1XPHULFDOVLPXODWLRQRIGHHSZDWHURLOEORZRXWV'DQLHO&DUGRVR&RUGHLUR኱㜰኱Ꮫᇶ♏ᕤᏛ◊✲⛉㸯㸬,QWURGXFWLRQ ,QWKHODUJHVWRIIVKRUHEORZRXWRIDOOWLPHKDSSHQHGLQWKH*XOIRI0H[LFR
86$7KHDFFLGHQWEHFDPHNQRZQDVWKH'HHSZDWHU+RUL]RQRLOVSLOOLQZKLFKDURXQG
PLOOLRQRLOEDUUHOVZHUHVSLOOHGLQWRWKHRFHDQDQGFKHPLFDOGLVSHUVDQWVZHUHDSSOLHG
LQDODUJHVFDOHLQWRWKHVXEVHDDVDZD\WRWUHDWWKHRLOEORZRXWSOXPH>@ *LYHQWKHSRVVLEOHQHJDWLYHRXWFRPHVWKDWVXEVHDLQMHFWLRQRIFKHPLFDOGLVSHUVDQWVPD\FDXVHWRWKHHQYLURQPHQWLWLVQHFHVVDU\WRDVVHVVFOHDUO\ZKHWKHUWKLVWHFKQLTXH
LVVSHFLILFDOO\DGHTXDWHIRUDFHUWDLQDFFLGHQWVFHQDULREHIRUHLWVDSSOLFDWLRQ+RZHYHU
VLQFHUHDOVFDOHH[SHULPHQWVDUHXQSUDFWLFDOGXHWRWKHLUREYLRXVHQYLURQPHQWDOULVNQXPHULFDO PRGHOV DQG ODERUDWRU\VFDOH H[SHULPHQWV DUH WKH RQO\ DYDLODEOH WRROV WR
LQYHVWLJDWHWKHEORZRXWSKHQRPHQRQ7KHUHIRUHWKHGHYHORSPHQWRIDQDFFXUDWHQXPHULFDOEORZRXWPRGHOZRXOGUHSUHVHQWDYDOXDEOHDVVHWLQWKHGHFLVLRQPDNLQJSURFHVVIRUWKH
UHPHGLDWLRQRIVXFKDFFLGHQWVZLWKFKHPLFDOGLVSHUVDQWV $ QXPEHU RI FKDOOHQJHV VWDQG LQ WKH ZD\ RI DFKLHYLQJ D PRUH H[DFW EORZRXW PRGHO$PRQJWKHPDUHWKHVHQVLWLYLW\RIPRGHOSUHGLFWLRQVWRFRPSOH[FKHPLFDODQGELRORJLFDOSKHQRPHQD WKH QHHG IRU D FRXSOLQJ RI RFHDQ FLUFXODWLRQ PRGHOV ZLWK WKH QHDUILHOGEORZRXWSOXPHG\QDPLFVDQGWKHDFFXUDF\RIWKHRLOJDVGURSOHWVL]HGLVWULEXWLRQ '6' >@3DUWLFXODUO\WKHGURSOHWVL]HGLVWULEXWLRQ '6' UHSUHVHQWVDVHULRXVWKUHDWWRWKH SUHFLVHQHVV RI WKH VSLOOHG RLO SDWK LQVLGH WKH VHD DV D VPDOOYDULDWLRQ LQ WKHGURSOHW GLDPHWHU UHVXOWV LQ D ODUJH GLVFUHSDQF\ LQ WKH GLVWDQFH WKDW WKH RLO FRXOG
WUDYHOERWKODWHUDOO\DQGYHUWLFDOO\LQVLGHWKHRFHDQ7KLVFRXOGLQGXFHWKHUHVSRQVH
WHDPWRFKRRVHXQVXLWDEOHUHPHGLDWLRQWHFKQLTXHVZLWKIXUWKHUGDPDJHWRWKHHQYLURQPHQW ,QWKLVUHVHDUFKZHSURSRVHWKHXVHRID/(6 /DUJH(GG\6LPXODWLRQ IRUWXUEXOHQFH
ZLWKDK\EULG(XOHU(XOHUDQGYROXPHRIIOXLG 92) PRGHOVWRDFFXUDWHO\SUHGLFWWKH
'6'E\FDOFXODWLQJWKHDFWXDOEUHDNXSDQGFRDOHVFHQFHFDXVHGE\WKHDWRPL]DWLRQRIWKHWXUEXOHQWRLOMHWLQWRDTXLHVFHQWZDWHUPHGLD 㸬1XPHULFDOPHWKRGV 7RVLPXODWHWKHRLOEORZRXWSKHQRPHQDDK\EULG(XOHULDQPXOWLIOXLGVROXWLRQIUDPHZRUNZLWKDYROXPHRIIOXLG 92) VKDUSLQWHUIDFHFDSWXULQJDOJRULWKPZDVXVHG,WLPSURYHV
WKHDFFXUDF\RIWKHWUDGLWLRQDO(XOHU(XOHUPHWKRGZLWKRXWWKHFRPSXWDWLRQDOEXUGHQRIFRXSOLQJ DQ HQWLUH LQWHUIDFHFDSWXULQJ PRGHO >@ 7KH SUHVHQW PRGHO ZDV YDOLGDWHG
DJDLQVW D VHULHV RI ODERUDWRU\VFDOH RLO EORZRXW H[SHULPHQWV 7KH GHWHUPLQLVWLF
DSSURDFKEDVHGRQWKHODUJHHGG\VLPXODWLRQGRHVQRWUHO\RQWKHLQSXWRIDQ\HPSLULFDOスーパーコンピューティングニュース- 22 -Vol. 23, No.6

2021

GDWD QRU FDOLEUDWLRQ SDUDPHWHUV LQFUHDVLQJ WKH UHOLDELOLW\ WR WKH UHDOVFDOH
SUHGLFWLRQRIWKH'6'LQGHHSZDWHUEORZRXWV
7KHJRYHUQLQJHTXDWLRQVVROYHGDUHWKH&RQWLQXLW\ (T DQG1DYLHU6WRNHV (T 
HTXDWLRQV
(1)

(2)

ZKHUHXLVWKHYHORFLW\LVWKHYROXPHIUDFWLRQWLVWLPHȨLVWKHGHQVLW\SLVWKH
SUHVVXUHJLVWKHJUDYLW\DFFHOHUDWLRQ)6NLVWKHVXUIDFHWHQVLRQIRUFH)'NLVWKH
GUDJ IRUFH )YPN LV WKH YLUWXDO PDVV IRUFH DQG WKH VXEVFULSW N LQGLFDWHV WKH IOXLGSKDVH 7KH(XOHU(XOHU PHWKRG ZDV XVHG WR PRGHO WKH PXOWLSKDVH IORZ FRXSOHG ZLWK D
6FKLOOHU1DXPDQQGUDJPRGHO7KHRSHQVRXUFH2SHQ)2$0YZDVXVHGIRUWKHFDOFXODWLRQV 7KHGRPDLQZDVPRGHOHGEDVHGRQWKHH[SHULPHQWDOGDWD>@DVDPKHLJKWFXERLG
WDQNZLWKDPSHUPZLGWK2LOIORZVWKURXJKDURXQGLQOHWDWWKHFHQWHURIWKHWDQNLQLWLDOO\ILOOHGZLWKZDWHU7KH'6'ZDVFRPSXWHGDSRVWHURLULE\LVRODWLQJWKHGURSOHWLQWKHLVRVXUIDFHDOSKD 㸱㸬5HVXOWVDQG'LVFXVVLRQ
7KHHIIHFWVRIGLIIHUHQWSDUDPHWHUVRYHUWKHMHWDWRPL]DWLRQLQWKH'6'ZHUHVKRZHGXVLQJQRQGLPHQVLRQDOQXPEHUVDQGILJXUHVRIWKHMHWEHKDYLRU
7KHYHORFLW\LQOHWDOWHUHGWKHUHJLPHLQGLIIHUHQWFDVHVZHUHDWRPL]DWLRQDQG
 ZHUH VHFRQG ZLQG LQGXFHG EUHDNXS %RWK WKH UHJLPHV VKRZHG YHU\ GLIIHUHQWFKDUDFWHULVWLFV UHJDUGLQJ WKH GURSOHW VL]H GLVWULEXWLRQ DQG WKH YHORFLW\ RI WKHSDUWLFOHVDVSHU)LJスーパーコンピューティングニュース- 23 -Vol. 23, No.62021)LJXUH'URSOHWGLDPHWHUGLVWULEXWLRQ OHIW DQGGURSOHWYHORFLW\GLVWULEXWLRQULJKW IRUFDVHVDQG)URPWKHGURSOHWVORFDOLQIRUPDWLRQLWZDVSRVVLEOHWRFRQFOXGHWKDWIRUWKHFDVH
RI VXUIDFH WHQVLRQ UHGXFWLRQ WKH GURSOHW GLDPHWHU ZDV VOLJKWO\ UHGXFHG ZKLOH WKHGURSOHWYHORFLW\GLVWULEXWLRQEHKDYHGGLIIHUHQWO\IRUWKHFDVHVLQGLIIHUHQWEUHDNXSUHJLPHV$V)LJDOVRVKRZVLQWKHDWRPL]DWLRQUHJLPH &DVHVDQG WKHGURSOHWYHORFLW\ZDVUHGXFHGDQGLQFUHDVHGLQWKHVHFRQGZLQGLQGXFHGUHJLPH &DVHVDQG 7KHLQOHWGLDPHWHUUHGXFWLRQGLGQRWFKDQJHWKHIORZUHJLPHKRZHYHULWLQWHQVLILHG
.HOYLQ+HOPKROW] LQVWDELOLWLHV QHDU WKH LQOHW DQG QDUURZHG WKH GURSOHW VL]HGLVWULEXWLRQ )LJ )LJXUH(IIHFWRIWKHGLDPHWHULQOHWUHGXFWLRQLQWKHVQDSVKRWVRIWKHLVRVXUIDFHDOSKD IRUFDVHV OHIW DQG ULJKW 7KHGHWDLOVVKRZWKH.HOYLQ+HOPKROW]LQVWDELOLWLHV7KHFDVHVZLWKYDULDWLRQLQWKHGHQVLW\  DQGWKHYLVFRVLW\UDWLR   VKRZHGLQ )LJV  DQG  UHVSHFWLYHO\ LOOXVWUDWHV WKH LPSDFW RI WKH QHDUILHOGLQVWDELOLWLHV LQ ERWK WKH GURSOHW VL]H GLVWULEXWLRQ DQG LQ WKH GURSOHW YHORFLW\GLVWULEXWLRQ 7KH YLVFRVLW\ UHGXFWLRQ GHFUHDVHG WKH .HOYLQ+HOPKROW] HIIHFW ZKLOHNHHSLQJVLPLODU'6'ZKLFKLVFDXVHGE\WKHLQFUHDVHLQWKHGURSOHW5H7KHGHQVLW\UHGXFWLRQ DFWHG WR HQKDQFH WKH LQVWDELOLWLHV QHDU WKH LQOHW LQGXFLQJ EUHDNXS PXFKスーパーコンピューティングニュース- 24 -Vol. 23, No.62021

HDUOLHUWKDQLQWKHKLJKHUGHQVLW\FDVHV)LJXUH(IIHFWRIWKHYLVFRVLW\UDWLRUHGXFWLRQLQWKHVQDSVKRWVRIWKHLVRVXUIDFHDOSKD IRUFDVHV OHIW DQG ULJKW 7KHGHWDLOVVKRZWKH.HOYLQ+HOPKROW]LQVWDELOLWLHVQHDUWKHLQOHW)LJXUH(IIHFWRIWKHGHQVLW\UDWLRUHGXFWLRQLQWKHVQDSVKRWVRIWKHLVRVXUIDFHDOSKD IRUFDVHV OHIW DQG ULJKW 7KHGHWDLOVVKRZWKH.HOYLQ+HOPKROW]LQVWDELOLWLHVQHDUWKHLQOHW㸬&RQFOXVLRQ 8VLQJ WKH K\EULG YROXPHRIIOXLG(XOHU(XOHU PRGHO ZLWK D ODUJH HGG\ VLPXODWLRQWXUEXOHQWPRGHOZDVHIIHFWLYHLQPRGHOLQJWKHODERUDWRU\VFDOHRLOEORZRXWLQDZDWHU
WDQN7KHHIIHFWVRIGLIIHUHQWSK\VLFDOSDUDPHWHUVRQWKHDWRPL]DWLRQZHUHFRPSOH[DQG
LWVKRZVWKHGLIILFXOW\LQXQGHUVWDQGLQJKRZWKHGLVWULEXWLRQRIGURSOHWVDUHDIIHFWHGE\WKLVSKHQRPHQRQ )XUWKHUUHVHDUFKLVQHFHVVDU\WRFUHDWHDQGRYHUDUFKLQJWKHRU\ WKDWFRXOGH[SODLQWKHMHWEUHDNXSLQDPRUHFOHDUDQGFRQFLVHZD\5HIHUHQFHV>@.XMDZLQVNLHWDO(QYLURQ6FL7HFKQROYROSS̽>@6RFRORIVN\HWDO2FHDQRJUDSK\YROSS
>@:DUGOH:HOOHU,QWHUQDWLRQDO-RXUQDORI&KHPLFDO(QJLQHHULQJYRO
>@0L\DWDHWDO-,0(YROSS


スーパーコンピューティングニュース- 25 -Vol. 23, No.6

2021