Deep Asymptotic Expansion with Weak Approximation

Yuga Iguchi, Riu Naito, Yusuke Okano, Akihiko Takahashi and Toshihiro Yamada
Additional contact information
Yuga Iguchi: MUFG Bank
Riu Naito: Japan Post Insurance and Hitotsubashi University
Yusuke Okano: SMBC Nikko Securitie
Akihiko Takahashi: Faculty of Economics, The University of Tokyo
Toshihiro Yamada: Graduate School of Economics, Hitotsubashi University and Japan Science and Technology Agency (JST)

No CIRJE-F-1168, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: This paper proposes a new spatial approximation method without the curse of dimensionalityfor solving high-dimensional partial differential equations (PDEs) by using an asymptotic expan-sion method with a deep learning-based algorithm. In particular, the mathematical justi cationon the spatial approximation is provided, and a numerical example for a 100 dimensional Kol-mogorov PDE shows effectiveness of our method.

Pages: 22 pages
Date: 2021-05
New Economics Papers: this item is included in nep-big and nep-cmp
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