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
Additional contact information
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-1167, CIRJE F-Series from CIRJE, Faculty of Economics, 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 pages
Date: 2021-05
New Economics Papers: this item is included in nep-big and nep-cmp
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.cirje.e.u-tokyo.ac.jp/research/dp/2021/2021cf1167.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (http://www.cirje.e.u-tokyo.ac.jp/research/dp/2021/2021cf1167.pdf [302 Moved Temporarily]--> https://www.cirje.e.u-tokyo.ac.jp/research/dp/2021/2021cf1167.pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2021cf1167

Access Statistics for this paper

More papers in CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo Contact information at EDIRC.
Bibliographic data for series maintained by CIRJE administrative office ().