Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean–Vlasov stochastic differential equations

Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean–Vlasov stochastic differential equations

In this paper we prove that rectified deep neural networks do not suffer from the curse of dimensionality when approximating McKean–Vlasov SDEs in the sense that the number of parameters in the deep neural networks only grows polynomially in the space dimension d of the SDE and the reciprocal of the...

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Bibliographic Details
Main Authors: Neufeld, Ariel, Nguyen, Tuan Anh
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2024
Subjects:
Mathematical Sciences
McKean–Vlasov SDEs
High-dimensional SDEs
Online Access:https://hdl.handle.net/10356/180556
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Institution: Nanyang Technological University
Language: English
Description
Summary:In this paper we prove that rectified deep neural networks do not suffer from the curse of dimensionality when approximating McKean–Vlasov SDEs in the sense that the number of parameters in the deep neural networks only grows polynomially in the space dimension d of the SDE and the reciprocal of the accuracy ϵ.

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