Leray-Schauder Mappings for Operator Learning

Abstract

We present an algorithm for learning operators between Banach spaces, based on the use of Leray-Schauder mappings to learn a finite-dimensional approximation of compact subspaces. We show that the resulting method is a universal approximator of (possibly nonlinear) operators. We demonstrate the efficiency of the approach on two benchmark datasets showing it achieves results comparable to state of the art models.

arXiv comment15 pages, 2 figures, 1 table. Comments are welcome! v3: The article has been streamlined, and several further explanations have been added. References have been added too