⿠ח㜠デׁ׸׋植㹋׾鋅ג׫״ֲպ 植㹋׾ׅץגٌرٕ⻉ׅ׷ֿהכ♶〳腉 ̔׉ך㹀纏ַ׵׃גˑٌرٕ˒הכ⡦׵ַך䰍韋װ鵚⡂׾ろ׬կ

/ 166 俑柃ַ׵꧊׭׋㹋ꥷך㹋꿀ر٦ة㜠デ׾⢪ֲ 106 ⯋稆穈䧭㹋꿀勴⟝ 　桦鼅䫛䚍㼎韋כًةٝךꃐ⻉ؕحفؚٔٝ⿾䘔ծ湡涸㢌侧כ$ 　桦
䖞勻灇瑔 ;BWZBMPWBFUBM ח״׷䎃⟃⵸ך⢽ח ։䎃ך倜׋ז⢽׾⸇ִ⢽חתד䭁⯍ 堣唒㷕统ד✮庠

/ 166 ֿךהֹ堣唒㷕统ח⡦ָ䗳銲ַ 107 ֿך邌ر٦ةד堣唒㷕统ٌرٕ׾鎮箺׃✮庠ׅ׸ל葺ְ 堣唒㷕统ٌرٕ ˖ ⯋稆穈䧭嫰 ˖ 㹋꿀勴⟝
˖ 　桦 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y Ⰵ⸂ ⳿⸂ <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x Ⰵ⸂ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ⳿⸂ 鎮箺ر٦ة

˖ 　桦 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y Ⰵ⸂ ⳿⸂ <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x Ⰵ⸂ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ⳿⸂ 傀濼ך剑㣐　桦鎮箺ر٦ة

˖ 　桦 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">AAAChHichVHLSsNAFD1GrbW+qm4EN8WiuJBy6xsXUnTjsg9rC1VKEqc1mCYhSQu1+AO6VVy4UnAhfoAf4MYfcNFPEJcKblx4mwZEi3rDZM6cuefOmbmKpWuOS9Tskrp7egN9wf7QwODQ8Eh4dGzHMau2KrKqqZt2XpEdoWuGyLqaq4u8ZQu5ougipxxutvZzNWE7mmlsu3VL7FXksqGVNFV2mUrVi+EoxciLSCeI+yAKP5Jm+B672IcJFVVUIGDAZaxDhsNfAXEQLOb20GDOZqR5+wLHCLG2ylmCM2RmD/lf5lXBZw1et2o6nlrlU3QeNisjmKYnuqVXeqQ7eqaPX2s1vBotL3WelbZWWMWRk4nM+7+qCs8uDr5Uf3p2UcKq51Vj75bHtG6htvW1o4vXzFp6ujFD1/TC/q+oSQ98A6P2pt6kRPryDz8Ke+EX4wbFf7ajE+zMx+LLMUotRhMbfquCmMQUZrkfK0hgC0lkub7AKc5wLgWkOWlBWmqnSl2+ZhzfQlr/BNcbj/U=</latexit> y Ⰵ⸂ ⳿⸂ <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x Ⰵ⸂ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ⳿⸂ 傀濼ך剑㣐　桦如挿 鎮箺ر٦ة

/ 166 濼׶׋ְֿהח䘔ׄג堣唒㷕统ך倯岀װ岣䠐挿ָ㢌׻׷ 108 ˖ 　桦խָ넝ְ鍗㯭ה⡚ְ鍗㯭ך麩ְ׾鋉㹀ׅ׷㔓㶨כ⡦ ˖ 葺ְ　桦ָ䖤׵׸׷劢涪鋅ך鍗㯭כוך֮׋׶ח֮׷ 剑㣐　桦ָ䖤׵׸׋ךワ鴟זך׌׹ֲַ <latexit
sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">AAACiXichVFNLwNRFD0dX1VfxUZi02iIVXNHBOmq0Y1lP7QkiMyMh9H5ysy0UU3/gJWdYEViIX6AH2DjD1j0J4gliY2F2+kkguBO3rzzzrvnvvPeVR1D93yiVkTq6u7p7Yv2xwYGh4ZH4qNjZc+uupooabZhu+uq4glDt0TJ131DrDuuUEzVEGtqJdveX6sJ19Nta9WvO2LLVPYsfVfXFJ+p8qZqNg6b2/EkpSiIxE8ghyCJMHJ2/A6b2IENDVWYELDgMzagwONvAzIIDnNbaDDnMtKDfYEmYqytcpbgDIXZCv/3eLURshav2zW9QK3xKQYPl5UJTNMj3dALPdAtPdH7r7UaQY22lzrPakcrnO2R44ni278qk2cf+5+qPz372MVS4FVn707AtG+hdfS1o9OXYrow3ZihK3pm/5fUonu+gVV71a7zonDxhx+VvfCLcYPk7+34CcpzKXkhRfn5ZGY5bFUUk5jCLPdjERmsIIcS1z/ACc5wLg1IsrQkpTupUiTUjONLSNkPIVKSSQ==</latexit> x <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x Ⰵ⸂ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ⳿⸂ 傀濼ך剑㣐　桦 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y 湡涸䱱稊傀濼ך鍗㯭״׶葺ְ鍗㯭׾鋅אֽ׋ְ

˖ 　桦 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y Ⰵ⸂ ⳿⸂ LinearRegression() խ׾㣐ֹֻׅ׸ל 葺ְהְֲ閯ך 爙㇗׃ַֻ׸זְ <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x Ⰵ⸂ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ⳿⸂ <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x 6OEFSU

˖ 　桦 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y Ⰵ⸂ ⳿⸂ MLPRegressor(hidden_layer_sizes=(300,300,50), activation='tanh') ֿךפ׿ָ㣐ֹ׉ֲ ת֮׉ֲַ׮ <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x Ⰵ⸂ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ⳿⸂ ✮庠　桦ָ׭׍ׯ ⡚ְז˘

˖ 　桦 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y Ⰵ⸂ ⳿⸂ MLPRegressor(hidden_layer_sizes=(300,300,50), activation='relu') ֲ٦׿ <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x Ⰵ⸂ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ⳿⸂ BDUJWBUJPO׾չ3F-6պח 頾⦼׾ئٗ縧䳔 ׻׶ה״ׁ׉ֲַ׮

˖ 　桦 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y Ⰵ⸂ ⳿⸂ KernelRidge(kernel='rbf', gamma=100.0, alpha=0.05) ֲ٦׿ <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x Ⰵ⸂ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ⳿⸂ 暴חך皘䨽כ ֿ׸ד葺ְךַ ،٦ذ؍ؿ؋ؙز

˖ 　桦 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y Ⰵ⸂ ⳿⸂ KernelRidge(kernel='laplacian', gamma=10.0, alpha=0.01) ֲ٦׿ <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x Ⰵ⸂ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ⳿⸂

˖ 　桦 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y Ⰵ⸂ ⳿⸂ SVR(kernel='rbf', gamma=10, C=20) ֲ٦׿ <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x Ⰵ⸂ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ⳿⸂ 暴חך皘䨽כ ֿ׸ד葺ְךַ ،٦ذ؍ؿ؋ؙز

˖ 　桦 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y Ⰵ⸂ ⳿⸂ GaussianProcessRegressor(kernel=Matern(length_scale=100.0, nu=0.2)) <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x Ⰵ⸂ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ⳿⸂ 暴חך皘䨽כ ֿ׸ד葺ְךַ ،٦ذ؍ؿ؋ؙز ֲ٦׿

˖ 　桦 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y Ⰵ⸂ ⳿⸂ RandomForestRegressor(max_features='sqrt') <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x Ⰵ⸂ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ⳿⸂ ֲ٦׿

˖ 　桦 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y Ⰵ⸂ ⳿⸂ ExtraTreesRegressor() <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x Ⰵ⸂ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ⳿⸂ ֲ٦׿

˖ 　桦 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">AAAChHichVHLSsNAFD1GrbW+qm4EN8WiuJBy6xsXUnTjsg9rC1VKEqc1mCYhSQu1+AO6VVy4UnAhfoAf4MYfcNFPEJcKblx4mwZEi3rDZM6cuefOmbmKpWuOS9Tskrp7egN9wf7QwODQ8Eh4dGzHMau2KrKqqZt2XpEdoWuGyLqaq4u8ZQu5ougipxxutvZzNWE7mmlsu3VL7FXksqGVNFV2mUrVi+EoxciLSCeI+yAKP5Jm+B672IcJFVVUIGDAZaxDhsNfAXEQLOb20GDOZqR5+wLHCLG2ylmCM2RmD/lf5lXBZw1et2o6nlrlU3QeNisjmKYnuqVXeqQ7eqaPX2s1vBotL3WelbZWWMWRk4nM+7+qCs8uDr5Uf3p2UcKq51Vj75bHtG6htvW1o4vXzFp6ujFD1/TC/q+oSQ98A6P2pt6kRPryDz8Ke+EX4wbFf7ajE+zMx+LLMUotRhMbfquCmMQUZrkfK0hgC0lkub7AKc5wLgWkOWlBWmqnSl2+ZhzfQlr/BNcbj/U=</latexit> y Ⰵ⸂ ⳿⸂ ExtraTreesRegressor(bootstrap=True) <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">AAACiXichVFNLwNRFD0dX1VfxUZi02iIVXNHBOmq0Y1lP7QkiMyMh9H5ysy0UU3/gJWdYEViIX6AH2DjD1j0J4gliY2F2+kkguBO3rzzzrvnvvPeVR1D93yiVkTq6u7p7Yv2xwYGh4ZH4qNjZc+uupooabZhu+uq4glDt0TJ131DrDuuUEzVEGtqJdveX6sJ19Nta9WvO2LLVPYsfVfXFJ+p8qZqNg6b2/EkpSiIxE8ghyCJMHJ2/A6b2IENDVWYELDgMzagwONvAzIIDnNbaDDnMtKDfYEmYqytcpbgDIXZCv/3eLURshav2zW9QK3xKQYPl5UJTNMj3dALPdAtPdH7r7UaQY22lzrPakcrnO2R44ni278qk2cf+5+qPz372MVS4FVn707AtG+hdfS1o9OXYrow3ZihK3pm/5fUonu+gVV71a7zonDxhx+VvfCLcYPk7+34CcpzKXkhRfn5ZGY5bFUUk5jCLPdjERmsIIcS1z/ACc5wLg1IsrQkpTupUiTUjONLSNkPIVKSSQ==</latexit> x Ⰵ⸂ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ⳿⸂ TLMFBSOךرؿٕؓز כPזךד岣䠐 ֲ٦׿

˖ 　桦 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y Ⰵ⸂ ⳿⸂ GradientBoostingRegressor() <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x Ⰵ⸂ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ⳿⸂ ֲ٦׿

/ 166 ֿך⢽כ㹋כչ溪ךٌرٕظ؎ؤպך➂䊨ر٦ة 120 植㹋ך㹋庠ر٦ة ת׃גװ㜠デر٦ة חכ葿ղז衅ה׃瑎ָ

/ 166 ֿך⢽כ㹋כչ溪ךٌرٕظ؎ؤպך➂䊨ر٦ة 120 鵚ְ姻鍑⢽ָ JODPOTJTUFOU 侄䌌ظ؎ؤ 植㹋ך㹋庠ر٦ة ת׃גװ㜠デر٦ة חכ葿ղז衅ה׃瑎ָ

/ 166 ֿך⢽כ㹋כչ溪ךٌرٕظ؎ؤպך➂䊨ر٦ة 120 鵚ְ姻鍑⢽ָ JODPOTJTUFOU 侄䌌ظ؎ؤ Yך㼰׃ך麩ְד Zח䚈䃓ז㢌⻉ $MJT
植㹋ך㹋庠ر٦ة ת׃גװ㜠デر٦ة חכ葿ղז衅ה׃瑎ָ

/ 166 ֿך⢽כ㹋כչ溪ךٌرٕظ؎ؤպך➂䊨ر٦ة 120 鵚ְ姻鍑⢽ָ JODPOTJTUFOU 侄䌌ظ؎ؤ Yך㼰׃ך麩ְד Zח䚈䃓ז㢌⻉ $MJT
㢩׸⦼ 植㹋ך㹋庠ر٦ة ת׃גװ㜠デر٦ة חכ葿ղז衅ה׃瑎ָ

/ 166 ֿך⢽כ㹋כչ溪ךٌرٕظ؎ؤպך➂䊨ر٦ة 120 ر٦ةָזְ㼰זְ걄㚖鵚ְ姻鍑⢽ָ JODPOTJTUFOU 侄䌌ظ؎ؤ Yך㼰׃ך麩ְד Zח䚈䃓ז㢌⻉
$MJT 㢩׸⦼ 植㹋ך㹋庠ر٦ة ת׃גװ㜠デر٦ة חכ葿ղז衅ה׃瑎ָ

/ 166 ֿך⢽כ㹋כչ溪ךٌرٕظ؎ؤպך➂䊨ر٦ة 121 Neural Networks (ReLU) Random Forest Extra
Trees (bootstrap) Neural Networks (Tanh) Linear Regression Kernel Ridge (RBF) Kernel Ridge (Laplacian) Extra Trees (no bootstrap) Gradient Boosting “ਅͷ”Ϟσϧ

/ 166 3BTIPNPO⸬卓♧⡤ו׸׾⥋ׄ׸לְְ׿ׄׯְ 122 $堣唒㷕统ٌرٕװ鎮箺ر٦ةָ㢌׻׸ל✮庠כ㢌׻׷ ٌرٕהر٦ةך侧׌ֽ✮庠׮֮׷溪㹋כչ谞ך⚥պ ˖ $SPTTWBMJEBUJPO礵䏝כקרず瘝ךٌرָٕ搀侧ח֮׶䖤׷ ˖
ずٌׄرٕד׮)ZQFSQBSBNFUFSָ麩ִלַז׶麩ְ䖤׷ ˖ 植㹋דכ溪ךٌرٕכⴓַ׵זְ׋׭葺׃䝤׃ךⴻ倖כ㔭ꨇ ˖ Ⰵ⸂㢌侧׾䙼ְאֻ׌ֽⰅ׸ג넝如⯋ر٦ةחז׷הׁ׵ח 3BTIPNPO⸬卓ٔأָؙ㟓㣐猘ך如⯋⢽ך⡲捀䚍ח׀岣䠐 .-ָוְֲֲ䪮遭זךַ.-ך暴䚍הꣲ歲׾姻׃ֻ䪾䳢ׅ׷ ✮庠穠卓׾䔲鑩ⴓꅿך濼陎ח撑׵׃ג岣䠐帾ֻ嗚鏾٥鍑ꅸׅ׷

/ 166 ׍ז׫ח؟ٝفٕ侧ָ⼧ⴓ㣐ֹֽ׸ל׻׶הו׸ד׮0,123 ؟ٝفٕ侧ָ⼧ⴓ㢳ֽ׸ל⢽㢩涸ر٦ة挿כ窟鎘涸ח湱媷ׁ׸׷ ̔׋׌׃넝如⯋ד֮׷קו䭷侧涸ז侧ָ䗳銲דꬊ植㹋涸ז劍䖉 Neural Networks (ReLU) Random Forest
Extra Trees (bootstrap)

/ 166 㢳ֻכ䙀걧ח֮׷⦪酡瑞꟦ח㼎׃ر٦ةָ駈׶גְזְ 124 椚䟝涸זر٦ة ࣮ࡍʹखʹೖΔσʔλ (Underspeciﬁcation) Neural Networks (ReLU)
Random Forest Extra Trees (bootstrap) Neural Networks (ReLU) Random Forest Extra Trees (bootstrap) Neural Networks (Tanh) Linear Regression Kernel Ridge (RBF) Kernel Ridge (Laplacian) Extra Trees (no bootstrap) Gradient Boosting

/ 166 㢳ֻכ䙀걧ח֮׷⦪酡瑞꟦ח㼎׃ر٦ةָ駈׶גְזְ 124 椚䟝涸זر٦ة ࣮ࡍʹखʹೖΔσʔλ (Underspeciﬁcation) Neural Networks (ReLU)
Random Forest Extra Trees (bootstrap) Neural Networks (ReLU) Random Forest Extra Trees (bootstrap) Neural Networks (Tanh) Linear Regression Kernel Ridge (RBF) Kernel Ridge (Laplacian) Extra Trees (no bootstrap) Gradient Boosting ໘౗ͳ͜ͱʹ͜͜ͰRashomon͕ى͖ͯ͠·͏ʂ ͜ͷ΁ΜͷϞσϧ͸खʹೖΔࣄྫͰͷCVਫ਼౓͸ ಉϨϕϧ͕ͩςετͰͷڍಈ͸͍ͩͿҟͳΔʂ

/ 166 -FP#SFJNBOךٖحأٝ 125 ➙ד׮ֿך挿כת׌葿ղה0QFOז㉏겗׾㶱׿ד灇瑔ׁ׸גְ׷ Ӎ "Rashomon"葺ְٌرٕך㢳ꅾ䚍 ꬊ♧䠐䚍ず玎䏝ך葺ְ✮庠礵䏝׾䭯אⰋֻ殯ז׷ٌرָٕ׋ֻׁ׿㶷㖈ׅ׷
Ӎ "Occam"ٌرٕך鍑ꅸ䚍ה✮庠礵䏝ך؝ٝؿؙٔز ٌرٕךءٝفׁٕ 鍑ꅸ䚍 ה✮庠礵䏝ך⚕甧כהג׮ꨇ׃ְ Ӎ "Bellman"넝如⯋ر٦ةָ䒷ֹ饯ֿًׅٔحزהرًٔحز 넝如⯋ז邌植 ꟼ⤘׃׉ֲזדֹ׷׌ֽ㢳ֻך㢌ꆀ ׾䪔ֲץֹזךַ ⠗窟涸ז窟鎘㷕ך״ֲח佄ꂁ涸ז㼰侧ך㢌ꆀ׾嗚鎢׃ⴓ匿ׅץֹזךַ ̔ؗحثٝءؙٝ㔐䌓䙼ְאֻ㢌侧Ⰻ鿇Ⰵ׶ٌرٕ ٥暴䗙ꆀ ؒٝآٔ،ؚٔٝה亻⡂湱ꟼ٥3BTIPNPO⸬卓ך㟓㣐ٔأؙ 3BTIPNPO 0DDBN #FMMNBO

/ 166 堣唒㷕统ך✮庠⦼כ鎮箺ر٦ةך剑葺⦼׾סאֲ馄ִזְ 126 堣唒㷕统ٌرٕכ劍䖉铎䊴ָ剑㼭חז׷״ֲ 鎮箺ر٦ةך溪׿⚥׾鸐׷״ֲ חؿ؍حذ؍ׁؚٝ׸׷׋׭ <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x
<latexit sha1_base64="g1U7Tzgl+Lj3TSOL2Mnl/fuxw90=">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</latexit> x1 <latexit sha1_base64="HrABz/ySZPgA1Ybj81k3XV8tH68=">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</latexit> x2 <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ر٦ةך剑㣐⦼ ر٦ةך剑㼭⦼ 堣唒㷕统ך ✮庠⦼ סאֲֿך眔㔲

/ 166 堣唒㷕统ך✮庠⦼כ鎮箺ر٦ةך剑葺⦼׾סאֲ馄ִזְ 126 堣唒㷕统ٌرٕכ劍䖉铎䊴ָ剑㼭חז׷״ֲ 鎮箺ر٦ةך溪׿⚥׾鸐׷״ֲ חؿ؍حذ؍ׁؚٝ׸׷׋׭ <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x
<latexit sha1_base64="g1U7Tzgl+Lj3TSOL2Mnl/fuxw90=">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</latexit> x1 <latexit sha1_base64="HrABz/ySZPgA1Ybj81k3XV8tH68=">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</latexit> x2 <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">AAAChHichVHLSsNAFD1GrbW+qm4EN8WiuJBy6xsXUnTjsg9rC1VKEqc1mCYhSQu1+AO6VVy4UnAhfoAf4MYfcNFPEJcKblx4mwZEi3rDZM6cuefOmbmKpWuOS9Tskrp7egN9wf7QwODQ8Eh4dGzHMau2KrKqqZt2XpEdoWuGyLqaq4u8ZQu5ougipxxutvZzNWE7mmlsu3VL7FXksqGVNFV2mUrVi+EoxciLSCeI+yAKP5Jm+B672IcJFVVUIGDAZaxDhsNfAXEQLOb20GDOZqR5+wLHCLG2ylmCM2RmD/lf5lXBZw1et2o6nlrlU3QeNisjmKYnuqVXeqQ7eqaPX2s1vBotL3WelbZWWMWRk4nM+7+qCs8uDr5Uf3p2UcKq51Vj75bHtG6htvW1o4vXzFp6ujFD1/TC/q+oSQ98A6P2pt6kRPryDz8Ke+EX4wbFf7ajE+zMx+LLMUotRhMbfquCmMQUZrkfK0hgC0lkub7AKc5wLgWkOWlBWmqnSl2+ZhzfQlr/BNcbj/U=</latexit> y ̔傀濼ך׮ך״׶葺ְ׮ך׾鋅אֽ׷הְֲ䱱稊湡涸ח♶黝さ ر٦ةך剑㣐⦼ ر٦ةך剑㼭⦼ 堣唒㷕统ך ✮庠⦼ סאֲֿך眔㔲

/ 166 堣唒㷕统ך✮庠⦼כ鎮箺ر٦ةך剑葺⦼׾סאֲ馄ִזְ 127 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x ׁ׵חծ׮׃✮庠⦼ָ鎮箺ر٦ةך剑葺⦼׾♳㔐׷ה׃ג׮ծ ر٦ةָזְ걄㚖ד׉ך✮庠כ⟣䠐涸ד䔲גחדֹזְ˘ ر٦ةך
剑㣐⦼ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y

/ 166 堣唒㷕统ך✮庠⦼כ鎮箺ر٦ةך剑葺⦼׾סאֲ馄ִזְ 128 SVR(kernel='rbf', gamma=10, C=100) 如⯋ך⢽דכչⰻ䯏պַչ㢩䯏պַⴓַ׷䠬ָׄ׃ג׃תֲָ ♧菙ך넝如⯋דכֿךⴻⴽׅ׵湫䠬涸דכזְֿהח岣䠐 ֿֿכⰻ䯏㢩䯏ر٦ة㢩걄㚖

/ 166 չر٦ة㢩걄㚖דך䠐㔳׃זְ㢩䯏պٔأؙכ䩛岀ח⣛㶷 129 寸㹀加،ٝ؟ٝـٕ岀 3BOEPN'PSFTU瘝 דכֿך朐屣כ⾱椚♳ 饯ֿ׵זְָ简䕎㔐䌓װ/FVSBM/FUXPSLTזו➭ך䩛岀דכ岣䠐 Linear Regression
Kernel Ridge (RBF) Gradient Boosting Neural Networks (Tanh) Kernel Ridge (Laplacian) Extra Trees (no bootstrap) Neural Networks (ReLU) Random Forest Extra Trees (bootstrap)

/ 166 ✮庠⦼׌ֽדכזֻ׉ך✮庠ⴓ侔然䏝 ׮罋ִ׷ךָꅾ銲 130 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit
sha1_base64="g1U7Tzgl+Lj3TSOL2Mnl/fuxw90=">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</latexit> x1 <latexit sha1_base64="HrABz/ySZPgA1Ybj81k3XV8tH68=">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</latexit> x2 䱱稊חꟼׅ׷䠐䙼寸㹀ח崞欽ׅ׷ךד֮׸ל堣唒㷕统ٌرٕך ✮庠⦼ךⴓ侔ⴓ䋒⥋걾⼒꟦׾罋ִ׷ֿהָꅾ銲 <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ر٦ةך剑㣐⦼ FHչ　桦✮庠⦼כpպWTչ　桦✮庠⦼כpպ

/ 166 䱱稊ׅ׷ꥷכ✮庠⦼荈⡤׾䭷垥ה׃זְ 131 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="g1U7Tzgl+Lj3TSOL2Mnl/fuxw90=">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</latexit> x1
<latexit sha1_base64="HrABz/ySZPgA1Ybj81k3XV8tH68=">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</latexit> x2 <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">AAAChHichVHLSsNAFD1GrbW+qm4EN8WiuJBy6xsXUnTjsg9rC1VKEqc1mCYhSQu1+AO6VVy4UnAhfoAf4MYfcNFPEJcKblx4mwZEi3rDZM6cuefOmbmKpWuOS9Tskrp7egN9wf7QwODQ8Eh4dGzHMau2KrKqqZt2XpEdoWuGyLqaq4u8ZQu5ougipxxutvZzNWE7mmlsu3VL7FXksqGVNFV2mUrVi+EoxciLSCeI+yAKP5Jm+B672IcJFVVUIGDAZaxDhsNfAXEQLOb20GDOZqR5+wLHCLG2ylmCM2RmD/lf5lXBZw1et2o6nlrlU3QeNisjmKYnuqVXeqQ7eqaPX2s1vBotL3WelbZWWMWRk4nM+7+qCs8uDr5Uf3p2UcKq51Vj75bHtG6htvW1o4vXzFp6ujFD1/TC/q+oSQ98A6P2pt6kRPryDz8Ke+EX4wbFf7ajE+zMx+LLMUotRhMbfquCmMQUZrkfK0hgC0lkub7AKc5wLgWkOWlBWmqnSl2+ZhzfQlr/BNcbj/U=</latexit> y 䱱稊ך湡涸דכ劍䖉何㊣ &* װ⥋걾⼒꟦ך♳ꣲזו׾䭷垥ח ر٦ةך剑㣐⦼ 劍䖉何㊣ &* 　桦何㊣ꆀך劍䖉⦼ 　桦何㊣ꆀ׾剑㣐⦼׾馄ִ׷鿇ⴓך然桦ךꅾ׫ד琎ⴓ

/ 166 俑柃ַ׵꧊׭׋㹋ꥷך㹋꿀ر٦ة㜠デ׾⢪ֲ 132 http://www.fhi-berlin.mpg.de/acnew/department/pages/ocmdata.html https://www.nature.com/articles/s41467-019-08325-8#Sec19 Oxidative coupling of methane
(OCM) reactions Methane (CH4 ) is partially oxidized to C2 hydrocarbons such as ethane (C2 H6 ) and ethylene (C2 H4 ) in a single step Elemental composition of catalyst (mol%) Process parameters + Preparation Catalytic performance • Zavyalova, U.; Holena, M.; Schlögl, R.; Baerns, ChemCatChem 2011. • Followup: Kondratenko, E. V.; Schlüter, M.; Baerns, M.; Linke, D.; Holena, M. Catal. Sci. Technol. 2015. • Renalysis with Corrections & Outlier Removal Schmack, R.; Friedrich, A.; Kondratenko, E. V.; Polte, J.; Werwatz, A.; Kraehnert, R. Nat Commun 2019. 1866 catalyst records from 421 reports

/ 166 俑柃ַ׵　꧊׃׋ر٦ةך㉏겗 133 Ԩ 6OEFSTQFDJDBUJPO㹋꿀勴⟝ָ䓼ֻ䕦갟ׅ׷ָծ醱侧ך㹋꿀勴⟝ד 㜠デ⢽ך֮׷鍗㯭כ噰׭ג㼰זְկず♧勴⟝דך醱醡㹋꿀׮ז׃կ ̔⢽⚥ծ勴⟝⟃♳⢽ծ勴⟝⟃♳⢽ծ勴⟝⟃♳⢽ Ԩ 4QBSTJUZ穈䧭ד⢪׻׸׷⯋稆ךؔ٦غٓحفָ㼰זֻꬊ䌢חأػ٦أ
̔⢽ִל/B5J.Oˏה;O$Fˏ׾וֲ嫰鯰ׅץֹ 74 elements All pairwise comparisons

/ 166 俑柃ַ׵　꧊׃׋ر٦ةך㉏겗 134 Ԩ 4USPOH#JBT⳿晛ׁ׸׷猰㷕䧭卓ך䓼ְ䧭⸆غ؎،أծ崧遤װ㹋꿀ך ׃װׁׅח״׷鼅䫛غ؎،أծזו钠濼غ؎،أ٥爡⠓涸غ؎،أך䕦갟 LaO3, Li/MgO, Mn/Na2WO4/SiO2
זו 暴㹀ך鍗㯭ָꬊ䌢ח״ֻ灇瑔ׁ׸׷

/ 166 堣唒㷕统✮庠ך然䏝٥⥋걾䏝׮鋅ג黝欽眔㔲׾䢅ꅾח椚鍑 135 Gradient Boosted Trees Extra Trees (no
bootstrap) Random Forest Extra Trees (bootstrap) sample max sample min GradientBoostingRegressor LGBMRegressor RandomForestRegressor ExtraTreesRegressor By quantile regression to .16, .5, .84 quantiles Naturally by the law of total variance bounded prediction Ԩ 寸㹀加،ٝ؟ٝـٕך✮庠ⴓ侔 ⥋걾⼒꟦ 鎮箺ر٦ةךNBYNJOך꟦ח✮庠⦼ָֻ ׷ךד䠐㔳׃זְ㢩䯏ٔأָؙ㼰זְ

/ 166 暴䗙ꆀך鏣鎘鍗㯭ך⸬卓涸ז暴䗙邌植׾罋ִ׷ 136 ˖ ֿךתתדכծ涯瀧祩։ֹן瀧祩תדכءّ祩דչ欥㄂պծꄣ屘ח כչ㞁ⴓպָろת׸׷ծזוծ銲稆ךչ⦐䚍պכⰋֻ罋䣁ׁ׸זְկ ˖ 鎮箺ر٦ةחろת׸זְ銲稆ָⰅ׷ה✮庠ח⿾僥דֹזְկ ˖
銲稆׀הך걼䏝ָكؗ⛦⵱涸ד֮׶ꬊ䌢ח㣐ֹז⨉׶ָ֮׷կ ˖ 銲稆侧ָ㢳ֻ㜠デ⢽ח銲稆ךؔ٦غٓحفָ㼰זְկ 涯瀧祩 ♲庛祩 ؚٓصُ٦祩 랲祩 ג׿ְׁ祩 ֹן瀧祩㞁 ꄣ屘 ֲת׫锃㄂俱 ֿ׃׳ֲ ءشٌٝ ؖ٦ٔحؙ ؖٓيو؟ٓ ٕؕتٌٝ ؙىٝ ؟ؿٓٝ ؝ٔ،ٝت٦ ة٦ًٔحؙ شخًؚ ׻ׁן ׃׳ֲָ ְֶ׃ׁ 湡涸㢌侧锃椚勴⟝ 銲稆穈䧭

/ 166 ⯋稆ך⦐䚍׾⯋稆鎸鶢㶨كؙزٕד邌ׅⰅ⸂邌植 137 ⯋稆׾չءٝنٕպה׃ג䪔ֲךדכזֻ չ㢳如⯋ך⯋稆鎸鶢㶨كؙزٕպד䪔ֲ ⯋稆鎸鶢㶨ך䬄韋䏝׾㢌ִ׸לծꟼ䗰ך֮׷ 暴䚍ך׫ח滠湡׃ג⯋稆ך邌植٥嫰鯰ָ〳腉ח 鎮箺ر٦ةחろת׸זְ⯋稆׮䪔ִ׷

/ 166 ⯋稆ך⦐䚍׾⯋稆鎸鶢㶨كؙزٕד邌ׅⰅ⸂邌植 138 48&% 4PSUFE8FJHIUFE&MFNFOUBM%FTDSJQUPST 邌植 穈䧭嫰⯋稆鎸鶢㶨كؙزٕ׾穈䧭嫰ך꣬갫ח⚛ץ׋׮ך ̔ءٝفٕ׌ָ㹀ꆀ涸ז何㊣ָ䖤׵׸׋暴䗙كؙزٕ邌植 +

/ 166 48&%邌植ה欽ְ׷⯋稆鎸鶢㶨ח״׷䬄韋䏝ךⵖ䖴 139 74 elements Compositional (onehot-like) Catalyst: Mg
83.46, Li 16.53 SWED-8 83.46 × 16.53 × 0.00 0.00 … SWED-3 83.46 × 16.53 × 0.00 0.00 … SWED-3 features: electronegativity, density, enthalpy of fusion SWED-8 features: SWED-3 features + atomic weight, atomic radius, m.p., b.p., ionization enegy can control speciﬁcity & focus Ԩ ⯋稆鎸鶢㶨ה׃גוך״ֲז׮ך׾⢪ֲַח״׏ג磦鋔⻉ָⵖ䖴〳腉 Ԩ ⯋稆כ鼅׿׌⯋稆鎸鶢㶨ך侧⦼ד邌植ׁ׸ծֿך邌植ך׮הדⰻ䯏ׁ׸׷ ׋׭ծ鎮箺ر٦ةחכזְ⯋稆׮荈搫ח《׶䪔ֲֿהָדֹ׷կ

/ 166 倜׃ְزٖٝس׾⿾僥ׅ׷׋׭ر٦ةإحز荈⡤׮䭁⯍ 140 The original dataset: 1866 catalyst records
from 421 reports (1982 - 2009) Mine, S.; Takao, M.; Yamaguchi, T.; Toyao, T.*; Maeno, Z.; Hakim Siddiki, S. M. A.; Takakusagi, S.; Shimizu, K.*; Takigawa, I.* ChemCatChem 2021. https://doi.org/10.1002/cctc.202100495. 4559 catalyst records from 542 reports The update dataset: 4559 catalyst records from 542 reports (2010 - 2019)

/ 166 $　桦ך堣唒㷕统✮庠 141 1. Conventional: composition + condition 2.
Proposed(Exploitative): composition + SWED + condition 3. Proposed(Explorative): SWED + condition w/ SWED→composition estimator RFR (Random Forest); ETR (ExtraTrees); XGB (XGBoost) SWED-3 features: electronegativity, density, enthalpy of fusion SWED-8 features: SWED-3 features + atomic weight, atomic radius, m.p., b.p., ionization enegy

/ 166 48&%׾欽ְ׋鍗㯭⦪酡劍䖉何㊣⦼ד♳⡘⦐ 142 鎮箺ر٦ةחזְ⯋稆 "T )G 4F 0T
1N ׮䲿周⦪酡ח鋅׵׸׋ 嫩䚍ך׋׭㹋欽♳כ㉏ 겗ָ֮׷׮ךךծ׉ך ״ֲז⦪酡׮ֹ׍׿ה 䱱稊ׁ׸גְ׷

/ 166 㷕统חכչ濼陎ךⵃ欽պהչ䱱稊պךزٖ٦سؔؿָ⠵ֲ 143 倜׃ְֿה׾չ㷕עպꥷך剑׮㛇劤涸זزٖ٦سؔؿ ➙תד㷕׿׌ֿהךչⵃ欽պ ➙תדךر٦ةך堣唒㷕统ח㛇בֻ✮庠ך崞欽
➙תדח㷕׿דזְֿהךչ䱱稊պ 倜׃ְ穗꿀ծ倜׃ְ濼陎ךェ　ծ濼陎ך䭁⯍ ˟Ⰻ⡤ח⽑׭׷չ➙תדח㷕׿׌ֿהպךؕغ٦桦ָ ⡚ְ㜥さכ加׾鋅ג啾׾鋅׆חז׏ג׃תֲ ➙תדךر٦ةך然䏝ָ⡚ְ걄㚖ծر٦ةָזְ걄㚖ַ׵ך 刿ז׷ر٦ةך《䖤

/ 166 俑柃ر٦ةחכ圫ղז㉏겗ָ֮׶չ䱱稊պָ״׶ꅾ銲 144 Ԩ 㹋꿀כ➂꟦ָ鎘歗ׅ׷׋׭ծ钠濼غ؎،أװ爡⠓涸غ؎،أָ⿾僥ׁ׸ ג׃תֲ 䖞勻濼鋅ծ崧遤ծ⠗窟ծ㹋꿀׃װׁׅ˘ Ԩ
鎮箺ر٦ةך✲⢽ךⴓ䋒ח㣐ֹז⨉׶ָ֮׷ָծֿ׸כ荈搫ך䶏椚דכ זֻ猘׋׍ך鋔ꅿך杞ׁ 䙼ְ鴥׫ ׾⿾僥׃׋׮ך Ԩ وة؎⸬卓 .BUUIFXFFDU 䧭⸆⢽ח麓ⶱח䒷ֹ׆׵׸ָ׍ Ԩ 䧭⸆⢽ך׫ָ㜠デׁ׸׷׋׭㣟侁✲⢽ך䞔㜠ָ荜ㄏ涸ח妀䴦

/ 166 㹋꿀鎘歗ה堣唒㷕统 145 ˖ 䱱稊挿׾鎘歗דֹ׷㜥さכծ欰饯䟝㹀眔㔲חדֹ׷׌ֽչת׿ץ׿ז ֻպה׷קֲָ葺ְխ FHٓٝتي㹋꿀ծ㸣Ⰻ㹋倵銲㔓鎘歗ծٓذٝ 馄倯呓鎘歗ծ%剑黝鎘歗ծ˘
˖ 䱱稊װ㹋꿀鎘歗חְֶגכ.-כ植㹋ך➿椚ٌرٕחֺׅזְ ֿך✲⢽ⴓ䋒כ 䱱稊חכ♶銲ずׄ⢽侧ד嚊䕎ָ ⴓַ׶.-׮⸬卓涸

/ 166 㹋꿀鎘歗חֶֽ׷ؿ؍حءٍ٦ך♲⾱⵱ 146

/ 166 㹋꿀鎘歗חֶֽ׷ؿ؍حءٍ٦ך♲⾱⵱ 146 ⿾䗁SFQMJDBUJPO ̔ず勴⟝ד醱侧㔐ך㹋꿀׾遤ֲկⱄ植䚍ך䬐⥂ח⸇ִծ խֿך䞔㜠ָזְה禸窟铎䊴ה⩐搫铎䊴׾ⴻⴽדֹזְկ

/ 166 㹋꿀鎘歗חֶֽ׷ؿ؍حءٍ٦ך♲⾱⵱ 146 ⿾䗁SFQMJDBUJPO ̔ず勴⟝ד醱侧㔐ך㹋꿀׾遤ֲկⱄ植䚍ך䬐⥂ח⸇ִծ խֿך䞔㜠ָזְה禸窟铎䊴ה⩐搫铎䊴׾ⴻⴽדֹזְկ 搀⡲捀⻉SBOEPNJ[BUJPO
̔罋ִ׋ְ銲㔓⟃㢩ח湡涸㢌侧ח䕦갟׾♷ִ׷〳腉䚍ָ֮׷銲㔓ָ ֮׷㜥さծ〳腉זꣲ׶ٓٝتيחⶴ׶➰ֽׅ׷կ DG穠卓ָ״ַ׏׋勴⟝ת׻׶ד㢳׭ח鑐׃׋ְךכ椚鍑דֹ׷ ָ䱱稊ָ湡涸ז׵׬׃׹ٓٝتي㹋꿀勴⟝ךקֲָ葺ְ

/ 166 㹋꿀鎘歗חֶֽ׷ؿ؍حءٍ٦ך♲⾱⵱ 146 ⿾䗁SFQMJDBUJPO ̔ず勴⟝ד醱侧㔐ך㹋꿀׾遤ֲկⱄ植䚍ך䬐⥂ח⸇ִծ խֿך䞔㜠ָזְה禸窟铎䊴ה⩐搫铎䊴׾ⴻⴽדֹזְկ 搀⡲捀⻉SBOEPNJ[BUJPO
̔罋ִ׋ְ銲㔓⟃㢩ח湡涸㢌侧ח䕦갟׾♷ִ׷〳腉䚍ָ֮׷銲㔓ָ ֮׷㜥さծ〳腉זꣲ׶ٓٝتيחⶴ׶➰ֽׅ׷կ DG穠卓ָ״ַ׏׋勴⟝ת׻׶ד㢳׭ח鑐׃׋ְךכ椚鍑דֹ׷ ָ䱱稊ָ湡涸ז׵׬׃׹ٓٝتي㹋꿀勴⟝ךקֲָ葺ְ 㽷䨽盖椚MPDBMDPOUSPM ̔罋ִ׋ְ銲㔓⟃㢩ךغحؙؚٓؐٝس㔓㶨כדֹ׷׌ֽ խ㖱♧חז׷״ֲח㹋꿀׾盖椚ׅ׷կ DG㹋꿀勴⟝ך剑黝⻉כ镘׭ג㔿㹀׃穈䧭׌ֽס׷㹋꿀

/ 166 㹋꿀鎘歗ה堣唒㷕统 147 C2 yield Expected Improvement ML surrogate
w/ 95%CI n given data points Input representation (SWED + Exp. Cond.) .-חⰅ⸂ׅ׷ر٦ةחזְ⫘ぢכ⾱椚♳✮庠דֹזְ׋׭ ،ٕ؞ٔؤيך鑫稢״׶׮ر٦ةך　꧊鎘歗㹋꿀鎘歗 ծ 黝欽眔㔲ך椚鍑ծㅷ颵⥂鏾ָ䧭⸆ך꒲ד֮׷ֿה׾ְא׮䗰ח 葺ְ暴䗙邌植ה✮庠礵䏝 ך넝ְ➿椚ٌرٕ ✮庠ⴓ䋒׾罋䣁׃׋䱱稊䭷垥ך㽷䨽ؾ٦ؙ̕ず㹀如ח㹋꿀ׅ׷⣣⦼ך넝ְ ⦪酡挿׾EJWFSTJGZ׃䲿爙 ⡂׋⦪酡挿כؚٕ٦ف⻉׃➿邌挿׾邌爙

/ 166 堣唒㷕统ٌرָٕז׈׉ך✮庠׾׃׋ַך銲㔓ⴓ匿 148 堣唒㷕统ٌرٕ ˖ ⯋稆穈䧭嫰 ˖ 㹋꿀勴⟝ ˖
　桦 <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x Ⰵ⸂ ⳿⸂ 　桦խָ넝ְ鍗㯭ה⡚ְ鍗㯭ך麩ְ׾鋉㹀׃ֲ׷ 㔓㶨כ⡦׌׹ֲ ׋׌׃Ⰵ⸂ָろ׬䞔㜠ך眔㔲ד <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">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</latexit> x <latexit sha1_base64="Nr2ImZk9Gvp+/1cBWPwAK6yswp0=">AAACiXichVFNLwNRFD0dX1VfxUZi02iIVXNHBOmq0Y1lP7QkiMyMh9H5ysy0UU3/gJWdYEViIX6AH2DjD1j0J4gliY2F2+kkguBO3rzzzrvnvvPeVR1D93yiVkTq6u7p7Yv2xwYGh4ZH4qNjZc+uupooabZhu+uq4glDt0TJ131DrDuuUEzVEGtqJdveX6sJ19Nta9WvO2LLVPYsfVfXFJ+p8qZqNg6b2/EkpSiIxE8ghyCJMHJ2/A6b2IENDVWYELDgMzagwONvAzIIDnNbaDDnMtKDfYEmYqytcpbgDIXZCv/3eLURshav2zW9QK3xKQYPl5UJTNMj3dALPdAtPdH7r7UaQY22lzrPakcrnO2R44ni278qk2cf+5+qPz372MVS4FVn707AtG+hdfS1o9OXYrow3ZihK3pm/5fUonu+gVV71a7zonDxhx+VvfCLcYPk7+34CcpzKXkhRfn5ZGY5bFUUk5jCLPdjERmsIIcS1z/ACc5wLg1IsrQkpTupUiTUjONLSNkPIVKSSQ==</latexit> x Ⰵ⸂ <latexit sha1_base64="Qqfga3YaBoUI0Yb7fQVzumPP1Sw=">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</latexit> y ⳿⸂ ر٦ةإحز 䎂㖱

/ 166 堣唒㷕统ٌرָٕז׈׉ך✮庠׾׃׋ַך銲㔓ⴓ匿 149 SHAP (SHapley Additive exPlanations) https://speakerdeck.com/dropout009/shapley-additive-explanationsdeji-jie-xue-xi-moderuwojie-shi-suru ♷ִ׵׸׋✮庠⦼ךر٦ةإحز䎂㖱ַ׵ך㢌⻉ꆀ׾
չ暴䗙ꆀ׀הך㺔♷䏝 4)"1⦼ ךㄤպפⴓ鍑ׅ׷ٌرٕ铡僇岀 و؎شأ銲㔓׮֮׶ֲ׷

/ 166 堣唒㷕统ٌرָٕז׈׉ך✮庠׾׃׋ַך銲㔓ⴓ匿 150 Composition: (1) Mg 83.46 (2) Li
16.53 ]4)"1⦼] ך꣬갫 4)"1⦼ךㄤر٦ةإحز䎂㖱ַ׵ך㟓⸇ⴓ 㢳➂侧ך⼿⸂؜٦يד䖤׋㜠ꂹ׾ぐفٖ؎َפⰕ䎂חⴓꂁׅ׷ ؜٦ي椚锷ך㉏겗ה׫זֿׅהדぐղך暴䗙ꆀך㺔♷䏝׾皾⳿

/ 166 5SFF&YQMBJOFS寸㹀加،ٝ؟ٝـٕ欽ך4)"1 151 ؎ٝةؙٓذ؍ـז鍑匿׾䲿⣘ׅ׷הג׮ֿז׸׋خ٦ٕ׮֮׷ ̔ ♧菙חכ鎘皾㔭ꨇ /1㔭ꨇ זꆀ׌ָծ寸㹀加،ٝ؟ٝـٕדכ 4)"1⦼ָ㢳갪䒭実鍑〳腉
5SFF&YQMBJOFSPSUSFF4)"1 https://github.com/slundberg/shap

/ 166 4)"1ח״׷㷕统幥׫ٌرַٕ׵ך銲㔓ⴓ匿 152 ر٦ةװ㷕统׃׋ٌرַٕ׵䖤׵׸׷㢳錬涸䞔㜠׾〳鋔⻉זו ד䬄⳿׃ծ㼔Ꟍ㹺ה⼿⫴׃㼔Ꟍ濼鋅װ㹋ⵖ秈ח撑׵׃גⵃ崞欽 Feature Importance Partial Dependence
Interaction Effect

/ 166 4)"1ח״׷㷕统幥׫ٌرַٕ׵ך銲㔓ⴓ匿 153 1st: (1) Mn: 72.3 (2) Li:
27.7 2nd: (1) Sr:50.0 (2) Ce:45.0 (3) Yb:5.0 Mine, S.; Takao, M.; Yamaguchi, T.; Toyao, T.*; Maeno, Z.; Hakim Siddiki, S. M. A.; Takakusagi, S.; Shimizu, K.*; Takigawa, I.* ChemCatChem 2021. https://doi.org/10.1002/cctc.202100495.

/ 166 侄鎮 154 荈搫猰㷕ⴓꅿדךⵃ崞欽כ.-ך䪮遭灇熊׌ֽדכ䧭⸆׃זְկ ⴓꅿ㼔Ꟍ㹺הך⼿⫴ָ䗳銲♶〳妀 ˖ .-ָוְֲֲ䪮遭זךַ.-ך暴䚍הꣲ歲׾姻׃ֻ䪾䳢ׅ׷ ˖ չر٦ةך　꧊鎘歗
㹋꿀鎘歗 הㅷ颵⥂鏾ծ黝欽眔㔲ך椚鍑պ ָˑEBUBESJWFO˒ך䗰茖ד֮׷ֿה׾ְא׮䗰ח ˖ չ䱱稊պָ湡涸ז׵.-ך卓׋ׅ䕵ⶴכֻ֮תד♧鿇ה䗰䖤׷ " 㼔Ꟍ㹺הך⼿⫴ծⴓꅿך㼔Ꟍ濼陎ח撑׵׃׋嗚鏾٥鍑ꅸ " ءىُٖ٦ءّٝ٥㹋꿀荈⹛⻉٥锷椚䱿锷הך輐さ

˖ 堣唒㷕统㾊כ♧⡤⡦ָ嚂׃ְךַ ˖ ⴓ㶨ך邌植ה堣唒㷕统 ˖ ؚٖ؎نحؙأ剑黝⻉怴糊䌓秛 锷椚㷕ה窟鎘㷕ך輐さ ˖ 荈搫猰㷕灇瑔ד堣唒㷕统׾⢪ֲֶהׅ׷ה䗳׆עאַ׷劤䔲חꨇ׃ְ㉏겗 ˖ ر٦ةٌرؚٔٝה✮庠،ٕ؞ٔؤي 5IF5XP$VMUVSFT ˖ ✮庠ַ椚鍑ַ3BTIPNPO⸬卓 6OEFSTQFDJDBUJPO 鍑ꅸ㢳圫䚍 ˖ ➂꟦ך钠濼غ؎،أח歋勻ׅ׷㉏겗⟎铡ծ㣟侁ծ䧭⸆غ؎،أծFUD ˖ 堣唒㷕统ַ׵堣唒涪鋅פ ˖ չ涪鋅պչ椚鍑պך麣瘡כさ椚⻉דֹ׷ךַ荈⹛⻉דֹ׷ךַ

/ 166 堣唒涪鋅כ堣唒㷕统ך䪮遭灇熊׌ֽדכⵋ麦׃ִזְ 156 猰㷕ָ実׭׷ֿהⴓַ׵זַ׏׋ֿהָⴓַ׷ 猰㷕涸涪鋅ה猰㷕涸椚鍑涪鋅椚鍑⾱㔓ה穠卓㔓卓ꟼ⤘
׾鋅⳿ׅ ׉׃ג㹏錁涸ח铡僇דֹ׷ ➙תד鋅⳿ׁ׸גְזְ葺ְ㼎韋׾鋅⳿ׅ Ԩ ְ׆׸׮չ堣唒㷕统պ׌ֽדכ鍑ֽזְֿה׾ת׆椚鍑ׅ׷ֿהկ Ԩ ְ׆׸׮✮庠䪮遭ד֮׷堣唒㷕统ךأ؝٦ف㢩ך㉏겗ד֮׶ծ堣唒㷕统 ⟃㢩ך׮ך ➜Ⰵ㹋꿀ծ㼔Ꟍ涸濼鋅ծ㼔Ꟍ㹺הך⼿⫴ ָ䗳갭 Ԩ չ➂䊨濼腉 "* պה鎉ֲה傀ח鍑寸䪮遭ָ֮׷״ֲז孡ָ׃ג׃תֲָ 劢鍑寸㉏겗կ猰㷕罏ה䠐陎ך굸ְ麩ְָ饯ֿ׶װֻׅ湱✼椚鍑ָꅾ銲 Ԩ ➂䊨濼腉ⴓꅿדכչ涪鋅׾荈⹛⻉דֹ׷ךַպכꅾ銲ז劢鍑寸铬겗 ̔猘׋׍כ傈ղչ涪鋅պהչ㷕统պ׾粸׶鵤׃ג欰ֹגְ׷ ך麓玎׾➂꟦ךꣲ׵׸׋钠濼腉⸂ך眔㔲ד椚鍑ׅ׷ x!y <latexit sha1_base64="kaK7x7wFN3GZpVpMGGOJaQQWYoA=">AAACBXicbVC7SgNBFL0bXzG+opY2E4NgFXZF0DJoYxnBPCC7htnJJBkys7PMzIrLktpfsNXeTmz9Dlu/xEmyhSYeuHA4517O5YQxZ9q47pdTWFldW98obpa2tnd298r7By0tE0Vok0guVSfEmnIW0aZhhtNOrCgWIaftcHw99dsPVGkmozuTxjQQeBixASPYWOneD0X2OPErvpF+Je2Vq27NnQEtEy8nVcjR6JW//b4kiaCRIRxr3fXc2AQZVoYRTiclP9E0xmSMh7RraYQF1UE2+3qCTqzSRwOp7EQGzdTfFxkWWqcitJsCm5Fe9Kbiv14oFpLN4DLIWBQnhkZkHjxIODISTStBfaYoMTy1BBPF7O+IjLDCxNjiSrYUb7GCZdI6q3luzbs9r9av8nqKcATHcAoeXEAdbqABTSCg4Ble4NV5ct6cd+djvlpw8ptD+APn8wfECJj5</latexit> <latexit sha1_base64="kaK7x7wFN3GZpVpMGGOJaQQWYoA=">AAACBXicbVC7SgNBFL0bXzG+opY2E4NgFXZF0DJoYxnBPCC7htnJJBkys7PMzIrLktpfsNXeTmz9Dlu/xEmyhSYeuHA4517O5YQxZ9q47pdTWFldW98obpa2tnd298r7By0tE0Vok0guVSfEmnIW0aZhhtNOrCgWIaftcHw99dsPVGkmozuTxjQQeBixASPYWOneD0X2OPErvpF+Je2Vq27NnQEtEy8nVcjR6JW//b4kiaCRIRxr3fXc2AQZVoYRTiclP9E0xmSMh7RraYQF1UE2+3qCTqzSRwOp7EQGzdTfFxkWWqcitJsCm5Fe9Kbiv14oFpLN4DLIWBQnhkZkHjxIODISTStBfaYoMTy1BBPF7O+IjLDCxNjiSrYUb7GCZdI6q3luzbs9r9av8nqKcATHcAoeXEAdbqABTSCg4Ble4NV5ct6cd+djvlpw8ptD+APn8wfECJj5</latexit> <latexit sha1_base64="kaK7x7wFN3GZpVpMGGOJaQQWYoA=">AAACBXicbVC7SgNBFL0bXzG+opY2E4NgFXZF0DJoYxnBPCC7htnJJBkys7PMzIrLktpfsNXeTmz9Dlu/xEmyhSYeuHA4517O5YQxZ9q47pdTWFldW98obpa2tnd298r7By0tE0Vok0guVSfEmnIW0aZhhtNOrCgWIaftcHw99dsPVGkmozuTxjQQeBixASPYWOneD0X2OPErvpF+Je2Vq27NnQEtEy8nVcjR6JW//b4kiaCRIRxr3fXc2AQZVoYRTiclP9E0xmSMh7RraYQF1UE2+3qCTqzSRwOp7EQGzdTfFxkWWqcitJsCm5Fe9Kbiv14oFpLN4DLIWBQnhkZkHjxIODISTStBfaYoMTy1BBPF7O+IjLDCxNjiSrYUb7GCZdI6q3luzbs9r9av8nqKcATHcAoeXEAdbqABTSCg4Ble4NV5ct6cd+djvlpw8ptD+APn8wfECJj5</latexit> <latexit sha1_base64="kaK7x7wFN3GZpVpMGGOJaQQWYoA=">AAACBXicbVC7SgNBFL0bXzG+opY2E4NgFXZF0DJoYxnBPCC7htnJJBkys7PMzIrLktpfsNXeTmz9Dlu/xEmyhSYeuHA4517O5YQxZ9q47pdTWFldW98obpa2tnd298r7By0tE0Vok0guVSfEmnIW0aZhhtNOrCgWIaftcHw99dsPVGkmozuTxjQQeBixASPYWOneD0X2OPErvpF+Je2Vq27NnQEtEy8nVcjR6JW//b4kiaCRIRxr3fXc2AQZVoYRTiclP9E0xmSMh7RraYQF1UE2+3qCTqzSRwOp7EQGzdTfFxkWWqcitJsCm5Fe9Kbiv14oFpLN4DLIWBQnhkZkHjxIODISTStBfaYoMTy1BBPF7O+IjLDCxNjiSrYUb7GCZdI6q3luzbs9r9av8nqKcATHcAoeXEAdbqABTSCg4Ble4NV5ct6cd+djvlpw8ptD+APn8wfECJj5</latexit> ׾ⵃ欽׃ג葺ְ׾䭯א׾涪鋅ׅ׷ 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> x!y <latexit sha1_base64="kaK7x7wFN3GZpVpMGGOJaQQWYoA=">AAACBXicbVC7SgNBFL0bXzG+opY2E4NgFXZF0DJoYxnBPCC7htnJJBkys7PMzIrLktpfsNXeTmz9Dlu/xEmyhSYeuHA4517O5YQxZ9q47pdTWFldW98obpa2tnd298r7By0tE0Vok0guVSfEmnIW0aZhhtNOrCgWIaftcHw99dsPVGkmozuTxjQQeBixASPYWOneD0X2OPErvpF+Je2Vq27NnQEtEy8nVcjR6JW//b4kiaCRIRxr3fXc2AQZVoYRTiclP9E0xmSMh7RraYQF1UE2+3qCTqzSRwOp7EQGzdTfFxkWWqcitJsCm5Fe9Kbiv14oFpLN4DLIWBQnhkZkHjxIODISTStBfaYoMTy1BBPF7O+IjLDCxNjiSrYUb7GCZdI6q3luzbs9r9av8nqKcATHcAoeXEAdbqABTSCg4Ble4NV5ct6cd+djvlpw8ptD+APn8wfECJj5</latexit> <latexit sha1_base64="kaK7x7wFN3GZpVpMGGOJaQQWYoA=">AAACBXicbVC7SgNBFL0bXzG+opY2E4NgFXZF0DJoYxnBPCC7htnJJBkys7PMzIrLktpfsNXeTmz9Dlu/xEmyhSYeuHA4517O5YQxZ9q47pdTWFldW98obpa2tnd298r7By0tE0Vok0guVSfEmnIW0aZhhtNOrCgWIaftcHw99dsPVGkmozuTxjQQeBixASPYWOneD0X2OPErvpF+Je2Vq27NnQEtEy8nVcjR6JW//b4kiaCRIRxr3fXc2AQZVoYRTiclP9E0xmSMh7RraYQF1UE2+3qCTqzSRwOp7EQGzdTfFxkWWqcitJsCm5Fe9Kbiv14oFpLN4DLIWBQnhkZkHjxIODISTStBfaYoMTy1BBPF7O+IjLDCxNjiSrYUb7GCZdI6q3luzbs9r9av8nqKcATHcAoeXEAdbqABTSCg4Ble4NV5ct6cd+djvlpw8ptD+APn8wfECJj5</latexit> <latexit sha1_base64="kaK7x7wFN3GZpVpMGGOJaQQWYoA=">AAACBXicbVC7SgNBFL0bXzG+opY2E4NgFXZF0DJoYxnBPCC7htnJJBkys7PMzIrLktpfsNXeTmz9Dlu/xEmyhSYeuHA4517O5YQxZ9q47pdTWFldW98obpa2tnd298r7By0tE0Vok0guVSfEmnIW0aZhhtNOrCgWIaftcHw99dsPVGkmozuTxjQQeBixASPYWOneD0X2OPErvpF+Je2Vq27NnQEtEy8nVcjR6JW//b4kiaCRIRxr3fXc2AQZVoYRTiclP9E0xmSMh7RraYQF1UE2+3qCTqzSRwOp7EQGzdTfFxkWWqcitJsCm5Fe9Kbiv14oFpLN4DLIWBQnhkZkHjxIODISTStBfaYoMTy1BBPF7O+IjLDCxNjiSrYUb7GCZdI6q3luzbs9r9av8nqKcATHcAoeXEAdbqABTSCg4Ble4NV5ct6cd+djvlpw8ptD+APn8wfECJj5</latexit> <latexit sha1_base64="kaK7x7wFN3GZpVpMGGOJaQQWYoA=">AAACBXicbVC7SgNBFL0bXzG+opY2E4NgFXZF0DJoYxnBPCC7htnJJBkys7PMzIrLktpfsNXeTmz9Dlu/xEmyhSYeuHA4517O5YQxZ9q47pdTWFldW98obpa2tnd298r7By0tE0Vok0guVSfEmnIW0aZhhtNOrCgWIaftcHw99dsPVGkmozuTxjQQeBixASPYWOneD0X2OPErvpF+Je2Vq27NnQEtEy8nVcjR6JW//b4kiaCRIRxr3fXc2AQZVoYRTiclP9E0xmSMh7RraYQF1UE2+3qCTqzSRwOp7EQGzdTfFxkWWqcitJsCm5Fe9Kbiv14oFpLN4DLIWBQnhkZkHjxIODISTStBfaYoMTy1BBPF7O+IjLDCxNjiSrYUb7GCZdI6q3luzbs9r9av8nqKcATHcAoeXEAdbqABTSCg4Ble4NV5ct6cd+djvlpw8ptD+APn8wfECJj5</latexit>

/ 166 猰㷕涸椚鍑הכ荈搫猰㷕灇瑔כ➂꟦ך㌀׫ד֮׷ 157 Ԩ 荈搫ך׃ֻ׫׾ չ➂꟦ָպ椚鍑ׅ׷䗳銲ָ֮׷ չ椚鍑պחꟼ⤘ׅ׷灇瑔װ䪮遭ָ♧瘡篖דכְַזְךכׅץגֿךְׇ ˖ 钠濼ꣲ歲➂꟦כ㣐ꆀך䞔㜠׾椚鍑דֹזְ٥䙼ְ鴥׫
⟎铡 ָ䗳갭 ˖ 钠濼غ؎،أ٥爡⠓غ؎،أ➂꟦ָر٦ة׾ה׷הغ؎،أכ♶〳鼘 ˖ 䠬䞔䗰椚 猘׋׍ך䙼罋٥ⴻ倖כ䠬䞔ח鏮ִ׷倯岀װ䞔㜠乼⡲ח腚ְ ˖ 猰㷕涸椚鍑ך䧭⸆غ؎،أ猰㷕涸椚鍑כ⳿晛ׁ׸גכׄ׭ג⚅ך⚥ח 䎢ת׶涺ך猰㷕涸椚鍑הז׷ָծ⳿晛穠卓כ溪㹋ך♧鿇ך׫ח䓼ֻ⨉׷ ˖ ת׋ծ荈搫ך岀⵱ָ䗳׆׃׮➂꟦ך׃׳רְ钠濼ꣲ歲ך眔㔲ד知患ח鎸鶢׃׋׶ⵖ䖴דֹ׷הכꣲ׵זְ Ԩ 䩛חⰅ׷䞔㜠כ䌢ח鿇ⴓ涸➂欰ָ剣ꣲד֮׷⟃♳ծׅץג׾ٌرٕ⻉׃ ׋׶ծ֮׶ה֮׵ײ׷䞔㜠׾Ⰵ⸂㢌侧ח׃׋׶ׅ׷ֿהכ♶〳腉կֿך䠐㄂ד⡦׵ַךչ㷕统պװչ濼陎պכ♶〳鼘

/ 166 㹋꿀荈⹛⻉铩׌׏ג⽃锃ד鷌㾄ז⸤⫴ַ׵鍑佝ׁ׸׋ְ 158 Organic synthesis in a modular robotic
system. Science 363 (2019) A mobile robotic chemist. Nature 583 (2020) Automating drug discovery. Nature Reviews Drug Discovery 17 (2018) Ԩ 猰㷕灇瑔חְֶג׮ꬊ⸬桦ז⸤⫴ְָ׆׸荈⹛⻉ׁ׸׷ךכ娖〷涸䗳搫 ̔猰㷕חאֹתהֲⱄ植䚍٥㾩➂䚍٥麓ꃎ⸤⫴ך㉏겗鍑嶊ח׮项ׅ׷

/ 166 ׋׌׃⡲噟ך荈⹛⻉ה涪鋅׉ך׮ךך荈⹛⻉כⴽ如⯋ך㉏겗 159 Ԩ ٗنحز禸ָ֮׸ל笺뜧ז㹋꿀ָ ➂䩛״׶כ ׋ֻׁ׿דֹ׷ָ׉׸ד׮ չ涪鋅պחכ⸂䪮ך⸇鸞⻉דכⵋ麦דֹזְ 〳腉ז⦪酡瑞꟦ָ䎢ֺׅ
Ԩ 荈⹛⻉䪮遭ך灇瑔הさ׻ׇגչ⡦׾וֲ涪鋅ׅ׷ךַպך䨌殛ָ䗳갭 ̔䱱稊ׅ׷禸٥أ؝٦فծ堣㐻ד鎘庠ׅץֹ㢌侧ծةأؙךرؠ؎ٝ

/ 166 ➂䊨濼腉ⴓꅿחֶֽ׷չ涪鋅պך灇瑔 160 涪鋅猰㷕ծ猰㷕涸涪鋅ך锷椚ծ濼陎涪鋅ծ堣唒㷕统ծ،ـتؙءّٝ

/ 166 涪鋅猰㷕ה堣唒涪鋅 161

/ 166 涪鋅猰㷕ה堣唒涪鋅 162 խխ䎷畍խ傈劤ך涪鋅猰㷕فٗآؙؑز剣䊛眍㣗 痥*鿇խ䱿锷ח״׷濼陎涪鋅 խխ痥畍խչ涪鋅պך猰㷕ㆸ㷕ˌ娖〷涸稆䲽ꅿ㹺㉔♧ խխ痥畍խ窟鎘涸鎸〾Ⳣ椚鎉铂13*4.✡靼歋ꥐ٥⡟谏岱➜ խխ痥畍խ✮庠ٌرַٕ׵ךٕ٦ٕ䬄⳿ˌ侧䒭ַ׵鎉铂פ剢劤խ峔٥啾歊⼪窩 խխ痥畍խ䌓秛锷椚فؚٗٓىؚٝה鏾僇酡㸣㿊劤畍⽆٥剣募⽆秀٥䎂歊罭♧
խխ痥畍խ,FZ(SBQIˌؗ٦ٙ٦س䬄⳿خ٦ַٕ׵涪鋅خ٦ٕפך㾜Ꟛ瀧㿊խ床٥㣐愮䎊欰٥靼ⰻ歊姻䕕 խխ痥畍խ*OUFMMJHFOU1BEךさ䧭הⱄⵃ欽ˌ䌓秛䱿锷ך甧㜥ַ׵⾱〡խ铆٥䎂歊խ幄 痥**鿇խ鎘皾㷕统椚锷ח㛇בֻ濼陎涪鋅 խխ痥畍խ腉⹛㷕统ה涪鋅猰㷕㸜⦓湫埠٥꼛鋅㝩խ䬪 խխ痥畍խֻ׶鵤׃؜٦يה׃גך㷕统،ٕ؞ٔؤي⚵䀤խ畍٥戣劤薉✳ խխ痥畍խ؝ٝؾُ٦ة؟؎ؒٝأך׋׭ך⽃秪ַא⸬桦涸ז؟ٝفؚٔٝ䪮岀床鴟խ屚 խխ痥畍խ㷕统،ٕ؞ٔؤيך鐰⣣♳⾱齥僻 խխ痥畍խ䎗⡦ؙٓأةؚٔٝך䞔㜠鎘皾䎗⡦圓鸡➙❁խ嵞 խխ痥畍խ4VQQPSU7FDUPS.BDIJOFח״׷ⴓ겲넝갭幄㸩 痥***鿇խ堣唒㷕统הر٦ةو؎صؚٝח㛇בֻ濼陎涪鋅 խխ痥畍խ؝ٝؾُ٦ة佄䴂ח״׷猰㷕涸濼陎ך涪鋅1BU-BOHMFZ衼㹧ꅿխ䝎٥⚵㿊խ⥜鏬 խխ痥畍խ㷕统ַծو؎صַؚٝծٌرַؚٔٝˌ〢欰䡾㷕ַ׵ך✲⢽灇瑔)FJLLJ.BOOJMBFUBM衼啾♴溪♧鏬 խխ痥畍խⴓ協ꣲ㹀岀׾欽ְ׋⚛⴨ؚٓؿ䱱稊ח״׷剑黝穠さٕ٦ٕך涪鋅⚥靼僇䒽٥啾♴溪♧ խխ痥畍խ濼陎涪鋅ה荈䊹穈籼㘗ך窟鎘ٌرٕ⻌䊛彁㔊龤٥垌〡濼⛒ խխ痥畍խ곁㹏ך飑顠㾶娖ַ׵ךر٦ةو؎صؚٝ濶歊⹧⤥٥⸇谏湫埠٥纷㹓遤⥋ խխ痥畍խ涪鋅ءأذيהؼُ٦وٝؒؗأػ٦زך؎ٝذؚٖ٦ءّٝ⚵㿊խ⥜٥㹧ꅿխ䝎 痥*7鿇խ㣐鋉垷侧⦼ر٦ةַ׵ך濼陎涪鋅 խխ痥畍խ㣕ꤿ㖑椔禸暟椚㷕פך濼陎涪鋅ך䘔欽㹺啾⤥䕕٥♳ꅿ桠㣕٥腉⹲姻➋٥歕歊խ䗼٥虠加խ䗡٥✡❁鞢宕٥畾歊꧇䕕 խխ痥畍խـٓ؎ٝسإػٖ٦ءّٝהؐؑ٦ـٖحزח״׷ꦀ誊歗⫷ך涪鋅倜䃊罭♧ խխ痥畍խ鎘皾堣ח״׷猰㷕涸岀⵱٥ٌرٕך涪鋅倯岀ך㾜Ꟛ똲㽵խꥐ٥⯋歊խ嵞 խխ痥畍խ㢳㢌ꆀر٦ةַ׵ך㢳갪䒭㘗岀⵱ך涪鋅⚥ꅿ葺䎂٥俕谏ㄤ䊻 խխ痥畍խ갈㡮ر٦ةك٦أַ׵ך갈㡮濼陎ך涪鋅ꈿ加㛇⛒٥暜ꅿ姻♲ խխ痥畍խ⟎䟝⻉ׁ׸׋➂⡤ַ׵ךشؽ؜٦ءّٝח㛇בֻ濼陎涪鋅ך佄䴂خ٦ٕ뢷谏鞢俑٥둷腜秪♧龤 痥7鿇խطحزٙ٦ؙ橆㞮חֶֽ׷濼陎涪鋅 խխ痥畍խى٦يًر؍،׾欽ְ׋濼頿崧鸐ה猰㷕䪮遭ر٦ةך〳鋔⻉歊⚥խ隁 խխ痥畍խؤ٦ىؚٝ䪮遭׾欽ְ׋㼎鑧涸䞔㜠嗚稊؎ٝةؿؑ٦أ鞢歊姻〷٥叝㿊䝜ㆂ խխ痥畍խؙٔٝ䞔㜠ַ׵ך濼陎笨圓䧭䑜䊛⡟⼪歑٥寑歊㣐鰊٥歊〡ⶌ〷 խխ痥畍խ؎ٝة٦طحزדך⟰噟꟦䞔㜠Ⱏ剣חぢֽ׋وٕثؒ٦آؑٝزءأذي嬁ⵃꥐ㣗٥넝歊酔䘊 1BU-BOHMFZה)FJLLJ.BOOJMBך ꅾ銲锷俑ךㄤ鏬׮אְגְ׷

/ 166 邌植ה➜Ⰵ堣唒㷕统ַ׵堣唒涪鋅פ荚׷׋׭ך䭷ꆙ 163 Ԩ 黝ⴖזⰅ⸂邌植ךرؠ؎ٝה㷕统 ⴓ㶨邌植ה(//Tծ暴ח✲⵸㷕统ה׉ך鯄獳 Ⰵ⸂暴䗙ꆀ 鎸鶢㶨 ך鏣鎘٥ؒٝآص،ؚٔٝ
Ԩ 堣唒㷕统ٌرٕ Ⰵ⳿⸂وحؾؚٝ ך邌植椚锷鎘皾堣唒㷕统 ؚٖ؎نحؙأ剑黝⻉ ➜Ⰵ湱ꟼַ׵㔓卓ך呎䬿׾䖤׷ 邌植䗳銲⼧ⴓז䞔㜠׾堣唒חⰅ׸׷ Ԩ 湱ꟼ׾㔓卓ה然鏾ׅ׷׋׭ך➜Ⰵ㹋꿀灇瑔䱱稊هٔء٦ה黝䘔涸㹋꿀鎘歗ךرؠ؎ٝ Ԩ ءىُٖ٦ءّٝװ㹋꿀荈⹛⻉הך輐さ

/ 166 堣唒㷕统٥堣唒涪鋅חה׏ג׮㹋⚅歲嗚鏾ך׋׭ך咿㿊屯 164 涪鋅٥椚鍑邌植 ➜Ⰵ ⟎铡 An exciting
“real-world” test bench for ML researchers! Ԩ 堣唒㷕统 .BDIJOF-FBSOJOH ꨄ侔圓鸡穈さׇ圓鸡׾⠵ֲ堣唒㷕统 ⴓ㶨ծ⿾䘔ծ⿾䘔穗騟/FUXPSL Ԩ 堣唒涪鋅 .BDIJOF%JTDPWFSZ 椚锷鎘皾.- ؚٖ؎نحؙأ剑黝⻉ ծ㹋꿀.- 䱱稊ה➜Ⰵ鎘歗䖤׵׸גְ׷庠㹀ر٦ة 傀濼ך✲㹋俑柃ر٦ة װ侄猰剅涸濼陎 ✲⵸䞔㜠 ٌرٕ 倜׋ז䞔㜠 ˖ 剣⸬זⰅ⸂㢌侧ךず㹀 ˖ إحز،حفךرؠ؎ٝ ˖ 㹋꿀ך鎘歗٥㹋倵 ˖ 穠卓ך鐰⣣٥鍑ꅸ ⟎铡 ٌرٕ ✲⵸䞔㜠

/ 166 ֿךأٓ؎س׮縧ְג֮׶תׅ 165 https://www.slideshare.net/itakigawa/presentations https://itakigawa.github.io/news.html

/ 166 תה׭➙傈ך鑧 166 ˖ 荈䊹稱➜ 堣唒㷕统ה荈搫猰㷕ך㞮歲 ˖ 堣唒㷕统הכ倜׃ְفؚٗٓىؚٝך倯岀
˖ 堣唒㷕统㾊כ♧⡤⡦ָ嚂׃ְךַ ˖ ⴓ㶨ך邌植ה堣唒㷕统 ˖ ؚٖ؎نحؙأ剑黝⻉怴糊䌓秛 锷椚㷕ה窟鎘㷕ך輐さ ˖ 荈搫猰㷕灇瑔ד堣唒㷕统׾⢪ֲֶהׅ׷ה䗳׆עאַ׷劤䔲חꨇ׃ְ㉏겗 ˖ ر٦ةٌرؚٔٝה✮庠،ٕ؞ٔؤي 5IF5XP$VMUVSFT ˖ ✮庠ַ椚鍑ַ3BTIPNPO⸬卓 6OEFSTQFDJDBUJPO 鍑ꅸ㢳圫䚍 ˖ ➂꟦ך钠濼غ؎،أח歋勻ׅ׷㉏겗⟎铡ծ㣟侁ծ䧭⸆غ؎،أծFUD ˖ 堣唒㷕统ַ׵堣唒涪鋅פ ˖ չ涪鋅պչ椚鍑պך麣瘡כさ椚⻉דֹ׷ךַ荈⹛⻉דֹ׷ךַ https://itakigawa.github.io/data/talk_20211026.pdf

(2021.10) 機械学習と機械発見 データ中心型の化学・材料科学の教訓とこれから

(2021.10) 機械学習と機械発見 データ中心型の化学・材料科学の教訓とこれから

More Decks by itakigawa

Featured

Transcript

(2021.10) 機械学習と機械発見データ中心型の化学・材料科学の教訓とこれから

(2021.10) 機械学習と機械発見データ中心型の化学・材料科学の教訓とこれから