Discussion Papers 2023
CIRJE-F-1212 |
"Solving Kolmogorov PDEs without the Curse of Dimensionality via Deep Learning and Asymptotic Expansion |
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Author Name | Takahashi, Akihiko and Toshihiro Yamada |
Date | April 2023 |
Full Paper | PDF file |
Remarks | Published in Partial Differential Equations and Applications Vol.4, June 2023. |
Abstract |
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This paper proposes a new spatial approximation method without the curse of dimensionality for solving high-dimensional partial differential equations (PDEs) by using an asymptotic expansion method with a deep learning-based algorithm. In particular, the mathematical justication |
Keywords: Asymptotic expansion, Deep learning, Kolmogorov PDEs, Malliavin calculus, Curse of dimensionality |