Acceleration of Automatic Differentiation of Solutions to Parabolic Partial Differential Equations: A Higher Order Discretization

Numerical Algorithms (2020)

Posted: 18 Jun 2020

See all articles by Kimiki Tokutome

Kimiki Tokutome

Mizuho-DL Financial Technology Co., Ltd.

Toshihiro Yamada

Hitotsubashi University

Date Written: March 24, 2020

Abstract

The paper proposes a new automatic/algorithmic differentiation for the solutions to partial differential equations of parabolic type. In particular, we provide a higher order discretization scheme which is a natural extension of the standard automatic differentiation. A Brownian polynomial approach is introduced to avoid the Lévy area simulation. The Lie brackets of vector fields associated with stochastic differential equation play an important role in the proposed scheme. The case that the test function is non-smooth but has Gateaux derivative is considered. Numerical examples are shown to confirm the effectiveness.

Keywords: Automatic differentiation, Parabolic partial differential equations, Higher order discretization, Stochastic differential equations

Suggested Citation

Tokutome, Kimiki and Yamada, Toshihiro, Acceleration of Automatic Differentiation of Solutions to Parabolic Partial Differential Equations: A Higher Order Discretization (March 24, 2020). Numerical Algorithms (2020), Available at SSRN: https://ssrn.com/abstract=3609558

Kimiki Tokutome

Mizuho-DL Financial Technology Co., Ltd. ( email )

Japan

Toshihiro Yamada (Contact Author)

Hitotsubashi University ( email )

2-1 Naka Kunitachi-shi
Tokyo 186-8601
Japan

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