JSIAM Letters
Online ISSN : 1883-0617
Print ISSN : 1883-0609
ISSN-L : 1883-0617
Higher-order deep solver of non-linear PDEs implied by a non-linear discrete Clark-Ocone formula
Jiro AkahoriYui FuruichiKaori Okuma
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2022 Volume 14 Pages 9-12

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Abstract

In the present paper, we introduce a variant of the numerical scheme called the deep solver of PDE. Our scheme is based on a non-linear version of the discrete-time Clark--Ocone formula, which describes the convergent expansion of the error terms. Our new scheme incorporates the higher-order error terms, which we conjecture to stabilize the stochastic gradient descent procedure, and also the irregularities in the driver and the terminal function of the associated forward-backward stochastic differential equation.

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© 2022, The Japan Society for Industrial and Applied Mathematics
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