[2410.01746] Leray-Schauder Mappings for Operator Learning

Computer Science > Machine Learning arXiv:2410.01746 (cs) [Submitted on 2 Oct 2024 (v1), last revised 2 Mar 2026 (this version, v3)] Title:Leray-Schauder Mappings for Operator Learning Authors:Emanuele Zappala View a PDF of the paper titled Leray-Schauder Mappings for Operator Learning, by Emanuele Zappala View PDF HTML (experimental) 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. Comments: Subjects: Machine Learning (cs.LG); Numerical Analysis (math.NA) Cite as: arXiv:2410.01746 [cs.LG]   (or arXiv:2410.01746v3 [cs.LG] for this version)   https://doi.org/10.48550/arXiv.2410.01746 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Emanuele Zappala [view email] [v1] Wed, 2 Oct 2024 17:01:01 UTC (208 KB) [v2] Mon, 3 Mar 2025 06:17:54 UTC (215 KB) [v3] Mon, 2 Mar 2026 04:37:06 UTC (217 KB) Full-text links: Access Paper: View a PDF of the paper titled Leray-Schauder Mappings for Operator Learning, by Emanuele ZappalaView PDFHTML (experimental)TeX Source view license Current browse context: cs.LG < prev   |   next > new | recent | 2024-10 Change to browse by: cs cs.NA math math.NA Re...