Approximation of Functionals by Neural Network without Curse of Dimensionality

05/28/2022

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by   Yahong Yang, et al.

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In this paper, we establish a neural network to approximate functionals, which are maps from infinite dimensional spaces to finite dimensional spaces. The approximation error of the neural network is O(1/√(m)) where m is the size of networks, which overcomes the curse of dimensionality. The key idea of the approximation is to define a Barron spectral space of functionals.