REVIEW 1 cited by
Approximation of Functionals by Neural Network without Curse of Dimensionality
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Approximation of Functionals by Neural Network without Curse of Dimensionality
abstract
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.
Forward citations
Cited by 1 Pith paper
-
Error analysis for learning the time-stepping operator of evolutionary PDEs
For reaction-diffusion, forced parabolic, and viscous conservation law PDEs, neural networks can learn the numerical one-step time map with generalization error that is polynomial in mesh size, not exponential.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.