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- W3115761617 endingPage "3746" @default.
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- W3115761617 abstract "It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-based approximation algorithms for attacking this problem have been proposed and tested numerically on a number of examples of high-dimensional PDEs. This has given rise to a lively field of research in which deep learning-based methods and related Monte Carlo methods are applied to the approximation of high-dimensional PDEs. In this article we offer an introduction to this field of research by revisiting selected mathematical results related to deep learning approximation methods for PDEs and reviewing the main ideas of their proofs. We also provide a short overview of the recent literature in this area of research." @default.
- W3115761617 created "2021-01-05" @default.
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- W3115761617 creator A5074382323 @default.
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- W3115761617 date "2023-01-01" @default.
- W3115761617 modified "2023-10-14" @default.
- W3115761617 title "An overview on deep learning-based approximation methods for partial differential equations" @default.
- W3115761617 cites W1520669850 @default.
- W3115761617 cites W1634261337 @default.
- W3115761617 cites W1835030294 @default.
- W3115761617 cites W1948872067 @default.
- W3115761617 cites W1970454553 @default.
- W3115761617 cites W1974555191 @default.
- W3115761617 cites W1980091117 @default.
- W3115761617 cites W1981151146 @default.
- W3115761617 cites W1994791309 @default.
- W3115761617 cites W1999483367 @default.
- W3115761617 cites W2003393668 @default.
- W3115761617 cites W2004794023 @default.
- W3115761617 cites W2004973016 @default.
- W3115761617 cites W2014945091 @default.
- W3115761617 cites W2018023106 @default.
- W3115761617 cites W2022684404 @default.
- W3115761617 cites W2035593604 @default.
- W3115761617 cites W2039366144 @default.
- W3115761617 cites W2040007132 @default.
- W3115761617 cites W2043281212 @default.
- W3115761617 cites W2046331573 @default.
- W3115761617 cites W2048370823 @default.
- W3115761617 cites W2050871708 @default.
- W3115761617 cites W2051031503 @default.
- W3115761617 cites W2055500345 @default.
- W3115761617 cites W2057093985 @default.
- W3115761617 cites W2068532642 @default.
- W3115761617 cites W2073001881 @default.
- W3115761617 cites W2078895915 @default.
- W3115761617 cites W2081864922 @default.
- W3115761617 cites W2082136723 @default.
- W3115761617 cites W2083017901 @default.
- W3115761617 cites W2090704787 @default.
- W3115761617 cites W2095273359 @default.
- W3115761617 cites W2126800238 @default.
- W3115761617 cites W2127975978 @default.
- W3115761617 cites W2129289929 @default.
- W3115761617 cites W2142895119 @default.
- W3115761617 cites W2146095861 @default.
- W3115761617 cites W2148965913 @default.
- W3115761617 cites W2150185235 @default.
- W3115761617 cites W2163715525 @default.
- W3115761617 cites W2167018969 @default.
- W3115761617 cites W2190148340 @default.
- W3115761617 cites W2256916148 @default.
- W3115761617 cites W2343510531 @default.
- W3115761617 cites W2419175238 @default.
- W3115761617 cites W2550134996 @default.
- W3115761617 cites W2556342349 @default.
- W3115761617 cites W2605147767 @default.
- W3115761617 cites W2610038766 @default.
- W3115761617 cites W2625995436 @default.
- W3115761617 cites W2743985642 @default.
- W3115761617 cites W2749028154 @default.
- W3115761617 cites W2754833785 @default.
- W3115761617 cites W2760972773 @default.
- W3115761617 cites W2770250658 @default.
- W3115761617 cites W2803629276 @default.
- W3115761617 cites W2890291741 @default.
- W3115761617 cites W2890968382 @default.
- W3115761617 cites W2899283552 @default.
- W3115761617 cites W2899507754 @default.
- W3115761617 cites W2903660960 @default.
- W3115761617 cites W2908429425 @default.
- W3115761617 cites W2908541468 @default.
- W3115761617 cites W2912649832 @default.
- W3115761617 cites W2921935427 @default.
- W3115761617 cites W2935339072 @default.
- W3115761617 cites W2948551291 @default.
- W3115761617 cites W2948801778 @default.
- W3115761617 cites W2949158470 @default.
- W3115761617 cites W2954388788 @default.
- W3115761617 cites W2958410505 @default.
- W3115761617 cites W2963139910 @default.
- W3115761617 cites W2963197286 @default.
- W3115761617 cites W2963350219 @default.
- W3115761617 cites W2963395620 @default.
- W3115761617 cites W2963870185 @default.
- W3115761617 cites W2964016242 @default.
- W3115761617 cites W2964110066 @default.
- W3115761617 cites W2964122806 @default.
- W3115761617 cites W2964242874 @default.
- W3115761617 cites W2969381807 @default.
- W3115761617 cites W2973886134 @default.
- W3115761617 cites W2974176966 @default.
- W3115761617 cites W2978515965 @default.
- W3115761617 cites W2981014499 @default.
- W3115761617 cites W2990035425 @default.
- W3115761617 cites W2990364650 @default.