# 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} }

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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