Leray-Schauder Mappings for Operator Learning
arXiv:2410.01746
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.
15 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