Deep ReLU neural networks overcome the curse of dimensionality when approximating semilinear partial integro-differential equations

Ariel Neufeld; Tuan Anh Nguyen; Sizhou Wu

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arXiv · 2310.15581

Deep ReLU neural networks overcome the curse of dimensionality when approximating semilinear partial integro-differential equations

Ariel Neufeld·Tuan Anh Nguyen·Sizhou Wu

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Abstract

In this paper we consider PIDEs with gradient-independent Lipschitz continuous nonlinearities and prove that deep neural networks with ReLU activation function can approximate solutions of such semilinear PIDEs without curse of dimensionality in the sense that the required number of parameters in the deep neural networks increases at most polynomially in both the dimension $ d $ of the corresponding PIDE and the reciprocal of the prescribed accuracy $\epsilon $.

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Ariel Neufeld, Tuan Anh Nguyen, Sizhou Wu. 2023-10-24. Deep ReLU neural networks overcome the curse of dimensionality when approximating semilinear partial integro-differential equations. https://arxiv.org/abs/2310.15581

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