Corpus ID: 219259849

Space-time deep neural network approximations for high-dimensional partial differential equations

@article{Hornung2020SpacetimeDN,
  title={Space-time deep neural network approximations for high-dimensional partial differential equations},
  author={Fabian Hornung and Arnulf Jentzen and Diyora Salimova},
  journal={ArXiv},
  year={2020},
  volume={abs/2006.02199}
}
  • Fabian Hornung, Arnulf Jentzen, Diyora Salimova
  • Published 2020
  • Mathematics, Computer Science
  • ArXiv
  • It is one of the most challenging issues in applied mathematics to approximately solve high-dimensional partial differential equations (PDEs) and most of the numerical approximation methods for PDEs in the scientific literature suffer from the so-called curse of dimensionality in the sense that the number of computational operations employed in the corresponding approximation scheme to obtain an approximation precision $\varepsilon>0$ grows exponentially in the PDE dimension and/or the… CONTINUE READING

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