物理モデリングツールとして有用な表現を探る/Exploring useful expressions as a physical modeling tool

2026年5月26日開催　第70回システム制御情報学会（SCI’26）招待講演発表資料
https://sci26.iscie.or.jp/plan/ts/ts04/

Transcript

1. ෺ཧϞσϦϯάπʔϧͱͯ͠༗༻ͳදݱΛ୳Δ 加藤 祥太 shota@human.sys.i.kyoto-u.ac.jp 京都大学大学院 情報学研究科 ヒューマンシステム論分野 2026-05-26 第70回システム制御情報学会 SCI’26
2. 
   ژେӃ޻ֶݚڀՊ Խֶ޻ֶઐ߈मྃ 
   ಉେֶӃ৘ใֶݚڀՊ γεςϜՊֶઐ߈मྃ r ಉॿڭ r
   ϚϯνΣελʔେֶ ٬һݚڀһ r
   ࢈૯ݚ
   টᡈݚڀһ r ࢈૯ݚ ಛఆϑΣϩʔʢΫϩεΞϙΠϯτϝϯτʣ ઐ໳ɿϓϩηεγεςϜ޻ֶ process systems engineering, PSE ɺࣗવݴޠॲཧ ݚڀ಺༰ɿ • ෺ཧϞσϧߏஙͷࣗಈԽɾࣗ཯Խ ˞෺ཧϞσϧɿՊֶݪཧʹجͮ͘਺ࣜ܈ • AI Ԡ༻ʢAI for Scienceʣ X Twitter 
   @s_kat0 ࣗݾ঺հɿՃ౻
   ↅଠ ෺ཧϞσϧ ࿦จ΍ॻ੶ ࣮ݧσʔλ ࣌ؒ ೱ౓ "* 1
3. ࿈ଓ૧ܕ൓Ԡثʢcontinuous stirred tank reactor, CSTRʣ • Խֶ޻ֶͷڭՊॻతͳϞσϧͷର৅ͱͯ͠޿͘༻͍ΒΕΔɻ • ྲྀೖɾྲྀग़͕࿈ଓతʹߦΘΕೱ౓΍Թ౓͸૧಺ͰҰ༷ɺ ൓Ԡث಺෦͕׬શʹࠞ߹͞Ε͍ͯΔɺͱΈͳ͢ɻ • Ծఆ΍ऩࢧΛද͢ඍ෼୅਺ํఔࣜ (differential algebraic equations, DAE) ΛϞσϧͱ͢Δɻ ؆୯ͳ෺ཧϞσϧͷྫ <latexit sha1_base64="YVL+39Cn4t5hsWRxApOt9xtsixE=">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</latexit> V dCA dt = FinCA,in → FoutCA,out → kV CA <latexit sha1_base64="WKW2vTfPz7siHJqqz56iJOApuQc=">AAACHXicbVDLSsNAFJ34rPUVdelmsAoupCQi1Y1Q7cZlBfuANoTJdNoOncmEmYlQQn7An/AX3OrenbgVt36JkzaL2nrgwuGce7n3niBiVGnH+baWlldW19YLG8XNre2dXXtvv6lELDFpYMGEbAdIEUZD0tBUM9KOJEE8YKQVjGqZ33okUlERPuhxRDyOBiHtU4y0kXz7uOYnXY70UPLk5gyKWKcpvIazapr6dskpOxPAReLmpARy1H37p9sTOOYk1JghpTquE2kvQVJTzEha7MaKRAiP0IB0DA0RJ8pLJt+k8MQoPdgX0lSo4USdnUgQV2rMA9OZnajmvUz81wv43Gbdv/ISGkaxJiGeLu7HDGoBs6hgj0qCNRsbgrCk5naIh0girE2gRROKOx/BImmel91KuXJ/Uare5vEUwCE4AqfABZegCu5AHTQABk/gBbyCN+vZerc+rM9p65KVzxyAP7C+fgFGM6JV</latexit> CA,out = CA <latexit sha1_base64="6hTU3DGUtrYX62/rQuYtZHNHC3k=">AAACInicbZDJSgNBEIZ74hbjFvXopTEIejDMiEQvQlAEj1GygRNCT6cmadKz0F0jhiHP4Ev4Cl717k08CZ58EjvLQaM/NPz8VUVVf14shUbb/rAyc/MLi0vZ5dzK6tr6Rn5zq66jRHGo8UhGqukxDVKEUEOBEpqxAhZ4Ehpe/2JUb9yB0iIKqziIoRWwbih8wRmaqJ0/6NMz2m/b1IX7mLoSfNynrq8YTw8vh+lNdUhdJbo9PGjnC3bRHov+Nc7UFMhUlXb+y+1EPAkgRC6Z1reOHWMrZQoFlzDMuYmGmPE+68KtsSELQLfS8ZeGdM8kHepHyrwQ6Tj9OZGyQOtB4JnOgGFPz9ZG4b81L5jZjP5pKxVhnCCEfLLYTyTFiI540Y5QwFEOjGFcCXM75T1m+KChmjNQnFkEf039qOiUiqXr40L5fIonS3bILtknDjkhZXJFKqRGOHkgT+SZvFiP1qv1Zr1PWjPWdGab/JL1+Q2Xk6LT</latexit> k = k0 exp →E RT ෺࣭ऩࢧࣜ ׬શࠞ߹Ծఆ ΞϨχ΢εͷࣜ ੡඼ !!,#$% , "#$% ᎟፩ػ ൓Ԡ A→B λϯΫ #, !& , !! ݪྉ !&,'( , "'( <latexit sha1_base64="N94FcyGrdq0KaxV3fAdi84wtMfk=">AAACHXicbVDLSsNAFJ34rPUVdelmsAoupCQi1Y1Q2o3LCvYBbSiT6aQdOpMJMxOhhPyAP+EvuNW9O3Erbv0SJ20WtfXAhcM593LvPX7EqNKO822trK6tb2wWtorbO7t7+/bBYUuJWGLSxIIJ2fGRIoyGpKmpZqQTSYK4z0jbH9czv/1IpKIifNCTiHgcDUMaUIy0kfr2ab2f9DjSI8mT2gUUsU5TeAvn1TTt2yWn7EwBl4mbkxLI0ejbP72BwDEnocYMKdV1nUh7CZKaYkbSYi9WJEJ4jIaka2iIOFFeMv0mhWdGGcBASFOhhlN1fiJBXKkJ901ndqJa9DLxX8/nC5t1cOMlNIxiTUI8WxzEDGoBs6jggEqCNZsYgrCk5naIR0girE2gRROKuxjBMmldlt1KuXJ/VarW8ngK4BicgHPggmtQBXegAZoAgyfwAl7Bm/VsvVsf1uesdcXKZ47AH1hfv0l1olc=</latexit> CB,out = CB <latexit sha1_base64="dmKZgqqqtPiaYCgOn9ccFySWCys=">AAACG3icbVDLSsNAFJ34rPUVdelmaBFclUSkuhGKgrisYB/QhjCZTtqhM5kwMxFKyN6f8Bfc6t6duHXh1i9x0mZRWw9cOJxzL/feE8SMKu0439bK6tr6xmZpq7y9s7u3bx8ctpVIJCYtLJiQ3QApwmhEWppqRrqxJIgHjHSC8U3udx6JVFRED3oSE4+jYURDipE2km9Xbv20z5EeSZ7SKMvgFZxTRKKzzLerTs2ZAi4TtyBVUKDp2z/9gcAJJ5HGDCnVc51YeymSmmJGsnI/USRGeIyGpGdohDhRXjr9JYMnRhnAUEhTkYZTdX4iRVypCQ9MZ36kWvRy8V8v4AubdXjpmZ/jRJMIzxaHCYNawDwoOKCSYM0mhiAsqbkd4hGSCGsTZ9mE4i5GsEzaZzW3Xqvfn1cb10U8JXAMKuAUuOACNMAdaIIWwOAJvIBX8GY9W+/Wh/U5a12xipkj8AfW1y8El6JQ</latexit> Fin = Fout ӷ໘ҰఆͷԾఆ <latexit sha1_base64="e9/D8LmNBduRGzqd0vDCINV9SyQ=">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</latexit> V dCB dt = →FoutCB,out + kV CA 2
4. ෳࡶͳ෺ཧϞσϧΛཁ͢Δϓϩηεͷྫ νϣΫϥϧεΩʔϓϩηε • γϦίϯ΢Σʔϋ༻ͷΠϯΰοτΛ ݁থ੒௕ʹΑͬͯ੡଄͢Δɻ • ߴ඼࣭ͳ੡඼Λ੡଄͢ΔͨΊʹɺ ݁থ൒ܘΛؚΉෳ਺ͷม਺Λ ॴ๬ͷ஋ʹ੍ޚ͢Δ͜ͱ͕ඞཁɻ • ೤ͷ఻ΘΓํ΍༥ӷ͕ݮΓଓ͚Δݱ৅Λ Ϟσϧʢ਺ࣜʣͰදݱ͢Δඞཁ͕͋Δɻ • কདྷ༧ଌʹج͍ͮͯӡస৚݅Λܾఆ͢Δ ͨΊʹɺϞσϧʢ਺ࣜ܈ʣΛߏஙͨ͠ɻ [Kato+, J. Cryst. Growth, 2021] https://www.sumcosi.com/products/process/step_01.html CZ: Czochralski 3
5. • ໿ͷ਺͔ࣜΒߏ੒͞ΕΔɻ • ͜ͷߏஙɾվળʹ͸ɺม਺ͱ਺ࣜͷҙຯ΍;Δ·͍ͷཧղ͕ඞཁɻ ෳࡶͳ෺ཧϞσϧͷྫɿ$;ϓϩηεͷ෺ཧϞσϧ <latexit sha1_base64="u+5hnTQRunWDVRfsj1ZrekzL3l4=">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</latexit> 1 = 1 ⇢cryr2 cry ⇢melr2 c,in + 1 r2 cry r2 c,in ! @hmen @rcry 2rcryhmen r2 c,in a2 r2 c,in cos ('0 + ') ! tan (') [Zheng+, J. Cryst. Growth, 2018; Kato+., J. Cryst. Growth, 2021] 4
6. ैདྷͷ෺ཧϞσϧߏஙख๏ ઐ໳Ո͕ࢼߦࡨޡతʹϞσϧΛ࡞੒ɾվળ͍ͯ͠ΔͨΊɺίετ͕ߴ͍ɻ ৘ใநग़ දه౷Ұ ର৅ϓϩηεͷจݙ ʢʙ਺ඦใʣ ෺ཧϞσϧߏஙʹ ඞཁͳ৘ใ ෺ཧϞσϧ ࢼߦࡨޡతͳ Ϟσϧߏஙɾੑೳվળ ࿦จ "
   ͱ࿦จ #
   ͷ਺ࣜ͸ Ұݟҧ͏͚Ͳಉ͔͡ʁ ෺ੑ஋ͷۙࣅ͕ࣜෳ਺͋Δ͚Ͳɺ ͲΕΛ࠾༻͢Ε͹͍͍ͷʁ 5
7. ओͳݚڀ಺༰ c
   ෺ཧϞσϧߏஙͷࣗಈԽɾࣗ཯Խ ݱ࣮ͷڍಈΛද͢ Պֶ๏ଇʹجͮ͘ ਺ࣜ܈ ෺ཧϞσϧ ୈҰݪཧϞσϧ モデル候補の 作成と検証 情報の 抽出と統合 対象プロセス 関連文献の収集 Ϟσϧߏஙʹඞཁͳ৘ใ ͷࣗಈநग़ɺಉٛੑ൑ఆɺ දه౷Ұ ʁ Ϟσϧީิͷ ࣗಈ࡞੒ɾݕূ 1/# ln ' O ࿈ଓ૧ܕ൓Ԡث จݙσʔλϕʔε͔Β ର৅ϓϩηεؔ࿈จݙ Λࣗಈऩूɺܗࣜ౷Ұ ๲େͳ࡞ۀͱߴ౓ͳ஌ࣝͱεΩϧ ࣌ؒΛ͔͚ͨࢼߦࡨޡ ैདྷख๏ɿख࡞ۀ "VUP1.P#ɿ"*ʹΑΔࣗಈԽ ߏங ߏங Ϟσϧީิ̍ Ϟσϧީิ̎ Ϟσϧީิ̏ 記号 定義 ! 温度 "! ⼊⼝流量 ⁝ ⁝ #" 反応速度 記号 定義 ! 温度 "! ⼊⼝流量 ⁝ ⁝ #" 反応速度 d" d# = %! − % ︙ ' = '! exp(− , -. ) −0" = '1" d1" d# = % " 1"! − 1" + 0" ֧፩ػ ݪྉ ੡඼ จݙ৘ใ͔Βͷ෺ཧϞσϧࣗಈߏங จݙ͔Β෺ཧϞσϧΛࣗಈߏங͢Δ࿮૊Έ ΛఏҊ͠ɺཁૉٕज़Λ։ൃ͍ͯ͠Δɻ [Kato&Kano, Comput. Aided. Chem. Eng., 2022] ෺ཧϞσϦϯάͷࣗ཯Խ ਺஋σʔλ͔Βͷ෺ཧϞσϧ֫ಘɺ ෺ཧϞσϧͷධՁɺධՁ݁Ռʹجͮ͘ ࣮ݧઃܭΛࣗಈͰ࣮ߦ͢ΔγεςϜͷ ࣮ݱΛ໨ࢦ͍ͯ͠Δɻ ࣮ݧσʔλ ෺ཧϞσϧ ! = #(%) 
   ࣮ݧઃܭ ࣮ݧύϥϝʔλ ੑೳ  Ϟσϧߏங ࣌ؒ ೱ౓ 
   ϞσϧධՁ ࣌ؒ ೱ౓ ๬·͍͠ ڍಈ ධՁ݁Ռ ఺਺
    6
8. • ෺ཧϞσϧͱ͸ɺ෺ཧతɾԽֶతݪཧʹجͮ͘਺ࣜ܈ɻ ਺ࣜ͸ɺҙຯΛ࣋ͭه߸΍ɺର৅ܥͷഎܠ৘ใʢจ຺ʣΛؚΉɻ • ෺ཧϞσϧͷཧղʹ໾ཱͭʮදݱʯ͸ɺ਺ࣜɾه߸ɾจষɾਤͳͲɻ ਺͕ࣜɺ෺ཧϞσϧͷදݱʹಛʹॏཁɻ ෺ཧϞσϧͷʮදݱʯͱ͸ʁ <latexit sha1_base64="YVL+39Cn4t5hsWRxApOt9xtsixE=">AAAChnicbVHLSgMxFM2Mr1pfVVfiJlgEF1pmRFs3QrUgLivYVrClZNKMDU1mhuSOUIZ8gh/o1l/wB0wfaB9eCJyccy73cm6QCK7B8z4dd2V1bX0jt5nf2t7Z3SvsHzR1nCrKGjQWsXoJiGaCR6wBHAR7SRQjMhCsFQxqI731zpTmcfQMw4R1JHmLeMgpAUt1Cx/NdqgIzdqSQF/JrGdq3d/PnTFmRgGDb/HDn8wjY/Cs/RyPqYtZU5zCkmvCXeBBE89P6xaKXskbF14G/hQU0bTq3cJXuxfTVLIIqCBav/peAp2MKOBUMJNvp5olhA7IG3u1MCKS6U42js3gU8v0cBgr+yLAY3a2IyNS66EMrHO0ol7URuS/WiAXJkN407FxJSmwiE4Gh6nAEOPRTXCPK0ZBDC0gVHG7O6Z9Ys8C9nJ5G4q/GMEyaF6W/HKp/HRVrN5P48mhY3SCzpCPKqiKHlEdNRBF386Rc+IU3Zxbcq/dysTqOtOeQzRXbvUHjc/HXA==</latexit> V dCA dt = FinCA,in → FoutCA,out → kV CA <latexit sha1_base64="WKW2vTfPz7siHJqqz56iJOApuQc=">AAACHXicbVDLSsNAFJ34rPUVdelmsAoupCQi1Y1Q7cZlBfuANoTJdNoOncmEmYlQQn7An/AX3OrenbgVt36JkzaL2nrgwuGce7n3niBiVGnH+baWlldW19YLG8XNre2dXXtvv6lELDFpYMGEbAdIEUZD0tBUM9KOJEE8YKQVjGqZ33okUlERPuhxRDyOBiHtU4y0kXz7uOYnXY70UPLk5gyKWKcpvIazapr6dskpOxPAReLmpARy1H37p9sTOOYk1JghpTquE2kvQVJTzEha7MaKRAiP0IB0DA0RJ8pLJt+k8MQoPdgX0lSo4USdnUgQV2rMA9OZnajmvUz81wv43Gbdv/ISGkaxJiGeLu7HDGoBs6hgj0qCNRsbgrCk5naIh0girE2gRROKOx/BImmel91KuXJ/Uare5vEUwCE4AqfABZegCu5AHTQABk/gBbyCN+vZerc+rM9p65KVzxyAP7C+fgFGM6JV</latexit> CA,out = CA <latexit sha1_base64="6hTU3DGUtrYX62/rQuYtZHNHC3k=">AAACInicbZDJSgNBEIZ74hbjFvXopTEIejDMiEQvQlAEj1GygRNCT6cmadKz0F0jhiHP4Ev4Cl717k08CZ58EjvLQaM/NPz8VUVVf14shUbb/rAyc/MLi0vZ5dzK6tr6Rn5zq66jRHGo8UhGqukxDVKEUEOBEpqxAhZ4Ehpe/2JUb9yB0iIKqziIoRWwbih8wRmaqJ0/6NMz2m/b1IX7mLoSfNynrq8YTw8vh+lNdUhdJbo9PGjnC3bRHov+Nc7UFMhUlXb+y+1EPAkgRC6Z1reOHWMrZQoFlzDMuYmGmPE+68KtsSELQLfS8ZeGdM8kHepHyrwQ6Tj9OZGyQOtB4JnOgGFPz9ZG4b81L5jZjP5pKxVhnCCEfLLYTyTFiI540Y5QwFEOjGFcCXM75T1m+KChmjNQnFkEf039qOiUiqXr40L5fIonS3bILtknDjkhZXJFKqRGOHkgT+SZvFiP1qv1Zr1PWjPWdGab/JL1+Q2Xk6LT</latexit> k = k0 exp →E RT ෺࣭ऩࢧࣜ ׬શࠞ߹Ծఆ ΞϨχ΢εͷࣜ ੡඼ !!,#$% , "#$% ᎟፩ػ ൓Ԡ A→B λϯΫ #, !& , !! ݪྉ !&,'( , "'( <latexit sha1_base64="N94FcyGrdq0KaxV3fAdi84wtMfk=">AAACHXicbVDLSsNAFJ34rPUVdelmsAoupCQi1Y1Q2o3LCvYBbSiT6aQdOpMJMxOhhPyAP+EvuNW9O3Erbv0SJ20WtfXAhcM593LvPX7EqNKO822trK6tb2wWtorbO7t7+/bBYUuJWGLSxIIJ2fGRIoyGpKmpZqQTSYK4z0jbH9czv/1IpKIifNCTiHgcDUMaUIy0kfr2ab2f9DjSI8mT2gUUsU5TeAvn1TTt2yWn7EwBl4mbkxLI0ejbP72BwDEnocYMKdV1nUh7CZKaYkbSYi9WJEJ4jIaka2iIOFFeMv0mhWdGGcBASFOhhlN1fiJBXKkJ901ndqJa9DLxX8/nC5t1cOMlNIxiTUI8WxzEDGoBs6jggEqCNZsYgrCk5naIR0girE2gRROKuxjBMmldlt1KuXJ/VarW8ngK4BicgHPggmtQBXegAZoAgyfwAl7Bm/VsvVsf1uesdcXKZ47AH1hfv0l1olc=</latexit> CB,out = CB <latexit sha1_base64="dmKZgqqqtPiaYCgOn9ccFySWCys=">AAACG3icbVDLSsNAFJ34rPUVdelmaBFclUSkuhGKgrisYB/QhjCZTtqhM5kwMxFKyN6f8Bfc6t6duHXh1i9x0mZRWw9cOJxzL/feE8SMKu0439bK6tr6xmZpq7y9s7u3bx8ctpVIJCYtLJiQ3QApwmhEWppqRrqxJIgHjHSC8U3udx6JVFRED3oSE4+jYURDipE2km9Xbv20z5EeSZ7SKMvgFZxTRKKzzLerTs2ZAi4TtyBVUKDp2z/9gcAJJ5HGDCnVc51YeymSmmJGsnI/USRGeIyGpGdohDhRXjr9JYMnRhnAUEhTkYZTdX4iRVypCQ9MZ36kWvRy8V8v4AubdXjpmZ/jRJMIzxaHCYNawDwoOKCSYM0mhiAsqbkd4hGSCGsTZ9mE4i5GsEzaZzW3Xqvfn1cb10U8JXAMKuAUuOACNMAdaIIWwOAJvIBX8GY9W+/Wh/U5a12xipkj8AfW1y8El6JQ</latexit> Fin = Fout ӷ໘ҰఆͷԾఆ <latexit sha1_base64="e9/D8LmNBduRGzqd0vDCINV9SyQ=">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</latexit> V dCB dt = →FoutCB,out + kV CA ྫɿCSTRͷϞσϧ 7
9. 2
   ҎԼͷࣜ͸ɺ࣍ݩͷຒΊࠐΈۭؒͰͲ͏഑ஔ͞ΕΔ΂͖͔ʁ  𝑥! + 𝑦! + 2𝑥𝑦  𝑥 + 𝑦 !  𝑥! + 𝑦! + 𝑥𝑦  2(𝑥 + 𝑦)  2 • ͱ͸୅਺తʹ౳Ձ • ͷඍ෼͕ɺͦͷඍ෼͕ ਺ࣜͷʮදݱʯʛ਺ࣜͷຒΊࠐΈ 1 2 3 5 d/dx 1 2 3 5 4 ୅਺తͳૢ࡞Λදݱ (例えば[Valentino+, NAACL, 2024]) ߏ଄తͳྨࣅੑΛදݱ (例えば[Mansouri+, ICTIR, 2019]) "
   λεΫʹΑͬͯҟͳΔ͕ɺຊࢿྉͰ͸਺ࣜͷҙຯʹै͏΂͖ͱ͢Δɻ 4 d/dx 8
10. ਺ࣜͷҙຯ͸ɺͲ͜ʹ͋Δͷ͔ʁ จ຺ [Krstovski&Blei, arXiv, 2018] ୅਺త౳Ձੑ [Gangwar&Kani, TMLR, 2023] ਺஋ڍಈ [Meidani+, ICLR, 2024] 9
11. ʮ਺ࣜͷҙຯʯΛϕΫτϧͰ࣋ͨͤΔํ๏͸ɺओʹ̏؍఺͋Δɻ  पลςΩετ͔ΒͳΔจ຺ [Krstovski&Blei, arXiv, 2018]  ୅਺త౳Ձͳ਺ࣜϖΞ [Gangwar&Kani, TMLR, 2023]
    
     ೖग़ྗͷ਺஋తৼΔ෣͍ [Meidani+, ICLR, 2024] ਺ࣜຒΊࠐΈʹඞཁͳͦΕҎ֎ͷݕ౼߲໨  ܇࿅ɾධՁσʔλɿจݙ͔Βऩूɺ౳Ձू߹ͷੜ੒  σʔλͷදݱํ๏ɿςΩετܗࣜɺτʔΫφΠζɺߏ଄Խ  Ϟσϧͱֶशํ๏ɿXPSEWFDɺTFRTFRɺରরֶशʢDPOTUSBTUJWF
    MFBSOJOHʣ  ධՁํ๏ɺԼྲྀλεΫɺԠ༻ઌ ਺ࣜͷҙຯΛද͢਺ࣜදݱֶश 10
12. ʮ਺ࣜͷҙຯʯΛϕΫτϧͰ࣋ͨͤΔํ๏͸ɺओʹ̏؍఺͋Δɻ  पลςΩετ͔ΒͳΔจ຺ [Krstovski&Blei, arXiv, 2018]  ୅਺త౳Ձͳ਺ࣜϖΞ [Gangwar&Kani, TMLR, 2023]
    
     ೖग़ྗͷ਺஋తৼΔ෣͍ [Meidani+, ICLR, 2024] ਺ࣜຒΊࠐΈʹඞཁͳͦΕҎ֎ͷݕ౼߲໨  ܇࿅ɾධՁσʔλɿจݙ͔Βऩूɺ౳Ձू߹ͷੜ੒  σʔλͷදݱํ๏ɿςΩετܗࣜɺτʔΫφΠζɺߏ଄Խ  Ϟσϧͱֶशํ๏ɿXPSEWFDɺTFRTFRɺରরֶशʢDPOTUSBTUJWF
    MFBSOJOHʣ  ධՁํ๏ɺԼྲྀλεΫɺԠ༻ઌ ਺ࣜͷҙຯΛද͢਺ࣜදݱֶश 11
13. ؍఺̍ɿपลςΩετ͔ΒͳΔจ຺ [Krstovski&Blei, arXiv, 2018] • &RVBUJPO
    FNCFEEJOH
    &R&NC ɿ਺ࣜΛ୯ޠͱΈͳͯ͠ɺ पล୯ޠͷ෼෍͔ΒຒΊࠐΈΛֶशɻ • &RVBUJPO
    VOJU
    FNCFEEJOH
    &R&NC6 ɿ਺ࣜΛߏ੒͢ΔϢχοτ ʢԋࢉࢠͱඃԋࢉࢠʣΛ୯ޠͱͨ͠ &R&NCɻ Ϣχοτʹ෼ׂͨ͠਺ࣜ [Krstovski&Blei, arXiv, 2018] 12
14. • BS9JW
    ͷ࿦จʢ/-1
    *3
    "*
    .-
    ͷ෼໺ʣ͔Βऩूͨ͠୯ޠͱ਺ࣜɻ • ୯ޠɿ/-5,
    <#JSE
    > Λ༻͍֤ͯ࿦จ͔Β໊ࢺ۟ͱܗ༰ࢺΛநग़͔ͯ͠Βɺ ετοϓϫʔυͷ࡟আ΍ώϡʔϦεςΟΫεॲཧʹΑͬͯબ୒ɻ • ਺ࣜɿσΟεϓϨΠ਺ࣜɻ୯Ұม਺͕ଟ͍ΠϯϥΠϯ਺ࣜ͸ෆ࢖༻ɻ &R&NC
    ͷߏஙʹ༻͍Δσʔλͱදݱํ๏ [Krstovski&Blei, arXiv, 2018] 13
15. ਺ࣜΛߏ੒͢ΔϢχοτͷ࡞੒ • ਺ࣜͷߏ੒ཁૉ͸ԋࢉࢠͱඃԋࢉࢠɻ • ਺ࣜΛ 4ZNCPM
    MBZPVU
    USFF
    4-5
    දݱ <;BOJCCJ
    4*(*3
    > ʹม׵ɻ [Krstovski&Blei, arXiv, 2018] 14
16. • #FSOPVMMJ
    FNCFEEJOHT <3VEPMQI
    /*14
    > Λ࠾༻ɻ 𝑝 𝑤! 𝑤"! = 𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 𝑏# = 𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 𝜎 𝜌#! $ / %&' |"!| 𝛼#" 𝑝 𝑤! 𝑤"! : probability of a word 𝑤! given its context 𝑤"! 𝜎: logistic function; 𝜌#! : embedding of 𝑤! ; 𝛼#" : embedding of context word 𝑤$ • ୯ޠຒΊࠐΈɿ𝑏# = 𝜎 𝜌#! $ ∑ %&' |"!| 𝛼#" + ∑ )&' |"! #| 𝛼*$ 𝛼%#  any equations that appear in a possibly larger window ( 𝑐! & = 16 > 𝑐! = 4) • ਺ࣜຒΊࠐΈɿ𝑏* = 𝜎 𝜌*% $ ∑ +&' |"%| 𝛼#& • ໨తؔ਺ɿ 𝐿 𝜌,, 𝛼#, 𝜌*, 𝛼* = ∑!&' , log(𝑝 𝑤!|𝑤"! ) + ∑-&' . log(𝑝 𝑒-|𝑒"% ) &R&NC
    ͷֶशํ๏ [Krstovski&Blei, arXiv, 2018] 15
17. • &R&NC
    ಉ༷ɺ#FSOPVMMJ FNCFEEJOHT
    Λ࠾༻ɻ 𝑝 𝑤! 𝑤"! = 𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 𝑏# = 𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 𝜎 𝜌#! $ / %&' |"!| 𝛼#" 𝑝 𝑤! 𝑤"! : probability of a word 𝑤! given its context 𝑤"! 𝜎: logistic function; 𝜌#! : embedding of 𝑤! ; 𝛼#" : embedding of context word 𝑤$ • ୯ޠຒΊࠐΈɿ𝑏# = 𝜎 𝜌#! $ ∑ %&' |"!| 𝛼#" + ∑ )&' |"! #| ∑ +&' |*$'() | 𝛼/$& 𝛼%#  any equations that appear in a possibly larger window ( 𝑐! & = 16 > 𝑐! = 4) • ਺ࣜϢχοτຒΊࠐΈɿ𝑏/ = 𝜎 𝜌/! $ ∑ +&' |"& *| 𝛼/& ਺ࣜຒΊࠐΈɿ𝜌* = ' |*'()| ∑ %&' |*'()| 𝜌/" • ໨తؔ਺ɿ 𝐿 𝜌,, 𝛼#, 𝜌/, 𝛼/ = ∑!&' , log(𝑝 𝑤!|𝑤"! ) + ∑!&' 0 log(𝑝 𝑢!|𝑢"! ) ˞਺ࣜຒΊࠐΈʹ͍ͭͯɺ&R&NC
    ͸पล୯ޠɺ&R&NC6
    ͸਺ࣜͷΈΛ࢖༻ɻ &R&NC6
    ͷֶशํ๏ [Krstovski&Blei, arXiv, 2018] 16
18. • ݕূɾςετσʔλʹର͢Δର਺໬౓Λൺֱɻ • ఏҊϞσϧ͸͍ͣΕ΋ैདྷϞσϧΛ্ճΓɺ&R&NC6
    ͕࠷ߴੑೳɻ &R&NC ͱ &R&NC6
    ͷධՁ [Krstovski&Blei, arXiv, 2018] 17
19. • ਺ࣜ·ͨ͸୯ޠΛΫΤϦͱͨ͠ݕࡧ &R&NC ͱ &R&NC6
    ͷԠ༻ [Krstovski&Blei, arXiv, 2018] 18
20. ʮ਺ࣜͷҙຯʯΛϕΫτϧͰ࣋ͨͤΔํ๏͸ɺओʹ̏؍఺͋Δɻ  पลςΩετ͔ΒͳΔจ຺ [Krstovski&Blei, arXiv, 2018]  ୅਺త౳Ձͳ਺ࣜϖΞ [Gangwar&Kani, TMLR, 2023]
    
     ೖग़ྗͷ਺஋తৼΔ෣͍ [Meidani+, ICLR, 2024] ਺ࣜຒΊࠐΈʹඞཁͳͦΕҎ֎ͷݕ౼߲໨  ܇࿅ɾධՁσʔλɿจݙ͔Βऩूɺ౳Ձू߹ͷੜ੒  σʔλͷදݱํ๏ɿςΩετܗࣜɺτʔΫφΠζɺߏ଄Խ  Ϟσϧͱֶशํ๏ɿXPSEWFDɺTFRTFRɺରরֶशʢDPOTUSBTUJWF
    MFBSOJOHʣ  ධՁํ๏ɺԼྲྀλεΫɺԠ༻ઌ ਺ࣜͷҙຯΛද͢਺ࣜදݱֶश 19
21. • ݟͨ໨͕ҟͳΔ͕୅਺తʹ౳ՁͳࣜΛ͚ۙͮΔຒΊࠐΈΛ֫ಘɻ • 4&.&.#ɿ 4FR4FR
    Ͱ౳Ձࣜੜ੒Λֶश͠ɺ Τϯίʔμ࠷ऴ૚ͷ NBYQPPM
    ΛࣜϕΫτϧͱͯ͠ར༻ɻ ؍఺̎ɿ୅਺త౳Ձͳ਺ࣜϖΞ
    <(BOHXBS,BOJ
    5.-3
    > 20
22. • &RVJWBMFOU
    &YQSFTTJPOT
    %BUBTFUɿ໿ສϖΞͷݟͨ໨͕ҟͳΔ ౳ՁͳࣜΛ 4ZN1Z ͷؔ਺Λར༻ͯ͠ੜ੒ʢ̍ม਺ɺ࠷େԋࢉࢠʣɻ 4&.&.#
    ͷߏஙʹ༻͍Δσʔλ [Gangwar&Kani, TMLR, 2023] 21
23. • લஔʢ1PMJTIʣه๏ʢԋࢉࢠΛલʹஔ͘ʣͰԋࢉࢠ໦Λྻʹม׵ɻ ྫɿ-./(1) 34-(1) ˠ
    <EJW
    TJO
    Y
    DPT
    Y> • ೖྗ͸ POFIPU
    FODPEJOH
    ˠ
    ຒΊࠐΈ૚ ˠ ҐஔຒΊࠐΈɻ • ग़ྗੜ੒͸ϏʔϜ୳ࡧɻ 4&.&.#
    ͷߏஙʹ༻͍Δσʔλͱදݱํ๏ [Gangwar&Kani, TMLR, 2023] 22
24. • Ϟσϧ͸ 5SBOTGPSNFSɻ • 
    FODPEFS
    MBZFST • 
    EFDPEFS
    MBZFST • 
    BUUFOUJPO
    IFBET • 3F-6 BDUJWBUJPO
    
    ESPQPVU • .PEFM
    EJNFOTJPO
    
    PS
     • ֶश໨ඪɿೖྗࣜͱ਺ֶతʹ౳ՁͳࣜΛσίʔυͰ͖ΔΑ͏ʹ܇࿅ ʢ౳Ձͳ਺ࣜ͸̍ͭʹݶΒͳ͍ͨΊɺݕূ࣌͸ 4ZNQZ Ͱ൑ఆʣɻ • 4&.&.#
    ͷൺֱख๏ͱͯ͠ɺΦʔτΤϯίʔμͷΑ͏ʹ ೖྗΛ࠶ߏ੒͢ΔϞσϧ 4536$5&.#
    ΋ֶशɻ 4&.&.#
    ͷֶशํ๏ [Gangwar&Kani, TMLR, 2023] 23
25. • 1$"
    Ͱ࣍ݩʹϓϩοτɻ4&.&.#
    ͸ΧςΰϦ෼཭͕໌ྎɻ 4&.&.# ͷධՁ̍ɿ࣍ݩϓϩοτͷఆੑతධՁ [Gangwar&Kani, TMLR, 2023] 24
26. • ྨࣅ౓ΛίαΠϯڑ཭ͷٯ਺ʢ1/(1 − (𝑐𝑜𝑠𝑖𝑛𝑒 𝑠𝑖𝑚𝑖𝑙𝑎𝑟𝑖𝑡𝑦))ʣͰఆٛɻ • 4536$56&.#
    ΑΓ΋ 4&.&.#
    ͸ߏ଄͕ྨࣅͨ͠਺ࣜΛग़ྗɻ 4&.&.# ͷධՁ̎ɿ਺ࣜݕࡧ [Gangwar&Kani, TMLR, 2023] 25
27. 4&.&.# ͷධՁ̏ɿΞφϩδʔ • l𝑥' JT
    UP
    𝑦' BT
    𝑥1 JT
    UP
    𝑦1 zʹ ౰ͯ͸·Δ 𝑥1 Λ࣍ࣜͰ༧ଌɻ 𝑥' = 𝑒𝑚𝑏 𝑥( − 𝑒𝑚𝑏 𝑦( + 𝑒𝑚𝑏(𝑦') • 4536$5&.#
    ΑΓ΋ 4&.&.#
    ͷํ͕ߴਖ਼ղ཰ɻ • Ξφϩδʔͷਖ਼ޡ൑ఆ͸೉ͦ͠͏ɻ ྫɿ𝑥! = 𝑥"
    𝑦! = 𝑥
    𝑦" = log 𝑥 ͸ ޡΓͰ͸ͳ͍ͷͰ͸ʁ [Gangwar&Kani, TMLR, 2023] 26
28. ʮ਺ࣜͷҙຯʯΛϕΫτϧͰ࣋ͨͤΔํ๏͸ɺओʹ̏؍఺͋Δɻ  पลςΩετ͔ΒͳΔจ຺ [Krstovski&Blei, arXiv, 2018]  ୅਺త౳Ձͳ਺ࣜϖΞ [Gangwar&Kani, TMLR, 2023]
    
     ೖग़ྗͷ਺஋తৼΔ෣͍ [Meidani+, ICLR, 2024] ਺ࣜຒΊࠐΈʹඞཁͳͦΕҎ֎ͷݕ౼߲໨  ܇࿅ɾධՁσʔλɿจݙ͔Βऩूɺ౳Ձू߹ͷੜ੒  σʔλͷදݱํ๏ɿςΩετܗࣜɺτʔΫφΠζɺߏ଄Խ  Ϟσϧͱֶशํ๏ɿXPSEWFDɺTFRTFRɺରরֶशʢDPOTUSBTUJWF
    MFBSOJOHʣ  ධՁํ๏ɺԼྲྀλεΫɺԠ༻ઌ ਺ࣜͷҙຯΛද͢਺ࣜදݱֶश 27
29. • 4/*1
    4ZNCPMJD/VNFSJD
    *OUFHSBUFE
    1SFUSBJOJOH
    NPEFM 
    ਺ࣜʢTZNCPMJDʣͱ਺஋σʔλʢOVNFSJDʣͷ֤ϞμϦςΟΛຒΊࠐΈɺ ରরֶशͰରԠ෇͚Δ͜ͱͰɺৼΔ෣͍ʹجͮ͘ҙຯΛଊ͑Δɻ ؍఺̏ɿೖग़ྗͷ਺஋తৼΔ෣͍
    <.FJEBOJ
    *$-3
    > 28
30. • ࣄલֶश༻ɿҎԼͷखॱͰ໿ ສϖΞੜ੒ɻ  ԋࢉࢠ໦͔Βࣜ
    𝑓 Λ߹੒ʢ࢛ଇɾࡾ֯ɾࢦ਺ɾର਺ͳͲʣɻ  ࢦఆͨ͠ఆٛҬ͔Βαϯϓϧͨ͠ 𝑥
    ʹରͯ͠ 𝑦 = 𝑓(𝑥) Λܭࢉ͠ɺ਺஋ྻΛੜ੒ɻ  σʔλͷඪ४Խɺ
    ఆٛҬ֎΍ۃ୺ͳ஋Λ࣋ͭ 𝑦 ͷআ֎ɾ࠶ੜ੒ɻ  ಉ͡ 𝑓 ͷʢ਺ࣜɼ਺஋ྻʣͷ૊Λਖ਼ྫɺଞͷ 𝑓 ͱͷ૊Λෛྫͱͯ͠αϯϓϧ࡞੒ɻ • ϑΝΠϯνϡʔχϯά༻ɿԼྲྀλεΫ͝ͱʹ࡞੒ɻ " $SPTTNPEBM
    1SPQFSUZ
    1SFEJDUJPOʢֶश
     ɺධՁ
     
    αϯϓϧʣ • ೖྗɿ਺ࣜͱ਺஋σʔλɺग़ྗɿ਺஋తੑ࣭ʢྫɿ/PO$POWFYJUZ
    3BUJP
    /$3 ʣ /$3
    ͷग़ྗ͸ತੑͷఔ౓ʢ׬શʹತ
    ׬શʹԜʣ # 4ZNCPMJD
    3FHSFTTJPO
    43#FODI <-B
    $BWB
    /FVS*14
    > Λ࠾༻ • ೖྗɿ਺஋σʔλɺग़ྗɿ਺ࣜ 4/*1
    ͷߏஙʹ༻͍Δσʔλ 29
31. • ਺ࣜɿલஔʢ1PMJTIʣه๏ͰτʔΫϯྻԽɻ
    
    • ਺஋ྻɿ(𝑥, 𝑦) Λ਺஋σʔλͱͯ͠ೖྗʢ௕͞ɾॱংΛࣄલʹ౷Ұʣɻ • ఆ਺ɿ base-10 floating-point notation [Charton, arXiv, 2022; Kamienny+, NeurIPS, 2022] • ਺஋จࣈྻΛ༗ݶޠኮͰѻ͍ɺεέʔϧʹؤ݈ʹɻ • نଇɿ
    TJHO
    NBOUJTTB
    FYQPOFOU
    ͷτʔΫϯ΁෼ղɻ
    
    • ྫɿ
    ˠ
    <
    
    &>ɼ
    ˠ
    <
    
    &> • ਺ࣜɾ਺஋ྻதͷఆ਺Λ͍ͣΕ΋τʔΫϯ΁෼ղɻ 4/*1
    ͷߏஙʹ༻͍Δσʔλͷදݱํ๏ 30
32. • ਺ࣜɾ਺஋ྻΤϯίʔμɿ5SBOTGPSNFS
    ϕʔεͷΞʔΩςΫνϟ • ࣄલֶश໨ඪɿ $-*1
    ܕରরֶशɻ • ϑΝΠϯνϡʔχϯά໨ඪɿ ԼྲྀλεΫ͝ͱʹઃఆɻ 4/*1
    ͷֶशํ๏ [Meidani+, ICLR, 2024] 31
33. 4/*1
    ͷϑΝΠϯνϡʔχϯάɿ4ZNCPMJD
    3FHSFTTJPO [Meidani+, ICLR, 2024] 32
34. 4/*1
    ͷධՁɿϑΝΠϯνϡʔχϯάલޙͷຒΊࠐΈ [Meidani+, ICLR, 2024] 33
35. 4/*1
    ͷධՁɿ਺ࣜຒΊࠐΈͷ U4/&
    ϓϩοτ [Meidani+, ICLR, 2024] 34
36. ʮ਺ࣜͷҙຯʯΛϕΫτϧͰ࣋ͨͤΔํ๏͸ɺओʹ̏؍఺͋Δɻ  पลςΩετ͔ΒͳΔจ຺ [Krstovski&Blei, arXiv, 2018]  ୅਺త౳Ձͳ਺ࣜϖΞ [Gangwar&Kani, TMLR, 2023]
    
     ೖग़ྗͷ਺஋తৼΔ෣͍ [Meidani+, ICLR, 2024] ਺ࣜຒΊࠐΈʹඞཁͳͦΕҎ֎ͷݕ౼߲໨  ܇࿅ɾධՁσʔλɿจݙ͔Βऩूɺ౳Ձू߹ͷੜ੒  σʔλͷදݱํ๏ɿςΩετܗࣜɺτʔΫφΠζɺߏ଄Խ  Ϟσϧͱֶशํ๏ɿXPSEWFDɺTFRTFRɺରরֶशʢDPOTUSBTUJWF
    MFBSOJOHʣ  ධՁํ๏ɺԼྲྀλεΫɺԠ༻ઌ ਺ࣜͷҙຯΛද͢਺ࣜදݱֶश 35
37. ෺ཧϞσϧߏஙͷࣗಈԽɾࣗ཯Խʹ͓͚Δදݱֶश ݱ࣮ͷڍಈΛද͢ Պֶ๏ଇʹجͮ͘ ਺ࣜ܈ ෺ཧϞσϧ ୈҰݪཧϞσϧ モデル候補の 作成と検証 情報の 抽出と統合 対象プロセス 関連文献の収集 Ϟσϧߏஙʹඞཁͳ৘ใ ͷࣗಈநग़ɺಉٛੑ൑ఆɺ දه౷Ұ ʁ Ϟσϧީิͷ ࣗಈ࡞੒ɾݕূ 1/# ln ' O ࿈ଓ૧ܕ൓Ԡث จݙσʔλϕʔε͔Β ର৅ϓϩηεؔ࿈จݙ Λࣗಈऩूɺܗࣜ౷Ұ ๲େͳ࡞ۀͱߴ౓ͳ஌ࣝͱεΩϧ ࣌ؒΛ͔͚ͨࢼߦࡨޡ ैདྷख๏ɿख࡞ۀ "VUP1.P#ɿ"*ʹΑΔࣗಈԽ ߏங ߏங Ϟσϧީิ̍ Ϟσϧީิ̎ Ϟσϧީิ̏ 記号 定義 ! 温度 "! ⼊⼝流量 ⁝ ⁝ #" 反応速度 記号 定義 ! 温度 "! ⼊⼝流量 ⁝ ⁝ #" 反応速度 d" d# = %! − % ︙ ' = '! exp(− , -. ) −0" = '1" d1" d# = % " 1"! − 1" + 0" ֧፩ػ ݪྉ ੡඼ จݙ৘ใ͔Βͷ෺ཧϞσϧࣗಈߏங จݙ͔Β෺ཧϞσϧΛࣗಈߏங͢Δ࿮૊Έ ΛఏҊ͠ɺཁૉٕज़Λ։ൃ͍ͯ͠Δɻ [Kato&Kano, Comput. Aided. Chem. Eng., 2022] ෺ཧϞσϦϯάͷࣗ཯Խ ਺஋σʔλ͔Βͷ෺ཧϞσϧ֫ಘɺ ෺ཧϞσϧͷධՁɺධՁ݁Ռʹجͮ͘ ࣮ݧઃܭΛࣗಈͰ࣮ߦ͢ΔγεςϜͷ ࣮ݱΛ໨ࢦ͍ͯ͠Δɻ ࣮ݧσʔλ ෺ཧϞσϧ ! = #(%) 
    ࣮ݧઃܭ ࣮ݧύϥϝʔλ ੑೳ  Ϟσϧߏங ࣌ؒ ೱ౓ 
    ϞσϧධՁ ࣌ؒ ೱ౓ ๬·͍͠ ڍಈ ධՁ݁Ռ ఺਺
     36
38. • Elsevier ͕ࣾൃߦ͢ΔԽֶ޻ֶؔ࿈จݙΛ༻͍ͯ#&35ϞσϧΛࣄલֶशɻ • จݙ͔Βͷม਺΍਺ࣜͷநग़ɺநग़ͨ͠৘ใͷಉٛੑ൑ఆʹར༻ɻ • ਺ࣜ͸ XML ܗࣜɻ લॲཧʹ͓͍ͯλάΛ࡟আɻ • ޙͷݕ౼Ͱम০ه߸ͷ৘ใΛ อ͕࣋ͨ͠ɺλεΫͷੑೳ͸ มΘΒͣɻ
    [ுΒ, NLP, 2023] υϝΠϯಛԽݴޠϞσϧʹదͨ͠දݱɾલॲཧ͸Կ͔ʁ 37 ࣄલֶशʹར༻ ʜ ChemECorpus ࿦จ133,319 ใ, 6.8ԯ୯ޠ Fine-tuned ProcessBERT ԼྲྀλεΫʹԠͯ͡fine-tune ProcessBERT BERTʹ௥Ճࣄલֶश Fine-tune [Kato+, IFAC-PapersOnLine, 2022] <mml:math> <mml:msub> <mml:mi>v</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> 𝑣8 in XML format “v”,“##n” ޙͷݕ౼ʹ͓͚Δલॲཧޙͷ𝑣) [VAR],“v”,[SUB],[VAR],“n”
39. • ෳ਺ͷจݙ͔Βநग़ͨ͠਺ࣜΛ૊Έ߹Θͤͯ෺ཧϞσϧΛߏங͢Δ໰୊ΛఆࣜԽɻ • શ਺ࣜͷ૊߹ͤ୳ࡧΛαϒγεςϜ͝ͱͷখن໛୳ࡧʹ෼ղ͠ɺ αϒγεςϜ͝ͱʹ෺ཧϞσϧΛߏங͔ͯ͠Β౷߹͢Δɻ ʢαϒγεςϜɿ෺࣭ऩࢧɺΤωϧΪʔऩࢧͱ͍ͬͨҟͳΔ؍఺ʹجͮ͘෼ׂʣ • ਺ࣜΛϊʔυɺม਺ڞ༗ؔ܎ΛΤοδͱ͢ΔάϥϑΛ༻͍ͯϞσϧΛදݱ͢Δɻ ෺ཧϞσϧߏஙʹ͓͚Δ༗༻ͳදݱ͸Կ͔ʁ ... ਺ࣜू߹ <latexit sha1_base64="oKTEt7sVC588BEaFHyUp5iMPcWI=">AAACDXicbVDLSsNAFJ34rPUVHzs3g0VwVRKR6kaoduOygn1AG8JkOmmHzkzCzESoId/gL7jVvTtx6ze49UuctFlo64ELh3Pu5R5OEDOqtON8WUvLK6tr66WN8ubW9s6uvbffVlEiMWnhiEWyGyBFGBWkpalmpBtLgnjASCcYN3K/80CkopG415OYeBwNBQ0pRtpIvn0o4RUcw4af9jnSI8nT6yzz7YpTdaaAi8QtSAUUaPr2d38Q4YQToTFDSvVcJ9ZeiqSmmJGs3E8UiREeoyHpGSoQJ8pLp+kzeGKUAQwjaUZoOFV/X6SIKzXhgdnMI6p5Lxf/9QI+91mHl15KRZxoIvDscZgwqCOYVwMHVBKs2cQQhCU12SEeIYmwNgWWTSnufAWLpH1WdWvV2t15pX5T1FMCR+AYnAIXXIA6uAVN0AIYPIJn8AJerSfrzXq3PmarS1ZxcwD+wPr8ATZpm1Y=</latexit> r = kCA <latexit sha1_base64="O8fJ+uz/JxW437W6TFONwOpZgfI=">AAAB+3icbVDLSgNBEOyNrxhfUY9eBoPgKeyKRI9BETxGMA9IljA7mU2GzMwuM71CCPkFr3r3Jl79GK9+ibvJHjSxoKGo6qaaCmIpLLrul1NYW9/Y3Cpul3Z29/YPyodHLRslhvEmi2RkOgG1XArNmyhQ8k5sOFWB5O1gfJv57SdurIj0I05i7is61CIUjGIm3fW9Ur9ccavuHGSVeDmpQI5Gv/zdG0QsUVwjk9TarufG6E+pQcEkn5V6ieUxZWM65N2Uaqq49afzX2fkLFUGJIxMOhrJXP19MaXK2okK0k1FcWSXvUz81wvUUjKG1/5U6DhBrtkiOEwkwYhkRZCBMJyhnKSEMiPS3wkbUUMZpnVlpXjLFayS1kXVq1VrD5eV+k1eTxFO4BTOwYMrqMM9NKAJDEbwDC/w6sycN+fd+VisFpz85hj+wPn8ATU9lDI=</latexit> E1 <latexit sha1_base64="p/2NAPM7dHKtxnpFZmSpJ0yNovA=">AAACD3icbVDLSsNAFJ3UV62vqODGzWARXJWkSHUjVLtxWcE+wMYwmU7aoTOTMDMRSsxH+Atude9O3PoJbv0Sp20W2nrgwuGce7mHE8SMKu04X1ZhaXllda24XtrY3NresXf32ipKJCYtHLFIdgOkCKOCtDTVjHRjSRAPGOkEo8bE7zwQqWgkbvU4Jh5HA0FDipE2km8fSHgBR7Dhpz2O9FDy9DLL7qu+XXYqzhRwkbg5KYMcTd/+7vUjnHAiNGZIqTvXibWXIqkpZiQr9RJFYoRHaEDuDBWIE+Wl0/wZPDZKH4aRNCM0nKq/L1LElRrzwGxOQqp5byL+6wV87rMOz72UijjRRODZ4zBhUEdwUg7sU0mwZmNDEJbUZId4iCTC2lRYMqW48xUskna14tYqtZvTcv0qr6cIDsEROAEuOAN1cA2aoAUweATP4AW8Wk/Wm/VufcxWC1Z+sw/+wPr8AXLum/o=</latexit> r = kC2 A <latexit sha1_base64="yJB16PPF/imRXb1zOPVEoXu0dSI=">AAAB+nicbVDLSgMxFL1TX7W+qi7dBIvgqswUaV0WRXBZ0T6gHUomzbShSWZIMkIZ+wlude9O3Pozbv0S03YW2nrgwuGcezmXE8ScaeO6X05ubX1jcyu/XdjZ3ds/KB4etXSUKEKbJOKR6gRYU84kbRpmOO3EimIRcNoOxtczv/1IlWaRfDCTmPoCDyULGcHGSvc3/Uq/WHLL7hxolXgZKUGGRr/43RtEJBFUGsKx1l3PjY2fYmUY4XRa6CWaxpiM8ZB2LZVYUO2n81en6MwqAxRGyo40aK7+vkix0HoiArspsBnpZW8m/usFYinZhJd+ymScGCrJIjhMODIRmvWABkxRYvjEEkwUs78jMsIKE2PbKthSvOUKVkmrUvaq5erdRal+ldWThxM4hXPwoAZ1uIUGNIHAEJ7hBV6dJ+fNeXc+Fqs5J7s5hj9wPn8AATyUHw==</latexit> E2 <latexit sha1_base64="hI9IbGDfZbCoq0DaaLgq2Ft0WIM=">AAACC3icbVDLSsNAFJ3UV62vWJduBovgqiQi1Y1QFIrLCvYBbQiT6aQdOjMJMxOxhHyCv+BW9+7ErR/h1i9x0mah1QMXDufcyz2cIGZUacf5tEorq2vrG+XNytb2zu6evV/tqiiRmHRwxCLZD5AijArS0VQz0o8lQTxgpBdMr3O/d0+kopG407OYeByNBQ0pRtpIvl1twUvY8tMhR3oieUqzzLdrTt2ZA/4lbkFqoEDbt7+GowgnnAiNGVJq4Dqx9lIkNcWMZJVhokiM8BSNycBQgThRXjrPnsFjo4xgGEkzQsO5+vMiRVypGQ/MZh5RLXu5+K8X8KXPOrzwUiriRBOBF4/DhEEdwbwYOKKSYM1mhiAsqckO8QRJhLWpr2JKcZcr+Eu6p3W3UW/cntWaV0U9ZXAIjsAJcME5aIIb0AYdgMEDeALP4MV6tF6tN+t9sVqyipsD8AvWxzcCppq2</latexit> F = Fi <latexit sha1_base64="2Yy0sun5KFQq+BtUsW4F90h7aKU=">AAAB+nicbVDLSgMxFL1TX7W+qi7dBIvgqsxoqS6LIrisaB/QDiWTZtrQJDMkGaGM/QS3uncnbv0Zt36JaTsLbT1w4XDOvZzLCWLOtHHdLye3srq2vpHfLGxt7+zuFfcPmjpKFKENEvFItQOsKWeSNgwznLZjRbEIOG0Fo+up33qkSrNIPphxTH2BB5KFjGBjpfub3nmvWHLL7gxomXgZKUGGeq/43e1HJBFUGsKx1h3PjY2fYmUY4XRS6CaaxpiM8IB2LJVYUO2ns1cn6MQqfRRGyo40aKb+vkix0HosArspsBnqRW8q/usFYiHZhJd+ymScGCrJPDhMODIRmvaA+kxRYvjYEkwUs78jMsQKE2PbKthSvMUKlknzrOxVy9W7Sql2ldWThyM4hlPw4AJqcAt1aACBATzDC7w6T86b8+58zFdzTnZzCH/gfP4AAtCUIA==</latexit> E3 +BDDBSEྨࣅ౓ʹ جͮ͘਺ࣜάϥϑ <latexit sha1_base64="O8fJ+uz/JxW437W6TFONwOpZgfI=">AAAB+3icbVDLSgNBEOyNrxhfUY9eBoPgKeyKRI9BETxGMA9IljA7mU2GzMwuM71CCPkFr3r3Jl79GK9+ibvJHjSxoKGo6qaaCmIpLLrul1NYW9/Y3Cpul3Z29/YPyodHLRslhvEmi2RkOgG1XArNmyhQ8k5sOFWB5O1gfJv57SdurIj0I05i7is61CIUjGIm3fW9Ur9ccavuHGSVeDmpQI5Gv/zdG0QsUVwjk9TarufG6E+pQcEkn5V6ieUxZWM65N2Uaqq49afzX2fkLFUGJIxMOhrJXP19MaXK2okK0k1FcWSXvUz81wvUUjKG1/5U6DhBrtkiOEwkwYhkRZCBMJyhnKSEMiPS3wkbUUMZpnVlpXjLFayS1kXVq1VrD5eV+k1eTxFO4BTOwYMrqMM9NKAJDEbwDC/w6sycN+fd+VisFpz85hj+wPn8ATU9lDI=</latexit> E1 <latexit sha1_base64="yJB16PPF/imRXb1zOPVEoXu0dSI=">AAAB+nicbVDLSgMxFL1TX7W+qi7dBIvgqswUaV0WRXBZ0T6gHUomzbShSWZIMkIZ+wlude9O3Pozbv0S03YW2nrgwuGcezmXE8ScaeO6X05ubX1jcyu/XdjZ3ds/KB4etXSUKEKbJOKR6gRYU84kbRpmOO3EimIRcNoOxtczv/1IlWaRfDCTmPoCDyULGcHGSvc3/Uq/WHLL7hxolXgZKUGGRr/43RtEJBFUGsKx1l3PjY2fYmUY4XRa6CWaxpiM8ZB2LZVYUO2n81en6MwqAxRGyo40aK7+vkix0HoiArspsBnpZW8m/usFYinZhJd+ymScGCrJIjhMODIRmvWABkxRYvjEEkwUs78jMsIKE2PbKthSvOUKVkmrUvaq5erdRal+ldWThxM4hXPwoAZ1uIUGNIHAEJ7hBV6dJ+fNeXc+Fqs5J7s5hj9wPn8AATyUHw==</latexit> E2 <latexit sha1_base64="2Yy0sun5KFQq+BtUsW4F90h7aKU=">AAAB+nicbVDLSgMxFL1TX7W+qi7dBIvgqsxoqS6LIrisaB/QDiWTZtrQJDMkGaGM/QS3uncnbv0Zt36JaTsLbT1w4XDOvZzLCWLOtHHdLye3srq2vpHfLGxt7+zuFfcPmjpKFKENEvFItQOsKWeSNgwznLZjRbEIOG0Fo+up33qkSrNIPphxTH2BB5KFjGBjpfub3nmvWHLL7gxomXgZKUGGeq/43e1HJBFUGsKx1h3PjY2fYmUY4XRS6CaaxpiM8IB2LJVYUO2ns1cn6MQqfRRGyo40aKb+vkix0HosArspsBnqRW8q/usFYiHZhJd+ymScGCrJPDhMODIRmvaA+kxRYvjYEkwUs78jMsQKE2PbKthSvMUKlknzrOxVy9W7Sql2ldWThyM4hlPw4AJqcAt1aACBATzDC7w6T86b8+58zFdzTnZzCH/gfP4AAtCUIA==</latexit> E3 Ϋϥελ෼ׂޙͷ ਺ࣜάϥϑ Ϋϥελ   ֤Ϋϥελͷ Ϟσϧީิ Ϋϥελͷ Ϟσϧީิ Ϋϥελͷ Ϟσϧީิ Ϋϥελͷ Ϟσϧީิ ࠷ऴ Ϟσϧީิ 38 [Kato&Kano, CACE, 2025, Kato&Kano, ESCAPE, 2026]
40. • ෳ਺ཁૉͷ଍͠߹Θͤ΍ҟͳΔϓϩηεͷ஌ࣝసҠʹΑΔϞσϧൃݟ ల๬ʛ޻ֶʢϞσϦϯάʣʹ͓͚Δ਺ࣜදݱֶशͷԠ༻ 1 2 3 ੡଄ϓϩηε"
    ʢྫɿ੡ༀϓϩηεʣ ೤ͷ ӨڹΛ௥Ճ ୯७ͳϞσϧ ؀ڥมԽͷ ӨڹΛ௥Ճ ? Ճ೤ͱ؀ڥมԽͷ ӨڹΛ௥Ճ ੡଄ϓϩηε#ʢྫɿόΠΦϓϩηεʣ 1 ? 3 ೤ͷ ӨڹΛ௥Ճ ୯७ͳϞσϧ 39
41. * ʮ਺ࣜͷҙຯʯΛϕΫτϧͰ࣋ͨͤΔ̏ͭͷํ๏Λઆ໌ɻ  पลςΩετ͔ΒͳΔจ຺ [Krstovski&Blei, arXiv, 2018]  ୅਺త౳Ձͳ਺ࣜϖΞ [Gangwar&Kani, TMLR, 2023]
    
     ೖग़ྗͷ਺஋తৼΔ෣͍ [Meidani+, ICLR, 2024] ্هͷΑ͏ʹ·ͱΊ͕ͨɺάϥϑߏ଄Λར༻ͨ͠ݚڀͳͲ΋͋Δɻ ** ෺ཧϞσϧߏஙʹ༗༻ͳදݱΛٞ࿦ɻ  υϝΠϯಛԽݴޠϞσϧʹదͨ͠දݱɾલॲཧ͸Կ͔ʁ [Kato+,IFAC-PapersOnLine,2022]  ෺ཧϞσϧߏஙʹ͓͚Δ༗༻ͳදݱ͸Կ͔ʁ [Kato&Kano, CACE, 2025, Kato&Kano, ESCAPE, 2026] • ޻ֶͰͷطଘݚڀɾԠ༻ల๬Λ঺հ͕ͨ͠ɺ঺հͨ͠ͷ͸Ұ෦ɻ ͨͩɺݱࡏ஍ͱԠ༻ʢଟม਺ͷҙຯɺه߸ͷදه༳Εʹ͸ະରԠʣʹ͸Ϊϟοϓ͕͋Δɻ • ਺ࣜΛ׆༻ͨ͠ݚڀʹڵຯ͕͋ΔํɺҰॹʹٞ࿦͠·͠ΐ͏ɻ ·ͱΊ 40
42. [Kato+., J. Cryst. Growth, 2021] Kato et al., ”Gray-box modeling of 300 mm diameter Czochralski single-crystal Si production process,” J. Cryst. Growth, 553, 125929, 2021. [Zheng+, J. Cryst. Growth, 2018] Zheng et al., “A first-principle model of 300 mm Czochralski single-crystal Si production process for predicting crystal radius and crystal growth rate,” 492, 105–113, 2018. [Valentino+, NAACL, 2024] Valentino, M. et al., “Multi-Operational Mathematical Derivations in Latent Space,” NAACL, 1446– 1458, 2024. [Mansouri+, ICTIR, 2019] Mansouri, B. et al., “Tangent-CFT: An Embedding Model for Mathematical Formulas,” ICTIR, 11–18, 2019. [Krstovski&Blei, arXiv, 2018] Krstovski, K. and Blei, D.M., “Equation Embeddings,” arXiv, 2018. [Gangwar&Kani, TMLR, 2023] Gangwar, N. and Kani, N., “Semantic Representations of Mathematical Expressions in a Continuous Vector Space,” TMLR, 2023. [Meidani+, ICLR, 2024] Meidani, K. et al., “SNIP: Bridging mathematical symbolic and numeric realms with unified pre-training,” ICLR, 2024. [Bird+, 2009] Bird, S., Klein, E., & Loper, E., “Natural Language Processing with Python: Analyzing Text with the Natural Language Toolkit,” O’Reilly Media, Inc., 2009. [Rudolph+, NIPS, 2016] Rudolph, M. et al., “Exponential Family Embeddings,” NIPS, 2016. [Zanibbi+, SIGIR, 2016] Zanibbi, R. et al., “Multi-stage math formula search: Using appearance-based similarity metrics at scale,” SIGIR, 145–154, 2016. 3FGFSFODFT  41
43. [La Cava+, NeurIPS, 2021] La Cava, W. et al., “Contemporary Symbolic Regression Methods and their Relative Performance,” NeurIPS, 2021. [Charton, arXiv, 2022] Charton, F., “Linear algebra with transformers.” arXiv, 2022. [Kamienny+, NeurIPS, 2022] Kamienny, P.-A. et al., “End-to-end Symbolic Regression with Transformers,” NeurIPS, 2022. [Kato&Kano, Comput. Aided Chem. Eng., 2022] Kato, S. and Kano, M., “Towards an automated physical model builder: CSTR case study,” Comput. Aided Chem. Eng., 1669–1674, 2022. [Kato+, IFAC-PapersOnLine, 2022] Kato et al., “ProcessBERT: A pre-trained language model for judging equivalence of variable definitions in process models,” 55 (7), 126299, 2021. [ுΒ, NLP, 2023] ுΒ, “਺ֶతදݱͷߏ଄త৘ใͷτʔΫϯԽख๏ʹΑΔProcessBERT ͷੑೳվળ,” ݴޠॲཧֶձୈ29ճ೥࣍ େձൃද࿦จूɺ2940–2944, 2023. [Kato&Kano, CACE, 2025] Kato and Kano, “Automated physical model building from literature sources: Combining equations based on four predefined requirements,” Comput. Chem. Eng., 200, 109147, 2025. [Kato&Kano, ESCAPE, 2026] Kato and Kano, “Equation-Variable Graph Partitioning for Modular Physical Model Building from Literature,” 2026. 3FGFSFODFT
     42