Spectral methods for Neural Integral Equations

arXiv:2312.05654v3 Announce Type: replace-cross
Abstract: Neural integral equations are deep learning models based on the theory of integral equations, where the model consists of an integral operator and the corresponding equation (of the second kind) which is learned through an optimization procedure. This approach allows to leverage the nonlocal properties of integral operators in machine learning, but it is computationally expensive. In this article, we introduce a framework for neural integral equations based on spectral methods that allows us to …

abstract arxiv cs.lg cs.na deep learning equation integral kind math.na operators optimization physics.comp-ph theory through type