Asymptotic expansion and deep neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with nonlinear coefficients

Akihiko Takahashi and Toshihiro Yamada
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Akihiko Takahashi: University of Tokyo
Toshihiro Yamada: Hitotsubashi University, Japan Science and Technology Agency (JST)

No CARF-F-547, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: 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 on the spatial approximation is provided, and a numerical example for a 100 dimensional Kolmogorov PDE shows effectiveness of our method.

Pages: 19
Date: 2022-11
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Persistent link: https://EconPapers.repec.org/RePEc:cfi:fseres:cf547

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