论文标题
通过神经网络对功能的近似，而没有维度的诅咒
Approximation of Functionals by Neural Network without Curse of Dimensionality
论文作者
论文摘要
在本文中，我们建立了一个神经网络以近似功能，该功能是从无限尺寸空间到有限维空间的地图。神经网络的近似误差为$ O（1/\ sqrt {m}）$，其中$ m $是网络的大小，它克服了维度的诅咒。近似值的关键思想是定义功能的巴隆光谱空间。
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 $O(1/\sqrt{m})$ 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.
