Matches in SemOpenAlex for { <https://semopenalex.org/work/W3201436609> ?p ?o ?g. }
- W3201436609 endingPage "1846" @default.
- W3201436609 startingPage "1803" @default.
- W3201436609 abstract "The model reduction of a mesoscopic kinetic dynamics to a macroscopic continuum dynamics has been one of the fundamental questions in mathematical physics since Hilbert’s time. In this paper, we consider a diagram of the diffusion limit from the Vlasov–Poisson–Fokker–Planck (VPFP) system on a bounded interval with the specular reflection boundary condition to the Poisson–Nernst–Planck (PNP) system with the no-flux boundary condition. We provide a Deep Learning algorithm to simulate the VPFP system and the PNP system by computing the time-asymptotic behaviors of the solution and the physical quantities. We analyze the convergence of the neural network solution of the VPFP system to that of the PNP system via the Asymptotic-Preserving (AP) scheme. Also, we provide several theoretical evidence that the Deep Neural Network (DNN) solutions to the VPFP and the PNP systems converge to the a priori classical solutions of each system if the total loss function vanishes." @default.
- W3201436609 created "2021-09-27" @default.
- W3201436609 creator A5003733262 @default.
- W3201436609 creator A5011429476 @default.
- W3201436609 creator A5086339183 @default.
- W3201436609 date "2021-09-01" @default.
- W3201436609 modified "2023-10-17" @default.
- W3201436609 title "The model reduction of the Vlasov–Poisson–Fokker–Planck system to the Poisson–Nernst–Planck system <i>via</i> the Deep Neural Network Approach" @default.
- W3201436609 cites W1808002509 @default.
- W3201436609 cites W1963509441 @default.
- W3201436609 cites W1967714339 @default.
- W3201436609 cites W1967997397 @default.
- W3201436609 cites W1971735090 @default.
- W3201436609 cites W1973839534 @default.
- W3201436609 cites W1974007886 @default.
- W3201436609 cites W1974770235 @default.
- W3201436609 cites W1974969839 @default.
- W3201436609 cites W1974987146 @default.
- W3201436609 cites W1978434425 @default.
- W3201436609 cites W1984719861 @default.
- W3201436609 cites W1988115241 @default.
- W3201436609 cites W1989989844 @default.
- W3201436609 cites W1990262185 @default.
- W3201436609 cites W1993045312 @default.
- W3201436609 cites W1993618814 @default.
- W3201436609 cites W1995341919 @default.
- W3201436609 cites W1997785623 @default.
- W3201436609 cites W1999955260 @default.
- W3201436609 cites W2001032670 @default.
- W3201436609 cites W2003926133 @default.
- W3201436609 cites W2008436424 @default.
- W3201436609 cites W2009385069 @default.
- W3201436609 cites W2009566405 @default.
- W3201436609 cites W2015470839 @default.
- W3201436609 cites W2020319476 @default.
- W3201436609 cites W2024304037 @default.
- W3201436609 cites W2024961472 @default.
- W3201436609 cites W2029633978 @default.
- W3201436609 cites W2031982439 @default.
- W3201436609 cites W2032502639 @default.
- W3201436609 cites W2034624900 @default.
- W3201436609 cites W2038322642 @default.
- W3201436609 cites W2040230915 @default.
- W3201436609 cites W2045971795 @default.
- W3201436609 cites W2059073834 @default.
- W3201436609 cites W2066934546 @default.
- W3201436609 cites W2067857689 @default.
- W3201436609 cites W2070066346 @default.
- W3201436609 cites W2075044992 @default.
- W3201436609 cites W2080330641 @default.
- W3201436609 cites W2083744164 @default.
- W3201436609 cites W2084236951 @default.
- W3201436609 cites W2086011386 @default.
- W3201436609 cites W2091860601 @default.
- W3201436609 cites W2097301883 @default.
- W3201436609 cites W2103496339 @default.
- W3201436609 cites W2117709159 @default.
- W3201436609 cites W2126967209 @default.
- W3201436609 cites W2128652391 @default.
- W3201436609 cites W2137983211 @default.
- W3201436609 cites W2148340421 @default.
- W3201436609 cites W2148666448 @default.
- W3201436609 cites W2325859011 @default.
- W3201436609 cites W2514809555 @default.
- W3201436609 cites W2535406322 @default.
- W3201436609 cites W2582105014 @default.
- W3201436609 cites W2749028154 @default.
- W3201436609 cites W2794129349 @default.
- W3201436609 cites W2801347329 @default.
- W3201436609 cites W2899283552 @default.
- W3201436609 cites W2935339072 @default.
- W3201436609 cites W2958706811 @default.
- W3201436609 cites W2963672187 @default.
- W3201436609 cites W2963678152 @default.
- W3201436609 cites W3022657828 @default.
- W3201436609 cites W3032805918 @default.
- W3201436609 cites W3035647965 @default.
- W3201436609 cites W3101260193 @default.
- W3201436609 cites W3105179757 @default.
- W3201436609 cites W4254355536 @default.
- W3201436609 cites W756921862 @default.
- W3201436609 doi "https://doi.org/10.1051/m2an/2021038" @default.
- W3201436609 hasPublicationYear "2021" @default.
- W3201436609 type Work @default.
- W3201436609 sameAs 3201436609 @default.
- W3201436609 citedByCount "3" @default.
- W3201436609 countsByYear W32014366092022 @default.
- W3201436609 countsByYear W32014366092023 @default.
- W3201436609 crossrefType "journal-article" @default.
- W3201436609 hasAuthorship W3201436609A5003733262 @default.
- W3201436609 hasAuthorship W3201436609A5011429476 @default.
- W3201436609 hasAuthorship W3201436609A5086339183 @default.
- W3201436609 hasBestOaLocation W32014366091 @default.
- W3201436609 hasConcept C119857082 @default.
- W3201436609 hasConcept C121332964 @default.
- W3201436609 hasConcept C121864883 @default.
- W3201436609 hasConcept C134306372 @default.
- W3201436609 hasConcept C28826006 @default.