A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drif

BibTeX Reference

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@article{JenSalWel2021,
    author = {Jentzen, Arnulf and Salimova, Diyora and Welti, Timo},
    title = {A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drif},
    journal = {Communications in Mathematical Sciences},
    volume = 19,
    number = 5,
    pages = {1167–1205},
    month = jul,
    year = 2021,
    keywords = {curse of dimensionality, partial differential equations, numerical approximation, Feynman–Kac, deep neural networks},
    url = {http://www.nari.ee.ethz.ch/pubs/p/JenSalWel2021}
}

LaTeX Reference

\bibitem{JenSalWel2021} A. Jentzen, D. Salimova, and T. Welti, ``A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drif,'' \emph{Communications in Mathematical Sciences}, Vol. 19, No. 5, pp. 1167–1205, July 2021.

HTML Reference

A. Jentzen, D. Salimova, and T. Welti, "A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drif," Communications in Mathematical Sciences, Vol. 19, No. 5, pp. 1167–1205, July 2021.