TY - JOUR
T1 - Approximation of Functionals by Neural Network Without Curse of Dimensionality
AU - Yang , Yahong
AU - Xiang , Yang
JO - Journal of Machine Learning
VL - 4
SP - 342
EP - 372
PY - 2022
DA - 2022/12
SN - 1
DO - http://doi.org/10.4208/jml.221018
UR - https://global-sci.org/intro/article_detail/jml/21297.html
KW - Functionals, Neural networks, Infinite dimensional spaces, Barron spectral space, Fourier series.
AB - <p style="text-align: justify;">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 $\mathcal{O}(1/\sqrt{m})$ where $m$ is the size of networks. In other words, the error of the network is no dependence on the
dimensionality respecting to the number of the nodes in neural networks. The key idea of the approximation
is to define a Barron space of functionals.</p>