Deep ReLU neural networks overcome the curse of dimensionality when approximating semilinear partial integro-differential equations
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909461763850240 |
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| author | Neufeld, Ariel Nguyen, Tuan Anh Wu, Sizhou |
| author_facet | Neufeld, Ariel Nguyen, Tuan Anh Wu, Sizhou |
| contents | 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 $ε$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15581 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Deep ReLU neural networks overcome the curse of dimensionality when approximating semilinear partial integro-differential equations Neufeld, Ariel Nguyen, Tuan Anh Wu, Sizhou Numerical Analysis Analysis of PDEs Probability 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 $ε$. |
| title | Deep ReLU neural networks overcome the curse of dimensionality when approximating semilinear partial integro-differential equations |
| topic | Numerical Analysis Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2310.15581 |