{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T13:29:07Z","timestamp":1761744547753,"version":"build-2065373602"},"reference-count":34,"publisher":"IOP Publishing","issue":"4","license":[{"start":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T00:00:00Z","timestamp":1761696000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T00:00:00Z","timestamp":1761696000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. 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For the second-kind Fredholm integral equation, the convergence rate of this method is rigorously analyzed through the establishment of upper bounds on three critical parameters: the number of training samples, neurons per hidden layer, and network depth. The derived convergence rate comprises two distinct components: a statistical error term induced by Monte Carlo sampling, and an approximation error term stemming from ReLU network architecture constraints. Finally, numerical examples verify the validity of the proposed method.<\/jats:p>","DOI":"10.1088\/2632-2153\/ae13cf","type":"journal-article","created":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T22:49:35Z","timestamp":1760568575000},"page":"045025","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Convergence analysis of deep ReLU networks for solving integral equations"],"prefix":"10.1088","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-6327-7814","authenticated-orcid":true,"given":"Min","family":"Zhou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Tan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2025,10,29]]},"reference":[{"key":"mlstae13cfbib1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2024.128878","type":"journal-article","article-title":"Gegenbauer polynomial-based numerical technique for a singular integral equation of order four and its application to a crack problem","volume":"479","author":"Yadav","year":"2024","journal-title":"Appl. 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