Imfihlakalo yezibalo zeNavier-Stokes kanye ne-Millennium Challenge

Isibuyekezo sokugcina: 15 September ka-2026
  • Inkinga ihlose ukuthola ukuthi ukugeleza koketshezi olungacindezelwa kungadala yini izinto ezingavamile lapho ijubane noma ingcindezi ingenamkhawulo.
  • I-OpenAI inikeze ikhambi elingenzeka isebenzisa ama-ejenti e-AI, yize kunezimpikiswano ezinkulu mayelana nokukopishwa kwemisebenzi yizazi zezibalo zaseSpain.
  • Isixazululo esiphelele sihilela ukufakazela ukufana komhlaba wonke kanye nokuba khona kwezixazululo ezibushelelezi, inselele exhumanisa izibalo ezihlanzekile nefiziksi yokuphazamiseka.

Uchungechunge lwezibalo eziyinkimbinkimbi ezibhalwe ebhodini, ezimele inselele yemfundiso yenkinga yeNavier-Stokes.

Cabanga uzama ukubikezela ngqo ukuthi ithonsi ngalinye lamanzi lizohamba kanjani emfuleni noma umdanso ongaqondakali wentuthu kagwayi emoyeni. Kubonakala sengathi umsebenzi olula, kodwa empeleni, sibhekene nenye yezinselelo ezinkulu kakhulu zezibalo emlandweni, eyaziwa ngokuthi inkinga yeNavier-Stokes. Le nselele akuyona nje into ethakazelisayo yezemfundo; ingenye yezinkinga eziyisikhombisa zeMillennium Prize, lapho i-Clay Mathematics Institute inikeze khona isigidi samaRandi kunoma ubani ongaxazulula lezi zibalo—insimu eyisisekelo kulabo abafunda isayensi esemthethweni.

Indaba isibuyisela emuva ekhulwini le-19, lapho umFulentshi uClaude-Louis Marie Navier kanye nomIrish uGeorge Gabriel Stokes babeka isisekelo salolu hlobo lomkhiqizo. Inhloso yabo kwakuwukuchaza ukugeleza koketshezi, begxila ikakhulukazi koketshezi olungacindezeleki —labo ubuningi babo obungashintshi ngisho nalapho behamba, njengegazi emithanjeni yethu noma ubisi engilazini. Ingqikithi yale ndaba ukuthi ngabe lezi zibalo zihlala ziyiqiniso noma zingase “ziqhekeke,” zidale izinto ezingafani —amaphuzu lapho ijubane noma ingcindezi iba khona ngokungenamkhawulo futhi imodeli iyeka ukuba wusizo ekubikezeleni ikusasa.

physics ekuphileni kwansuku zonke
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Imfihlakalo yokuhleleka kanye nokungafani

I-whirlpool enamandla emanzini aluhlaza okwesibhakabhaka ekhombisa ngokubonakalayo ukuxokozela kanye nokuguquguquka koketshezi.

Ukuze uwine umklomelo, izibalo ezilinganiselwe azanele; kudingeka ubufakazi obuqinile bezibalo bokuba khona kanye nokuhleleka kwezixazululo. Ngamagama alula, kumele kufakazelwe ukuthi uketshezi luziphatha kancane kancane futhi ngokuqhubekayo noma ukuthi, ngokuphambene nalokho, lungashintsha ngokuzumayo isiqondiso siye kokungapheli. Inkinga ihlukaniswe ngezitatimende ezine zobuchwepheshe (A, B, C, kanye no-D). Ezokuqala ezine zigxile ekuhlelekeni okuphelele ngaphandle kwamandla angaphandle, kanti ezokugcineni ezine zihlaziya okwenzekayo lapho amandla angaphandle ekhona nokuthi lokhu kungabangela yini ukuthi uhlelo luwe ngokwezibalo.

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Yilapho kuvela khona isiyaluyalu , leso siphithiphithi esibonakala sengathi senza onjiniyela kanye nososayensi befiziksi bahlanye. Ngenkathi isazi sezibalo sifuna ikhambi eliyingqayizivele nelibushelelezi, unjiniyela ukhetha amamodeli ekhompyutha abavumela ukuthi baklame indiza ngamahora ambalwa nje. Leli gebe lezinhloso libonisa ukuthi inkinga iyinkimbinkimbi yobunzima lapho ukuhlangana okungokoqobo kanye nokunemba kwezinombolo kuhlangana khona.

Umthelela we-AI embonini yezobuchwepheshe
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Ukuvela kobuhlakani bokwenziwa kanye nempikiswano ye-OpenAI

Intuthu emhlophe ijikeleza ngaphambili ibhekene nesizinda esimnyama, okubonisa ukunyakaza komoya okuphithizelayo nokugelezayo.

Muva nje, umhlaba wesayensi umangazwe yisimemezelo esivela ku-OpenAI. Le nkampani ithi ixazulule izimangalo C no-D zenkinga isebenzisa isu le-agent ye-AI : ama-agent angaba ngu-10.000 asebenza ngokungakhathali amahora angu-88. Ngokusho kwephepha labo elinamakhasi angu-166, bakhombisile ukuthi uketshezi oluphoqelelwe (njengamanzi angaphansi kwamandla adonsela phansi) lungakha izinto ezingafani. Uma lokhu kuqinisekiswa ngemuva kokubuyekezwa kontanga, bazohlangabezana nemigomo yokuwina umklomelo wesigidi samadola, yize besashiya icala loketshezi olungaphoqelelwe luvuliwe.

Kodwa-ke, akukhona konke okuhle, njengoba kuqubuke impi yokuzikhukhumeza kanye nokusolwa kokweba . I-OpenAI kuthiwa yasebenzisa umsebenzi wangaphambilini wezazi zezibalo zaseSpain uDiego Córdoba noLuis Martínez Zoroa. Laba ochwepheshe ababili abavela ku-ICMAT bebelokhu besebenza kule nkinga iminyaka eminingi, futhi imibono yabo yayiyisisekelo ebufakazini obubalulekile bukaTristan Buckmaster noLevent Alpöge. Umphakathi wesayensi manje usuphikisana ngokuthi i-OpenAI ibilokhu ithembekile yini ngokubhala ngobuhlakani kwale mpumelelo yomlando.

imboni yefektri yama-ejenti
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Isithombe sasemoyeni samagagasi olwandle anezivunguvungu sakha amaphethini aguquguqukayo, okubonisa ubunzima obubonakalayo bezibalo zeNavier-Stokes.

Ukuze siqonde ubunzima bendaba, kumelwe sihlolisise ubunzima bamafomula. Incazelo ye-Eulerian isetshenziswa , lapho i-substantial noma i-material derivative isetshenziswa khona ukulandelela ukuziphatha kwenhlayiya yoketshezi. Lokhu kuhlanganisa ukuhlukahluka kwendawo endaweni eqondile ne- convective derivative , okuwushintsho olubangelwa ukunyakaza koketshezi uqobo. Kuyindikimba ebanzi yezibalo ehlanganisa i-transport theorem kaReynolds kanye ne-Gauss theorem yokuguqula i-surface integrals ibe yi-volume integrals.

  Umhlahlandlela Ophelele Wokuqapha Impilo Yesakhiwo (SHM)

Empeleni, lezi zibalo aziqondile futhi zihlangene ngokuqinile , okwenza kube nzima ukuzixazulula ngepensela nephepha ezimweni eziyinkimbinkimbi. Yingakho siphendukela ezindleleni zezinombolo ezifana nezinto noma umehluko olinganiselwe. Ngokuthakazelisayo, le nkinga yezibalo inohlelo lokusebenza oluvame kakhulu: imidlalo yevidiyo . Ngenxa yomsebenzi ofana nokaJos Stam, izinguqulo ezilula zezibalo zeNavier-Stokes zisetshenziswa kuma-GPU ukudala umlilo nomusi ongokoqobo kakhulu ngesikhathi sangempela, yize zihlala zilwa nokusatshalaliswa kwezinombolo.

Lolu hambo oluvela kumabhodi amnyama ekhulu le-19 ukuya kumaseva e-OpenAI lusibonisa ukuthi, yize i-AI iyithuluzi elinamandla, ukuqonda komuntu kwezazi zezibalo ezifana neCórdoba kanye neMartínez-Zoroa kusalokhu kuyinjini yangempela yentuthuko. Ukuxazulula le nkinga akugcini nje ngokuletha umvuzo wezezimali, kodwa futhi kunikeza isihluthulelo sokuqonda ukuphazamiseka kanye nemikhawulo yamamodeli ethu angokwenyama, ukuvala umjikelezo owaqala ngoNavier futhi manje unwebeka ekubeni yi- quantum computing kanye ne-AI.

Ukubhala ngesandla izibalo ebhodini elimnyama, okufanekisela ukufuna ubufakazi obuqinile bokuxazulula inkinga yeminyaka eyinkulungwane.

imibiko kanye neziqondiso ze-supercomputing
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