Deep neural networks in the numerical approximation of PDEs (Diyora Salimova, ETH Zurich)

05.04.2019 10:30

In recent years deep artificial neural networks (DNNs) have very successfully been used in numerical simulations for a numerous of computational problems including, object and face recognition, natural language processing, fraud detection, computational advertisement, and numerical approximations of partial differential equations (PDEs). Such numerical simulations indicate that DNNs seem to admit the fundamental flexibility to overcome the curse of dimensionality in the sense that the number of real parameters used to describe the DNN grows at most polynomially in both the reciprocal of the prescribed approximation accuracy and the dimension of the function which the DNN aims to approximate in such computational problems. In this talk I present our recent result which rigorously proves that DNNs do overcome the curse of dimensionality in the numerical approximation of Kolmogorov PDEs with constant diffusion and nonlinear drift coefficients.

Lieu

Room 17, Séminaire d'analyse numérique

entrée libre