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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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

id	sg-ntu-dr.10356-180556
record_format	dspace
spelling	sg-ntu-dr.10356-1805562024-10-14T15:35:24Z Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean–Vlasov stochastic differential equations Neufeld, Ariel Nguyen, Tuan Anh School of Physical and Mathematical Sciences Mathematical Sciences McKean–Vlasov SDEs High-dimensional SDEs 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. Nanyang Technological University Submitted/Accepted version Financial support by the Nanyang Assistant Professorship Grant (NAP Grant) Machine Learning based Algorithms in Finance and Insurance is gratefully acknowledged. 2024-10-11T07:24:14Z 2024-10-11T07:24:14Z 2025 Journal Article Neufeld, A. & Nguyen, T. A. (2025). Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean–Vlasov stochastic differential equations. Journal of Mathematical Analysis and Applications, 541(1), 128661-. https://dx.doi.org/10.1016/j.jmaa.2024.128661 0022-247X https://hdl.handle.net/10356/180556 10.1016/j.jmaa.2024.128661 2-s2.0-85199091793 1 541 128661 en NTU-NAP Journal of Mathematical Analysis and Applications © 2024 Elsevier Inc. All rights reserved. This article may be downloaded for personal use only. Any other use requires prior permission of the copyright holder. The Version of Record is available online at http://doi.org/10.1016/j.jmaa.2024.128661. application/pdf
institution	Nanyang Technological University
building	NTU Library
continent	Asia
country	Singapore Singapore
content_provider	NTU Library
collection	DR-NTU
language	English
topic	Mathematical Sciences McKean–Vlasov SDEs High-dimensional SDEs
spellingShingle	Mathematical Sciences McKean–Vlasov SDEs High-dimensional SDEs Neufeld, Ariel Nguyen, Tuan Anh Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean–Vlasov stochastic differential equations
description	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.
author2	School of Physical and Mathematical Sciences
author_facet	School of Physical and Mathematical Sciences Neufeld, Ariel Nguyen, Tuan Anh
format	Article
author	Neufeld, Ariel Nguyen, Tuan Anh
author_sort	Neufeld, Ariel
title	Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean–Vlasov stochastic differential equations
title_short	Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean–Vlasov stochastic differential equations
title_full	Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean–Vlasov stochastic differential equations
title_fullStr	Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean–Vlasov stochastic differential equations
title_full_unstemmed	Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean–Vlasov stochastic differential equations
title_sort	rectified deep neural networks overcome the curse of dimensionality when approximating solutions of mckean–vlasov stochastic differential equations
publishDate	2024
url	https://hdl.handle.net/10356/180556
_version_	1814777740718505984

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

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