Discussion Papers 2021
CIRJE-F-1167 |
"Asymptotic Expansion and Deep Neural Networks Overcome the Curse of Dimensionality in the Numerical |
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Author Name | Takahashi, Akihiko and Toshihiro Yamada |
Date | May 2021 |
Full Paper | |
Remarks | Revised in November 2022. Subsequently published as "Solving Kolmogorov PDEs without the Curse of Dimensionality via Deep Learning and Asymptotic Expansion with Malliavin Calculus" 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 justification |
Keywords. Asymptotic expansion, Deep learning, Kolmogorov PDEs, Malliavin calculus, Curse of dimensionality |