Izigaba ukumodeliswa izibalo, ezomnotho kanye computer science

Ngo samuntu, umfuziselo walo simele ezithile imephu yesithombe, umdwebo, incazelo, isithombe into noma inqubo. Lo mkhuba ubizwa ngokuthi i original zezibalo noma onobuhle kwezomnotho.

Kuyini ukumodeliswa?

Modeling ukulitadisha uhlelo oluthile into. Ukuze ukusetshenziswa kwaso yakhiwe futhi ihlaziye model.

Zonke sekulingisa esiteji kuhilela lwesayensi, into okuyinto imodeli abstract noma inhloso. Lapho efeza umsebenzi into eqondile ukuhlola esikhundleni kohlelo noma imodeli lula (ikhophi). Kwezinye izimo, babuthe isabelo imodeli sisebenzela Ngokwesibonelo yayo ukuqonda indlela yokusebenza, ukuhlaziya zibheke kwezomnotho kwezinhlelo imiphumela isipiliyoni emnothweni emakethe. Lomkhuba efanayo angabhekwa onobuhle ezahlukene.

Umcwaningi kufanele ukhethe izigaba ledzingekako yokumodela, sokusebenzisa ngokuyimpumelelo kubo. Ukusetshenziswa onobuhle efanele ezimweni lapho into yangempela ayitholakali, noma ukuhlolwa nalo ezihlobene nokusebenzelana izinkinga ezinkulu emvelweni. Imodeli zamanje sisetshenziswa ezimweni lapho experiment bangempela izindleko ngemali okukhulu.

Izici ukumodeliswa zezibalo

Ngo isayensi, onobuhle zezibalo kubalulekile, kanye namathuluzi ngabo - Tibalo.Sib. Zeminyaka eziningana, bona ezinqwabelene, olwesimanje. Esifundweni sezibalo zanamuhla zikhona izindlela jikelele nabanamandla uphenyo. Ngutiphi tintfo kubhekwe "Indlovukazi wesayensi", ukumela imodeli zezibalo. Ukuze uthole analysis eningiliziwe kwento ekhethiwe akhethiwe izigaba ukumodeliswa zezibalo. Ngosizo lwabo ukuhlukanisa imininingwane, izici, izici, codify ulwazi, ukwenza incazelo ephelele into.

kube semthethweni Mathematical kuhilela nokuphatha uphenyo imiqondo ekhethekile:-matrix umsebenzi, esuselwe, bakudala, izinombolo. Labo ubudlelwano nokuxhumana ongayitholi into ngaphansi cwaningo emkhatsini wetincenye teluhlaka abamelwe nemininingwane elotshiwe ubuhlobo zezibalo: zibalo, ukungalingani, equalities. Ngenxa yalokho, into yalungiswa incazelo zezibalo yenqubo, futhi ngenxa yalokho, imodeli yayo zezibalo.

Imithetho kokutadisha isibonelo zezibalo

Kukhona i-oda ezithile sekulingisa izinyathelo, okuyinto ikuvumela ukuba wenze uxhumano kwembangela nomphumela. Emaphakathi design esiteji of uhlelo ucwaningo ukwakha umfuziselo umnyuziki zezibalo. Kuyimfanelo imisebenzi eyenziwa ngqo kuncike Uhlaziyo luqhubeka into. Ukwakhiwa imodeli zezibalo noma kwezomnotho akuyona nenqubo esemthethweni. Kufanele kube ukhululekile ukusetshenziswa, enembile, ukuthi akukho ukuhlanekezela imiphumela ukuhlaziywa.

On Ukwahlukaniswa onobuhle zezibalo

Amabili izinhlobo: deterministic futhi stochastic onobuhle. onobuhle Deterministic ukuphakamisa ukusungulwa okukodwa-eyodwa ukuxhumana phakathi eziguquguqukayo elisetshenziselwa ukuchaza mkhuba noma into.

indlela okunjalo kusekelwe ulwazi isimiso yokusebenza into. Ezimweni eziningi, lomkhuba eyenziwe has a isakhiwo eziyinkimbinkimbi, ukuze ususe okufakwe kwindawo kuthatha isikhathi esiningi kanye nolwazi. Ezimweni ezinjalo, zikhethwa enjalo ukumodeliswa izigaba ukuthi uyoqhuba ukucwaninga yokuqala, enze ukucutshungulwa imiphumela, ngaphandle kokuya izici theory into. Ngokuvamile zisebenzisa izibalo kanye okungenzeka theory. Imiphumela iba yinhlanganisela yokukhandleka imodeli stochastic. Kuyo kukhona ubuhlobo okungahleliwe phakathi eziguquguqukayo. Inani elikhulu of izici ezahlukene iqoqo okungahleliwe lokwehlukile, esibonakala by into noma into.

Modern sekulingisa izigaba asetshenziselwa onobuhle static kanye ashukumisayo. incazelo Static we izinhlobo budlelwane emkhatsini wetinombolo imihlola elakhiwe yokungathathi bangeniswa izinguquko akhawunti nemingcele main isikhathi. onobuhle Dynamic ukuchaza ukuxhumana phakathi eziguquguqukayo Kwenziwa ikhumbula izinguquko isikhathi.

Izinhlobonhlobo onobuhle:

• okuqhubekayo;
• ezehlukene;
• hybrid

izigaba ezahlukene ukumodeliswa zezibalo asivumela ukuchaza onobuhle yomugqa, ubudlelwano nemisebenzi usebenzisa ngqo isixhumanisi eziguquguqukayo.

Yiziphi izimfuneko onobuhle?

• Ezihlukahlukene zokusisebenzisa. Imodeli kufanele kube ukubonisa ngokugcwele zonke izakhiwo umuntu azalwa nalo lokuhlaziya into yangempela.
• Amandla okwenza. izici ezibalulekile bento akufanele kwinani kusengaphambili iphutha.
• Ukunemba. Ephawula degree of ukuqondana kwezinto izici into ekhona empeleni, nge nemingcele efanayo etholakale ekuhloleni imodeli.
• Umnotho. Imodeli kufanele kube ubuncane izindleko impahla.

izigaba ukumodeliswa

Izigaba eyinhloko ukumodeliswa zezibalo.

• Umsebenti Ukukhethwa. Chosen Injongo yesifundo, akhethiwe izindlela kusebenta kwaso, isu ezivezwa isilingo. Lesi sigaba kuhilela umsebenzi wangempela. Kukithi ngokunemba umsebenzi kuncike yi ekupheleni sekulingisa.

• Ukuhlaziywa lezisekelo theory, Efingqa ulwazi wathola mayelana into. isinyathelo okunjalo kuhilela Ukukhetha noma ukudalwa le mfundiso. In the ukungabikho ulwazi theory mayelana into ukusungula ubudlelwano esiyimbangela phakathi kwawo wonke eziguquguqukayo akhethiwe ukuchaza mkhuba noma into. Kulesi sigaba, ukucacisa kokuqala nokokugcina hypothesize idatha.
• Semthethweni. Olusetshenziswa ukukhetha simiso nezimpawu ezikhethekile ukusiza irekhodi ngohlobo wokuboniswa zezibalo, ubudlelwano phakathi kwezingxenye into.

U-algorithm

Emva kokuhlela imodeli nemingcele akhethiwe indlela ethize noma isixazululo indlela.

• Ukwenza umsebenzi we-imodeli athuthukile. Ngemva osikhethile izinhlelo ukumodeliswa esiteji, setha uhlelo uyahlolwa futhi esetshenziswa ukuxazulula le nkinga.
• Ukuhlaziya ulwazi oluqoqiwe. Isifaniso phakathi umsebenzi kanye nekhambi etholwe kunqunywa akhombe iphutha.
• Ihlola eqhuma imodeli ukuba into yangempela. Uma kukhona umehluko okukhulu, imodeli entsha iyakhiwa phakathi kwazo. Kuze kube yileso sikhathi, kuze kube Gap imodeli ukuze Analogue walo wangempela, aphethwe intuthuko, ukushintsha izingxenye.

Isici ukumodeliswa

Phakathi nekhulu leminyaka eledlule empilweni yomuntu wesimanje Computing imishini, kukhuphuke ukuhlobana izindlela zezibalo isifundo lezinto kanye izenzakalo. Kwakukhona izigaba ezifana "Mathematical Chemistry", "yezilimi zezibalo", "ezomnotho zezibalo", abazinikele cwaningo imihlola, izinto adalwa ezigabeni eyinhloko yokumodela.

injongo yabo eyinhloko kwaba isibikezelo kokuma kuhlelwe, ukutadisha izinto ezithile. Ngaphezu kwalokho, ngosizo sekulingisa ungafunda mayelana nezwe, ukuba ufune izindlela zokuziphindiselela ukuyilawula. Kuphethe ikhompyutha ukumbumbuluzwa Kusolwa ezimweni lapho ukuziphatha akusebenzi okwamanje. Ngemva bakha imodeli zezibalo lomkhuba ngaphansi cwaningo esebenzisa eseyi ungakwazi ukufunda kuqhuma yenuzi, isifo nokunye. D.

Ochwepheshe ukukhomba izigaba ezintathu ukumodeliswa zezibalo, futhi ngamunye has izici zayo siqu:

• Ukwakhiwa imodeli. Lesi sigaba kuhilela umsebenzi uhlelo kwezomnotho, asho into yemvelo, umklamo, inqubo ukukhiqizwa. ukuchaza Ngokusobala isimo kuleli cala kunzima. Okokuqala udinga ukukhomba ngokucacile lomkhuba, ukucacisa ubudlelwano phakathi kwalo kanye nezinye izinto. Khona-ke zonke izici qualitative zihunyushelwa olimini zezibalo, wakha imodeli zezibalo. Lesi sigaba Kunzima kakhulu yonke inqubo yokumodela.
• isixazululo Isigaba yenkinga zezibalo ukuthi lihlotshaniswa ukuthuthukiswa algorithm, izindlela yokuxazulula le nkinga iyabheda bama-computer, ukuhlonza nesilinganiso amaphutha.
• Ukuhumusha ulwazi wathola ngokuhamba izifundo ngolimi endaweni okuyiwona ukuhlola lwenziwe.

Lezi izigaba ezintathu ukumodeliswa zezibalo kuthiwa kwahambisana sokuqinisekisa nokwanela imodeli okuholela. Uhlola ukuvumelana phakathi imiphumela eyatholakala ku linga ngamasu ahlukahlukene ngenhloso ulwazi theory. Uma kunesidingo, ukuguqulwa imodeli wadala. Izinkinga noma lula ke, kuye ngokuthi imiphumela.

ukumodeliswa kwezomnotho Ikakhulukazi

3 izinyathelo ezihilela ukusetshenziswa ukumodeliswa nezibalo algebraic, umehluko zibalo. Yakha izinto eziyinkimbinkimbi usebenzisa igrafu theory. Luhilela iqoqo amaphuzu emkhathini noma indiza ingxenye izimbambo axhunyiwe. Izigaba eyinhloko ukumodeliswa kwezomnotho ziyabonisa futhi ezihlukahlukene imithombo, ukusatshalaliswa zabo, ikhumbula ezokuthutha, ukuhlelwa inethiwekhi. Isiphi isinyathelo alusona isinyathelo kule sekulingisa? Kunzima ukuphendula lo mbuzo nangokunembile, konke kuncike esimweni esithile. Izigaba eyinhloko inqubo Sokuzenzela Kusolwa izinjongo ekwakhiweni nocwaningo isihloko, ukukhethwa izici eziyisisekelo ukufeza inhloso, ubudlelwano phakathi incazelo izingcezwana imodeli. izibalo Ngaphezu kwalokho kwenziwa ngokusebenzisa zezibalo.

Ngokwesibonelo, inkonzo theory zinkinga queuing. Kubalulekile ukuthola ukuzimelela phakathi kwezidingo izindleko amadivayisi nokuqukethwe ukuhlala izindleko emgqeni. Ngemva bakha incazelo esisemthethweni imodeli izibalo kwenziwe ngokusebenzisa amathekhiniki yezamakhompyutha kanye kohlaziyo. Ungathola izimpendulo kuyo yonke imibuzo qualitative kwakha luhlaka imodeli. Uma imodeli kubi, akunakwenzeka ukuba baqonde indlela isenzo alusona isinyathelo kule sekulingisa.

Ukusebenziseka iyona umbandela kweqiniso nokuhlola nokwanela lomkhuba noma imodeli. Multicriteria imodeli, kuhlanganise ongakhetha nokwenza kahle, ngenhloso ohlosiwe ekwakhiweni. Kodwa indlela ukufezekisa lokhu kuhlukile. Phakathi nezinkinga ezingase zibe zingenzeka kule nqubo, kufanele ezigqanyisiwe:

• kwakha isimiso esiyinkimbinkimbi emkhatsini wetincenye teluhlaka, kukhona link eziningana;
• kunzima ukuba acabangele zonke izici okungahleliwe, ukuhlaziya uhlelo yangempela;
• kunzima ukuqhathanisa apharathasi zezibalo ngemiphumela ofuna ukuthola

Ngenxa phasi ubudisi obunengi eziphakamayo inqubo ukutadisha izinhlelo multidimensional, ukumbumbuluzwa lakhiwe. Libhekisela iqoqo izinhlelo ezikhethekile amakhompyutha, echaza umsebenzi izakhi ngabanye kohlelo kanye ubudlelwano phakathi kwazo. Ukusetshenziswa eziguquguqukayo okungahleliwe kuhilela ukuphindaphindwa zokuhlolwa, processing izibalo kwemiphumela. Ukusebenza kohlelo sekulingisa isilingo ukuthi wenziwa esebenzisa Computing. Yiziphi izinzuzo zalesi simiso? Ngokufanayo, ungakwazi sifinyelele ukusondela enkulu ohlelweni yangempela, kuyinto engenakwenzeka esimweni umfuziselo zezibalo. Ukusebenzisa block isimiso kungenzeka ukuhlaziya amabhlogo ngabanye ngaphambi kokuba kwenziwe uhlelo olulodwa. inketho okunjalo kwenza ukusetshenziswa ukuncika eziyinkimbinkimbi ezingeke esachazwa ubudlelwano ezivamile zezibalo.

Phakathi nemibi uhlelo sekulingisa, ukwaba izindleko isikhathi nezinto zethu, kanye nesidingo ukusebenzisa ubuchwepheshe bama-computer anamuhla.

Izigaba yentuthuko sekulingisa ifaniswe izinguquko ezenzekayo emphakathini. On ukusetshenziswa wonke amamodeli ihlukaniswe zokuqeqesha, abaqeqeshi, nezinsiza zemfundo ezibukwayo. Prototypes zingancishiswa amakhophi netintfo mbamba (izimoto). embodiments yezesayensi lobuchwepheshe kukhona zezitsha wadala for the ukuhlaziywa electronics. Awokuzenzisa onobuhle hhayi kuphela libonise ekhona ngokoqobo, bavele baphethe evivinywa amagundane laboratory, ucwaningo ohlelweni lwezemfundo. Mbumbulu ubonakala indlela amaphutha.

Kukhona division of wonke amamodeli we okukhethwa ethulwa. onobuhle Physical abizwa ngokuthi neziqinile. ezahlukeneyo enjalo afakwa izici yejeyomethri nabonakalayo tekucala, lingase lihunyushwe libe into engokoqobo. imodeli Imininingwane akunakwenzeka ngayo uma icindezelwa. Bona njani isimo nezakhiwo into wafunda, mkhuba, inqubo, futhi ukuxhumana nabo emhlabeni wangempela. ongakhetha Verbal ihlanganise ulwazi onobuhle ukusebenza ngendlela ka ezikhulunywayo noma engqondweni. ukubukwa yisakhiwo sodumo esashiwo ukusetshenziswa izimpawu ezithile enezici ulimi zezibalo.

isiphetho

ukumodeliswa Mathematical njengoba indlela ulwazi lwesayensi uvele kanyekanye okusemqoka wezibalo ephakeme. Indima ebalulekile inqubo enjalo yayi- eyadlalwa u-Isaac Newton, Descartes, Leibniz. onobuhle Mathematical abangu lokuqala elakhiwa Fermat, B. Pascal. ukumodeliswa Mathematical ekukhiqizeni, umnotho alalelwa V. Leontev, VV Novozhilov, A. L. Lure. Namuhla, okuhlukile ezifanayo into yokutadisha iyiphi mkhuba isetshenziswa ezinhlakeni ezahlukene umsebenzi. Nge izinhlelo yakhelwe onjiniyela aphenya izenzakalo ezinjalo nezinqubo ukuthi ayikwazi ukuhlaziywa ezimweni zangempela.

Ucwaningo by ukumodeliswa lalisetshenziswa ezikhathini zasendulo, ekugcineni ekuthumbeni izinhlobo ezahlukene ulwazi lwesayensi: izakhiwo, ubunjiniyela, amakhemikhali nokusebenzelana kwawo, ukwakhiwa, i-physics, i-biology, ngesimiso semvelo, geography, kanye nezifundo social. Kunoma inqubo Sokuzenzela isebenzisa tincenye letintsatfu: ihloko yemusho, mentiwa, imodeli. Yiqiniso, isifundo sekulingisa into noma mkhuba akugcini, kunezinye izindlela ukuthola ulwazi oludingekayo.