Nonlocality and Nonlinearity Implies Universality in Operator Learning

arXiv:2304.13221v2 Announce Type: replace-cross
Abstract: Neural operator architectures approximate operators between infinite-dimensional Banach spaces of functions. They are gaining increased attention in computational science and engineering, due to their potential both to accelerate traditional numerical methods and to enable data-driven discovery. As the field is in its infancy basic questions about minimal requirements for universal approximation remain open. It is clear that any general approximation of operators between spaces of functions must be both nonlocal and nonlinear. In this paper …

abstract architectures arxiv attention basic computational cs.lg cs.na data data-driven discovery engineering functions math.na numerical operators potential questions replace science spaces type