Learning smooth functions in high dimensions: from sparse polynomials to deep neural networks

arXiv:2404.03761v1 Announce Type: cross
Abstract: Learning approximations to smooth target functions of many variables from finite sets of pointwise samples is an important task in scientific computing and its many applications in computational science and engineering. Despite well over half a century of research on high-dimensional approximation, this remains a challenging problem. Yet, significant advances have been made in the last decade towards efficient methods for doing this, commencing with so-called sparse polynomial approximation methods and continuing most recently with …

abstract applications approximation arxiv computational computing cs.lg cs.na dimensions engineering functions math.na networks neural networks research samples science scientific type variables